Engineer's Calculators
Working tools, not toys — every card runs in your browser, keeps a local history of your runs, and shows the formula it uses. New calculators land weekly.
By industry
Aerospace & Defense
Atmosphere, compressible flow, and flight-side math.
53 calculators →
Electrical & RF
Power, impedance, antennas, and the dB family.
70 calculators →
Mechanical
Beams, bolts, shafts, and the things that bend.
66 calculators →
Civil & Structural
Concrete, walls, and welds.
31 calculators →
Chemical & Process
Pumps, pipes, and process fundamentals.
38 calculators →
Test & Instrumentation
Bridges, amplifiers, sensors, and signal chains.
71 calculators →
Unit Conversions
Between unit systems without the 3 a.m. mistakes.
13 calculators →
Materials & Fatigue
Fatigue life, fracture, creep, corrosion, and the metallurgy behind allowables.
18 calculators →
Software & Networks
Queueing, throughput, storage, and the classical laws of computing.
17 calculators →
Systems Engineering
Reliability math, Amdahl, Little's law, and the arithmetic of large systems.
11 calculators →
Cybersecurity
Entropy, key strength, hash collisions, and the math that hardens crypto.
10 calculators →
Industrial & Manufacturing
OEE, takt, EOQ, and the numbers behind a well-run line.
14 calculators →
Defense Systems
Radar range, EO/IR seekers, blast overpressure, CEP, and the math the engineering cluster runs on.
12 calculators →
HVAC & Thermal
Refrigeration COP, duct friction, air changes, and R-values.
6 calculators →
Optics & Photonics
Lens equations, diffraction limits, and beam divergence.
10 calculators →
Power Electronics
SMPS efficiency, MOSFET losses, ripple, and core-loss math.
6 calculators →
Controls & Feedback
PID tuning, Bode margins, damping ratios, and state-space fundamentals.
8 calculators →
Signal Processing & DAQ
Nyquist, FFT bins, windowing, jitter, and the DAQ error budget.
11 calculators →
Reliability & Availability
MTBF, Weibull, series/parallel systems, and availability arithmetic.
12 calculators →
Statistics & Uncertainty
Sample sizes, ANOVA, GUM uncertainty, and the QA/QC math.
11 calculators →
Engineering Economics
NPV, IRR, LCOE, and the finance behind engineering decisions.
6 calculators →
All calculators
- dB ConverterConvert power between W, mW, dBm, and dBW in one shot.
- Ohm's LawEnter any two of voltage, current, and resistance — get the third plus power.
- Frequency ⇄ WavelengthWavelength for any frequency, with velocity factor for cables.
- Beam DeflectionMaximum deflection for the two textbook cases: cantilever and simply-supported.
- Standard AtmosphereISA temperature, pressure, density, and speed of sound at altitude.
- Voltage DividerVout, loading current, and dissipation for the two-resistor divider.
- Parallel ResistorsEquivalent resistance of two or three resistors in parallel.
- Wheatstone BridgeDifferential output of the four-arm bridge — the front end of half of all sensors.
- Strain Gauge OutputBridge output for a strain measurement — quarter, half, or full bridge.
- Resistor Color CodeFour-band resistor value from the band colors.
- Op-Amp GainClosed-loop gain for inverting and non-inverting configurations.
- Instrumentation Amp GainGain of the classic three-op-amp in-amp from the gain-set resistor.
- RC Low-Pass FilterCutoff frequency and time constant for the single-pole RC.
- ADC ResolutionLSB size, counts, and ideal dynamic range for an N-bit converter.
- RMS ⇄ Peak ⇄ Peak-to-PeakSine-wave conversions between RMS, peak, and peak-to-peak.
- 4–20 mA Loop ScalingConvert loop current to process value and back — with the burden check.
- Shunt ResistorDrop, dissipation, and required rating for a current-sense shunt.
- SNR ⇄ ENOBConvert between signal-to-noise ratio and effective number of bits.
- Crest FactorPeak-to-RMS ratio — the number that clips amplifiers and fools meters.
- LED Series ResistorThe resistor between your supply and the LED, plus its dissipation.
- Capacitor Energy & ChargeStored energy and charge at a given voltage.
- Battery LifeRuntime from capacity and load, with a usable-capacity derating.
- dB Voltage RatioGain in dB from two voltages — the 20·log flavor.
- VSWR / Return Loss / ΓEnter any one of VSWR, return loss, or reflection coefficient — get all of them plus mismatch loss.
- Free-Space Path LossFSPL between isotropic antennas — the first line of every link budget.
- RF Link BudgetReceived power and margin from TX power, gains, distance, and losses.
- Thermal Noise FloorkTB noise power for a bandwidth — the −174 dBm/Hz line.
- Noise Figure ⇄ Noise TemperatureConvert between NF in dB and equivalent noise temperature in kelvin.
- Cascade Noise FigureTwo-stage Friis cascade — why the LNA wins.
- Reactance (XL / XC)Inductive or capacitive reactance at frequency.
- LC Resonant FrequencyResonance of an LC pair — the Thomson formula.
- Q Factor ⇄ BandwidthLoaded Q from bandwidth, or bandwidth from Q, at a center frequency.
- Skin DepthHow deep current actually flows in a conductor at frequency.
- PCB Trace WidthIPC-2221 trace width for a current and temperature rise.
- Microstrip ImpedanceZ₀ and effective εr for a surface trace over a ground plane (Hammerstad).
- Pi AttenuatorResistor values for a Pi pad of given attenuation and impedance.
- T AttenuatorResistor values for a T pad of given attenuation and impedance.
- dBm ⇄ dBµV (50 Ω)Convert between the RF power and EMC voltage dialects.
- Frequency ⇄ Periodf to T and back, with the angular frequency thrown in.
- Dipole / Whip LengthCut lengths for a half-wave dipole and quarter-wave whip.
- Coax Loss & Power OutTotal cable loss from the per-100-ft spec, and what actually reaches the antenna.
- Doppler ShiftFrequency shift for a moving target — one-way or radar (two-way).
- Radio / Radar HorizonLine-of-sight distance from antenna heights, with standard refraction.
- Gain from BeamwidthsApproximate directive gain from the two −3 dB beamwidths.
- RF Power DensityFar-field power density from EIRP and distance — the exposure math.
- Transformer Turns RatioVoltage, current, and impedance transformation from the turns ratio.
- RC Charge TimeTime for a capacitor to reach a target percentage of the supply.
- Inductor EnergyStored energy in a current-carrying inductance.
- Bolt Torque from PreloadTightening torque for a target preload — the K-factor shortcut everyone actually uses.
- Shaft Power ⇄ TorqueP = Tω — convert between power, torque, and rotational speed.
- Gear RatioRatio, output speed, and output torque from tooth counts.
- Coil Spring RateRate of a round-wire helical compression/extension spring, plus spring index and Wahl factor.
- Belt & Pulley SpeedDriven speed, ratio, and belt velocity from pulley diameters.
- Linear Thermal ExpansionΔL = αLΔT for common structural materials.
- Axial Stress & Strainσ = F/A and ε = σ/E, with an optional yield-strength safety check.
- Shaft Torsion (Solid Round)Max shear stress τ = Tr/J for a solid circular shaft, plus optional twist angle.
- Euler Column BucklingCritical buckling load Pcr = π²EI/(KL)² with standard end conditions.
- Bearing L10 LifeBasic rating life in million revolutions and hours — ball or roller exponent.
- Flywheel Kinetic EnergyStored rotational energy E = ½Iω² from inertia and speed.
- Hydraulic Cylinder ForceExtend and retract force from pressure, bore, and rod diameter.
- Lever Mechanical AdvantageMoment balance about the fulcrum — ideal MA and load force.
- Kinetic EnergyKE = ½mv² — the energy of anything moving in a straight line.
- Gravitational Potential EnergyPE = mgh — energy banked by height.
- Projectile Range (No Drag)Range, max height, and flight time on flat ground — vacuum ballistics.
- Friction ForceMaximum static friction μN, with an optional slides-or-holds check.
- Mass Moment of Inertia (Shapes)Rotational inertia for the four shapes that cover most machine parts.
- Rectangular Section ModulusS = bh²/6 and I = bh³/12, with optional bending stress from a moment.
- Thin-Wall Pressure Vessel StressHoop and longitudinal stress σ = Pr/t, with the r/t > 10 validity gate.
- Plate Clutch Torque (Uniform Wear)Transmissible torque T = µ·F·n·R_mean for disc clutches and brakes.
- Fillet Weld Throat StressShear on the throat, a = 0.707z — the plane where fillet welds actually fail.
- Shaft Critical Speed (Deflection Method)First critical speed from static deflection — the Rayleigh one-liner.
- Natural Frequency (Spring–Mass)f = (1/2π)√(k/m) — the fundamental note of any stiffness and mass.
- Pendulum PeriodT = 2π√(L/g) — small-swing period of a simple pendulum.
- Speed of Sound in MaterialsLongitudinal bar velocity c = √(E/ρ) for common engineering solids.
- Isentropic Flow RatiosT/T₀, P/P₀, ρ/ρ₀, and A/A* from Mach number — the compressible-flow table, minus the table.
- Normal Shock RelationsJump conditions across a normal shock: M₂ and the pressure, density, temperature, and total-pressure ratios.
- Oblique Shock (θ-β-M)Weak-shock angle β and downstream conditions for a wedge at supersonic speed — with detached-shock detection.
- Mach Number from Airspeed & AltitudeTrue airspeed plus ISA altitude → Mach number and the local speed of sound.
- Dynamic Pressure (q)q = ½ρV² from velocity plus either an ISA altitude or a direct density.
- Reynolds NumberRe = ρVL/µ with one-click air or water properties, or your own fluid.
- Pipe Pressure Drop (Darcy-Weisbach)Friction loss in a round pipe — Swamee-Jain friction factor, automatic laminar branch.
- Pipe Flow VelocityMean velocity in a round pipe from volumetric flow and diameter.
- Bernoulli Pressure ChangeDownstream pressure from an upstream state, two velocities, and an elevation change.
- Orifice FlowFlow through a sharp-edged orifice from a pressure differential — Q = C_d·A·√(2ΔP/ρ).
- Manning Open-Channel FlowDischarge in a rectangular channel from geometry, slope, and roughness n.
- Pump Hydraulic & Shaft PowerWater power from flow and head, and the shaft power once efficiency takes its cut.
- NPSH AvailableNet positive suction head at the pump inlet — the cavitation margin.
- Airflow Units (CFM ⇄ m³/h ⇄ L/s)The three dialects of volumetric airflow, converted exactly.
- SCFM ⇄ ACFMStandard-to-actual airflow via the ideal-gas temperature and pressure correction.
- Drag ForceF = ½ρV²·C_d·A — aerodynamic drag and the power it costs.
- Lift ForceL = ½ρV²·C_L·S — lift from speed, wing area, and lift coefficient.
- Terminal VelocitySteady fall speed where drag balances weight: √(2mg / ρ·C_d·A).
- Tsiolkovsky Rocket EquationΔv from specific impulse and mass ratio — the tyranny, quantified.
- Circular Orbit Velocity & PeriodSpeed and period of a circular Earth orbit from altitude.
- Escape Velocity√(2µ/r) for Earth, Moon, or Mars — from the surface or from altitude.
- Hohmann TransferTwo-burn transfer between circular Earth orbits: Δv₁, Δv₂, total, and time of flight.
- Specific ImpulseI_sp and effective exhaust velocity from thrust and propellant mass flow.
- Water Hammer (Joukowsky)Pressure surge from a sudden velocity change: ΔP = ρ·a·Δv.
- Pressure ConverterPa, kPa, bar, psi, atm, mmHg, inH₂O, and Torr — one value, every dialect.
- Volumetric Flow ConverterL/s, L/min, m³/h, US GPM, and CFM — pump curves to duct specs.
- Torque ConverterN·m, lbf·ft, lbf·in, kgf·m, and ozf·in — wrench specs in every dialect.
- Energy ConverterJ, kJ, Wh, kWh, BTU, cal, ft·lbf — plus the eV for the physicists.
- Power ConverterW, kW, both horsepowers, BTU/h, and tons of refrigeration.
- Temperature Converter°C, °F, K, and °R — the one conversion with offsets, done right.
- Length Convertermm to nautical miles, with the PCB designer's mil in between.
- Mass & Force Converterkg, lb, oz, slug — and their weights in N, kgf, lbf at standard gravity.
- Area & Volume Converterm², ft², in² and L, gal(US), ft³, m³ — enter either or both.
- Angle ConverterDegrees, radians, gradians, arcminutes, mrad — and the NATO mil.
- Speed Converterm/s, km/h, mph, knots, ft/s — with the sea-level Mach number thrown in.
- Concrete Slab VolumeSlab volume from length, width, and thickness — plus bag counts and a waste allowance.
- Concrete Column VolumeVolume for round or square columns, any count — with bag equivalents.
- Concrete Block WallCMU count and mortar bags for a wall — standard 8×16 block.
- Rebar WeightTotal weight for a run of US bar sizes #3–#8.
- Aggregate TonnageTonnes of gravel, sand, or crushed stone from area and depth.
- Rankine Earth PressureActive earth pressure coefficient and resultant force on a retaining wall.
- Horizontal Tank VolumePartial-fill volume of a horizontal cylindrical tank from the dip level.
- Vertical Tank VolumeFill volume of a vertical cylindrical tank from the level.
- Ideal Gas Law (PV = nRT)Leave any one of P, V, n, T blank — the card solves for it.
- Gas DensityDensity of a gas from pressure and temperature — ρ = PM/RT.
- Log-Mean Temperature DifferenceLMTD for counterflow or parallel-flow heat exchangers from the four terminal temperatures.
- Heat Exchanger DutyQ = ṁ·cp·ΔT for one stream — the first number of every exchanger problem.
- Heat Conduction (Fourier)Steady heat flow through a flat layer — Q = k·A·ΔT/L.
- Dilution (C₁V₁ = C₂V₂)Leave any one of the four blank — stock, dose, or final volume solved.
- Pump Head ⇄ PressureConvert a pressure to metres of head for a fluid, plus static lift.
- Arrhenius Rate RatioHow much faster a reaction runs at a new temperature, from the activation energy.
- Half-Life DecayFraction remaining after any elapsed time, from the half-life.
- Dew Point & Absolute HumidityDew point from temperature and relative humidity — Magnus formula, plus g/m³ of water.
- L-Network Impedance MatchTwo-component L-match between resistive source and load — Q, L, and C at your frequency.
- 555 Timer — AstableR1, R2, C → frequency, duty cycle, and high/low times for the classic astable hookup.
- 555 Timer — MonostableOne-shot pulse width from R and C: t = 1.1·R·C.
- Zener Shunt RegulatorSeries resistor window and worst-case zener dissipation for a simple shunt regulator.
- Wire Gauge (AWG) PropertiesPick an AWG size — diameter, area, resistance, and rule-of-thumb ampacity for copper.
- Wire Voltage DropRound-trip drop over a copper pair: AWG size, one-way length, and load current.
- Power Sum in dBmAdd two incoherent powers expressed in dBm — the right way.
- Fresnel Zone ClearanceFirst-zone radius at mid-path and the 60% clearance a microwave link actually needs.
- ERP ⇄ EIRPRadiated power against the dipole or isotropic reference — the 2.15 dB everyone flips.
- Coax Impedance from DimensionsZ₀ of a coaxial line from shield ID, center-conductor OD, and the dielectric.
- Series RLC Impedance|Z| and phase of a series R-L-C at frequency, plus where it resonates.
- Battery Pack ConfigurationSeries × parallel cells → pack voltage, capacity, and watt-hours.
- Hold-Up Capacitor SizingBulk capacitance to ride through a dropout: C = 2·P·t / (V₁² − V₂²).
- Nearest E-Series ValueSnap a target resistance to the nearest E12 / E24 / E96 standard value.
- LED Array / String DesignerSupply, Vf, and current → LEDs per string, string count, and the ballast resistor.
- RC Snubber (Ring Killer)Size R and C from the measured ringing frequency and estimated parasitic capacitance.
- Inrush Limiter (NTC) SizingCold resistance to cap the surge into a capacitor bank, and the joules the NTC must swallow.
- Basquin S-N Fatigue LifeHigh-cycle fatigue life from the Basquin power law — enter stress amplitude to get cycles, or cycles to get allowable stress.
- Neuber Notch Stress (Local Strain)Estimate elastic-plastic notch-root stress and strain from nominal load using Neuber's rule and a Ramberg-Osgood curve.
- Paris Law Crack Growth RateFatigue crack growth per cycle from the stress-intensity range using the Paris power law.
- Fracture Toughness — Critical Stress / Crack SizeSolve linear-elastic fracture mechanics for critical stress, crack length, or the stress-intensity factor given K_IC.
- Larson-Miller Creep LifeTrade time against temperature for creep-rupture — solve the LMP, remaining life in hours, or allowable metal temperature.
- Hardness Conversion (HRC / HV / HB)Cross-convert Rockwell C, Vickers, and Brinell for non-austenitic steel per ASTM E140 Table 1, plus a tensile-strength estimate.
- Weld Cooling Rate (t8/5)Estimate the 800→500 °C cooling time of a weld from heat input, preheat, and plate thickness — the number that sets HAZ hardness.
- Corrosion Rate (Mass Loss & mm/y ⇄ mpy)Turn a coupon mass-loss test into a corrosion rate, or convert straight between mm/y and mils per year.
- Galvanic Couple PotentialEstimate the driving voltage and corrosion risk when two dissimilar metals touch in a wet environment.
- Hall-Petch Grain-Size StrengtheningPredict yield strength from average grain diameter — σ₀ + k·d^(-½), with the ASTM grain-size number thrown in.
- Hollomon-Jaffe Tempering ParameterTrade soak time against temperature in steel tempering — compute the HJ parameter and solve the equivalent time at a second temperature.
- Carbon Equivalent (IIW)Weldability index from steel chemistry — flags preheat need and cold-cracking risk before you strike an arc.
- Charpy V-Notch Impact EnergyTurn pendulum release and rise angles into absorbed impact energy — J, ft·lbf, and J/cm² over the notch ligament per ASTM E23.
- Thermal Shock Resistance (Kingery R′)First and second thermal-shock parameters for brittle ceramics — the max temperature drop a part survives, and how conductivity buys margin.
- CTE Mismatch Thermal StressThermal stress at a bonded bi-material interface from a temperature swing — the first-order constrained-strain estimate for die-attach, solder, and coating stacks.
- Hydrogen Embrittlement Threshold StressEstimate the sustained-load threshold stress for a high-strength steel from its notched fracture strength and an F519-style threshold ratio.
- Forman Crack Growth Rate (R-ratio)Fatigue crack growth per cycle with mean-stress (R-ratio) and fracture-toughness effects — the equation under NASGRO and AFGROW.
- Goodman Mean-Stress CorrectionFold a nonzero mean stress into an equivalent fully-reversed stress and get the Goodman fatigue safety factor, with Gerber for comparison.
- CIDR Subnet CalculatorTurn an IPv4 address and prefix length into network, broadcast, host range, and usable host count.
- TCP Bandwidth-Delay Product & WindowSize the TCP receive window for a fat pipe — get the bandwidth-delay product and whether window scaling is required.
- Amdahl's Law SpeedupPredict the ceiling on speedup when you only parallelize (or accelerate) part of a workload.
- Gustafson-Barsis Scaled SpeedupEstimate parallel speedup when the problem grows with the processor count — the optimistic counterpoint to Amdahl.
- M/M/1 QueueAverage wait, queue length, and utilization for a single-server queue with Poisson arrivals and exponential service.
- Little's Law (L = λW)Relate items in a system, arrival rate, and time-in-system — solve for whichever one you don't have.
- Shannon-Hartley Channel CapacityMaximum error-free bit rate for a channel given its bandwidth and signal-to-noise ratio.
- Hamming Code Parity BitsFind how many parity bits a SEC Hamming code needs for a given number of data bits, plus the overhead.
- Base64/Hex Encoding OverheadSize a payload after Base64, Base32, or hex encoding — exact RFC 4648 byte counts for link budgets, MTU checks, and storage estimates.
- RAID Usable CapacityUsable storage, efficiency, and fault tolerance for RAID 0/1/5/6/10 given drive count and size.
- Serial/Parallel System MTBFRoll up component failure rates into a system MTBF for series or active-parallel redundancy.
- Utilization Law (ρ = λS)Find how busy a server or resource is from its arrival rate and mean service time.
- Effective Memory Access TimeBlend cache-hit and miss-penalty times into the average access time your CPU actually sees.
- Bloom Filter False-Positive RateSize a Bloom filter — false-positive probability, optimal hash count, and bits-per-element for a given m, n, k.
- Password Entropy (bits)Estimate the brute-force strength of a password from its length and character pool, plus a crack-time sanity check.
- RSA Key Strength (equivalent symmetric bits)Estimate the symmetric-bit security level of an RSA modulus, with a NIST SP 800-57 comparison and deprecation flag.
- Birthday Collision ProbabilityOdds that two of N items share a hash (or birthday) drawn from a space of D values — the birthday-attack yardstick.
- bcrypt Cost Factor RuntimeEstimate how long a bcrypt hash takes at a given cost factor and how it scales when you bump the work factor.
- TLS Record OverheadWire-byte cost of pushing application data through the TLS record layer — records, tags, headers, and goodput efficiency.
- PBKDF2 Iteration Count from Target TimePick a PBKDF2 iteration count that hits a target derivation time given your platform's measured per-iteration cost.
- CVSS v3.1 Base ScoreScore a vulnerability from its eight base metrics — exact FIRST.org v3.1 math including the Roundup quirk.
- JWT Payload Byte SizePredict the on-the-wire size of a signed JWT before it blows past your cookie or proxy header limits.
- Token Bucket Rate LimiterSize a token bucket for an API or network path — sustained rate, burst allowance, and how long a burst can run before it throttles.
- Brute Force Time (Charset × Length)Estimate how long an exhaustive password search takes given alphabet size, length, and guess rate.
- Overall Equipment Effectiveness (OEE)Roll planned-time losses, speed losses, and defects into a single OEE score with its three factors.
- Takt TimeSet the production heartbeat — how often you must finish a unit to meet customer demand without over- or under-building.
- Line Balancing EfficiencySize a paced assembly line — cycle time, theoretical station count, and balance efficiency from total work content and demand.
- Economic Order Quantity (EOQ)Find the order size that minimizes combined ordering and holding cost for a steady-demand part.
- Cycle Time ⇄ Throughput (Little's Law)Relate work-in-process, cycle time, and throughput on a production line — enter any two, get the third plus takt.
- Cp / Cpk Process CapabilityTurn spec limits and process spread into Cp, Cpk, and the sigma level that predicts your reject rate.
- Sigma Level ⇄ DPMOConvert between process sigma level, DPMO, and yield — with the standard 1.5σ long-term shift baked in.
- Attribute-Data Sample SizeFind how many parts you must inspect to detect a defect at a target rate with a chosen confidence — the zero-acceptance sizing behind LTPD sampling.
- MTBF from Runtime + Failure CountTurn logged operating hours and failure counts into MTBF, failure rate, and availability.
- Weibull B10 Life (β, η)Turn a Weibull shape and characteristic life into B10 (or any B-life), median life, and MTTF — the numbers a warranty or bearing spec actually asks for.
- X̄ / R Control Chart LimitsCompute control limits and process capability from subgroup average and range data using AIAG SPC constants.
- Machine Utilization & AvailabilityTurn scheduled, run, and downtime hours into utilization, availability, and lost-capacity numbers for a work center.
- Radar Range EquationMaximum detection range for a monostatic radar from transmit power, gain, RCS, and receiver sensitivity — Skolnik's classic point-target form.
- RCS vs Detection RangeHow far a radar sees a target given its RCS, or the RCS reduction needed to shrink detection range by a set factor.
- IR Seeker Detection Range (NEP)Noise-limited detection range for a point IR target from radiant intensity, aperture, and detector NEP.
- Laser NOHD (Nominal Ocular Hazard Distance)Eye-safety standoff range for a CW laser from output power, beam divergence, and exit aperture — the ANSI Z136.1 range-safety number.
- Proportional Navigation Miss DistanceEstimate homing-loop miss distance from a heading error using Zarchan's dimensionless adjoint result.
- Circular Error Probable (CEP)Convert range and cross-range (bearing) miss-distance sigmas into the 50% circular error probable radius.
- Blackbody Radiance (Planck's Law)Spectral radiance, photon flux, Wien peak, and total exitance of a greybody target — the front end of every EO-IR link budget.
- Dawes Angular ResolutionSmallest resolvable double-star separation for a given aperture — the empirical bench limit for an optic.
- Blast Overpressure at Range (Hopkinson-Cranz)Peak incident overpressure from a hemispherical surface burst via Hopkinson-Cranz scaling and the Kinney-Graham correlation — a quick standoff and clearance estimate, not a substitute for UFC 3-340-02 design tables.
- TNT-Equivalent Blast RangePeak overpressure vs. standoff distance for a surface or free-air TNT charge using scaled distance.
- Rankine Cycle Efficiency (Ideal)First-cut thermal efficiency, work, and heat for an ideal Rankine steam power cycle from your four state enthalpies.
- Carnot Efficiency LimitUpper bound on thermal efficiency and refrigeration COP between two reservoir temperatures.
- Refrigeration Cycle COPCoefficient of performance for a cooling or heating cycle from duty and compressor power, with the Carnot ceiling for comparison.
- Heat-Pump COP + Reversible LimitGet heating COP from compressor work plus the Carnot ceiling for the same temperature lift.
- Entropy Change (Ideal Gas)Molar entropy change of an ideal gas between two T–P states using constant specific heat.
- Duct Static-Pressure LossFriction loss in a round duct run — Swamee-Jain friction factor on standard air, with in. w.g. per 100 ft for the ASHRAE-chart crowd.
- Air Changes Per Hour (ACH ⇄ CFM)Convert between room air changes per hour and supply airflow for any room volume.
- R-Value / U-Value (Series Wall)Stack up to five layer R-values, get the assembly U-value plus heat flux — SI and US units side by side.
- Cooling Tower Approach & RangeGet range, approach, and cooling effectiveness from hot/cold water temps and the ambient wet-bulb.
- Pump/Fan Affinity LawsScale flow, head/pressure, and power when a centrifugal pump or fan changes speed or impeller diameter.
- Availability (MTBF / MTTR)Steady-state availability of a repairable system from its mean time between failures and mean time to repair.
- Series/Parallel System ReliabilityCombine identical block reliabilities into a series chain, a parallel (redundant) bank, or a k-out-of-n voting group.
- Weibull Reliability R(t)Survival probability, failure fraction, and hazard rate at a given time for a two-parameter Weibull life model.
- Sample Size for a Mean (Known σ)How many samples you need to estimate a mean within a target margin of error, when the population standard deviation is known.
- Sample Size (Binomial Proportion)How many units to sample to estimate a pass/fail proportion within a target margin of error.
- χ² Goodness-of-FitCompare observed counts against expected counts and get the χ² statistic, degrees of freedom, and p-value.
- One-Way ANOVA F-StatisticCompare 2–4 group means from summary stats (n, mean, s) — get F, mean squares, and degrees of freedom for the table lookup.
- Student-t Mean Confidence IntervalConfidence interval for a population mean from a small sample — uses the t-distribution, not the normal.
- Normal Distribution Tail ProbabilityTurn a z-score into CDF, tail area, and two-sided probability — the guts of a Z-table without the table.
- Gage R&R (%P/T)Turn repeatability and reproducibility standard deviations into %Tolerance and %Study measurement-system metrics.
- Combined Uncertainty (GUM)Root-sum-square of up to five uncertainty components, with coverage factor for an expanded uncertainty.
- Type A / Type B Combined UncertaintyCombine a statistical (Type A) uncertainty with an instrument/spec (Type B) contribution per the GUM — get u_c, expanded U, and effective degrees of freedom.
- ISO 17025 CMC (Calibration & Measurement Capability)Roll reference-standard, repeatability, resolution, and other contributors into an ILAC P14-style CMC claim for your scope of accreditation.
- Sample Median Confidence Interval (Sign-Test / Order Statistic)Distribution-free confidence interval for the median from order statistics — no normality assumed.
- Nyquist Rate & AliasingCheck whether your sample rate clears Nyquist and find the alias frequency a tone folds down to.
- FFT Bin Width & ResolutionGet frequency resolution, capture time, and bin count from sample rate and FFT size before you set up a spectrum capture.
- Window Amplitude & Scallop LossCoherent gain, scallop loss, ENBW, and processing loss for common FFT windows — read off the amplitude penalty before you trust an FFT peak.
- Sinc Interpolation ErrorEstimate the aliasing/truncation error floor when reconstructing a band-limited signal from finite samples.
- Anti-Alias Filter AttenuationCheck how much a Butterworth anti-alias filter knocks down out-of-band energy at Nyquist and at the worst-case fold frequency before your ADC samples it.
- DAQ Offset + Gain ErrorTurn a two-point calibration into offset and gain-error terms, then correct any raw DAQ reading.
- FIR Filter Group DelayGroup delay and time lag of a linear-phase FIR filter from its tap count and sample rate.
- Butterworth Filter OrderMinimum Butterworth order to hit a stopband spec given passband ripple, attenuation, and the two edge frequencies.
- LSB Dither RMSRMS amplitude and quantization-noise floor for uniform (flat-PDF) dither in an ADC or DAC LSB.
- Envelope Detector RC ConstantSize the diode-detector RC so an AM envelope tracks cleanly — big enough to smooth carrier ripple, small enough to dodge diagonal clipping.
- SNR Loss from Sample JitterFind the jitter-limited SNR ceiling of a sampled sine — the number that kills your high-IF ADC's ENOB.
- Cross-Correlation Peak LagFind the time delay between two sampled signals from the lag of their cross-correlation peak.
- Ziegler-Nichols PID TuningTurn an ultimate gain and oscillation period into starting P, PI, or PID gains.
- IMC-Based PID Tuning (FOPDT)Turn a first-order-plus-dead-time model into PID gains using the Rivera-Morari IMC rules — one tuning knob, λ.
- Damping Ratio → % OvershootTranslate a second-order damping ratio into peak overshoot, peak time, and settling time.
- Phase & Gain MarginTurn a Bode reading — gain at the phase-crossover, phase at the gain-crossover — into gain and phase margins with a stability verdict.
- 2×2 State-Space EigenvaluesEigenvalues of a 2×2 system matrix A — the poles that set stability, natural frequency, and damping.
- Final-Value Theorem — Steady-State ErrorSteady-state error of a unity-feedback loop from system type and static error constant — step, ramp, or parabolic input.
- Controllability / Observability Rank TestBuild the Kalman controllability and observability matrices for a 2nd- or 3rd-order LTI system and check their rank.
- Lead / Lag Compensator DesignPlace the zero and pole of a lead or lag compensator to hit a target phase or gain at your crossover frequency.
- Thin-Lens Equation + MagnificationFind image distance and magnification from focal length and object distance for a single thin lens.
- Airy Disk Diffraction RadiusDiffraction-limited spot size and angular resolution for a circular aperture.
- Numerical Aperture ⇄ f/#Convert between numerical aperture, f-number, and half-cone angle for a lens or fiber.
- LED Junction TemperatureEstimate LED junction temperature from drive power, thermal resistance, and board temperature.
- Optical Power Budget (dBm)Check whether a fiber link closes: subtract fiber, connector, and splice losses from Tx power and compare against receiver sensitivity.
- Gaussian Beam DivergenceFar-field half-angle, Rayleigh range, and spot size for a TEM₀₀ Gaussian beam from its waist.
- SMPS Efficiency ChainCascade converter-stage efficiencies to get total efficiency, input power, and thermal loss.
- MOSFET Conduction + Switching LossEstimate total MOSFET power loss — I²R conduction plus turn-on/turn-off switching energy — for a hard-switched converter.
- Inductor Ripple Current (Buck)Size the buck-converter inductor from switching frequency and duty — get peak-to-peak ripple and peak current.
- Output Cap Ripple VoltageEstimate output-capacitor ripple in a switching converter from capacitance, ESR, and inductor ripple current.
- Buck Converter Duty CycleSolve duty cycle, output voltage, inductor ripple, and CCM boundary for a synchronous or diode buck.
- Steinmetz Core LossFerrite core loss from datasheet Steinmetz coefficients — loss density plus total dissipation for your core volume.
- Net Present Value (Uniform Cash Flow)Discount an initial cost plus a level annual cash flow to present value and get the NPV of the project.
- Internal Rate of Return (Newton)Solve the discount rate that zeroes an even-interval cash-flow series — Newton-Raphson on the NPV equation.
- Simple Payback PeriodHow many years an energy or capital retrofit takes to pay back its first cost from annual savings.
- Levelized Cost of Electricity (LCOE)Compare generation options on one number — annualized capital plus O&M and fuel, per MWh delivered.
- 1-Way Sensitivity Range (Tornado)Swing one input between its low and high bound and see how far the result moves — the bar length of a tornado diagram.
- Loan Amortization PaymentLevel periodic payment, total interest, and payoff for a fully amortized loan.
- Moody Friction Factor (Colebrook)Solve the Colebrook-White equation exactly by iteration — the friction factor behind the Moody chart, without squinting at log-log axes.
- Cipoletti Weir FlowOpen-channel flow over a trapezoidal (Cipoletti) weir from crest length and head.
- Choked Nozzle (Mach 1 Throat)Choked mass flow, throat conditions, and critical pressure ratio for a converging nozzle running sonic at the throat.
- Cavitation Number (σ)Dimensionless margin against cavitation for a pump, valve, or hydrofoil operating point.
- Two-Phase Pressure Drop (Lockhart-Martinelli)Estimate two-phase frictional ΔP from the single-phase liquid and gas drops using the Martinelli parameter and Chisholm two-phase multiplier.
- Compressor Polytropic WorkSpecific work, discharge temperature, and gas power for a polytropic compression — ideal-gas basis, any n you specify.
- Drag Divergence Mach NumberEstimate the Mach number where transonic wave drag takes off, from critical Mach or Korn's sweep/thickness relation.
- Oswald-Efficiency Induced DragInduced drag coefficient and force from lift, aspect ratio, and Oswald efficiency.
- Propeller Actuator-Disk ThrustIdeal thrust, induced velocity, and Froude efficiency for a propeller or rotor from disk loading and flight speed.
- CG Shift from Fuel BurnFind the new center of gravity after burning a mass of fuel located at a known station.
- Stagnation Temperature (Compressible Flow)Total (stagnation) temperature from static temperature and Mach number for a calorically perfect gas.
- Ballistic Coefficient β (Reentry)Compute a reentry body's ballistic coefficient from mass, drag coefficient, and reference area — the number that sets how deep it plunges before decelerating.
- Bipropellant O/F RatioSize oxidizer and fuel flow rates from a mixture ratio and total propellant flow.
- TVC Gimbal TorqueActuator torque needed to deflect a gimbaled rocket engine against thrust misalignment offset.
- ASCE 7-22 Wind PressureVelocity pressure and design wind pressure on a building surface using the ASCE 7-22 directional method.
- Seismic Base Shear (ASCE 7 ELF)Equivalent lateral force base shear per ASCE 7-22 §12.8 — Cs with upper and lower bounds, plus which equation governed.
- Bolt Shear (Lap Joint)Shear capacity of a bolted lap joint per AISC J3 — LRFD and ASD strengths plus utilization against your applied load.
- Flitch Beam Composite DeflectionSize a wood-and-steel-plate flitch beam by summing parallel EI — midspan deflection, steel share, and span ratio for a uniformly loaded simple span.
- Plate Critical Buckling StressElastic critical buckling stress of a thin rectangular plate — pick the k for your edge conditions and load case, get σ_cr and load per unit width.
- Footing Bearing Pressure (Eccentric)Soil pressure under a rectangular spread footing carrying axial load plus moment — checks for uplift and reports peak/min pressure.
- Shear-Wall Cantilever Deflection (SDPWS)Wood shear-wall deflection per the AWC SDPWS three-term equation — bending, panel shear via Ga, and anchorage slip, with drift ratio.
- Bolt Preload vs YieldTarget preload and installation torque for a fastener at a chosen fraction of proof or yield strength.
- Pt100 RTD (Callendar–Van Dusen)Convert Pt100/Pt1000 resistance to temperature and back using the IEC 60751 Callendar–Van Dusen coefficients.
- Thermistor Steinhart-HartConvert a measured NTC thermistor resistance to temperature with the Steinhart-Hart equation.
- Pressure-Gauge Accuracy Class → UncertaintyTurn an ASME B40.100 grade (or IEC/EN percent-of-span class) into an absolute error band at your reading.
- Flow-Meter Turndown RatioTurndown (rangeability) from max/min accurate flow, plus a quick accuracy-band check at the low end.
- Valve Sizing (Cv) — LiquidSize a control valve for liquid service: get required Cv from flow, pressure drop, and specific gravity.
- Calibration Drift ProjectionProject when an instrument's linear drift will breach tolerance and recommend the next cal interval.
- Pyrometer Emissivity CorrectionCorrect a radiation pyrometer reading when the target emissivity differs from the value the instrument assumed.
- Orifice β-Ratio Sizing (ISO 5167)Size a concentric square-edged orifice plate for a target flow — solves bore diameter, β, and differential pressure.