Test & Instrumentation Calculators
Bridges, amplifiers, sensors, and signal chains.
- Ohm's LawEnter any two of voltage, current, and resistance — get the third plus power.V = I · R P = V · I
- Voltage DividerVout, loading current, and dissipation for the two-resistor divider.Vout = Vin · R2 / (R1 + R2)
- Parallel ResistorsEquivalent resistance of two or three resistors in parallel.1/Rp = 1/R1 + 1/R2 (+ 1/R3)
- Wheatstone BridgeDifferential output of the four-arm bridge — the front end of half of all sensors.Vo = Vex · [ R2/(R1+R2) − R4/(R3+R4) ]
- Strain Gauge OutputBridge output for a strain measurement — quarter, half, or full bridge.Vo ≈ Vex · n · GF · ε / 4 (n = active gauges)
- Resistor Color CodeFour-band resistor value from the band colors.R = (10·D1 + D2) × 10^multiplier
- Op-Amp GainClosed-loop gain for inverting and non-inverting configurations.Non-inv: G = 1 + Rf/R1 Inv: G = −Rf/R1
- Instrumentation Amp GainGain of the classic three-op-amp in-amp from the gain-set resistor.G = 1 + 2R / Rg
- RC Low-Pass FilterCutoff frequency and time constant for the single-pole RC.fc = 1 / (2πRC) τ = RC
- ADC ResolutionLSB size, counts, and ideal dynamic range for an N-bit converter.LSB = FSR / 2ᴺ SNR(ideal) = 6.02·N + 1.76 dB
- RMS ⇄ Peak ⇄ Peak-to-PeakSine-wave conversions between RMS, peak, and peak-to-peak.Vpk = √2 · Vrms Vpp = 2 · Vpk (sine only)
- 4–20 mA Loop ScalingConvert loop current to process value and back — with the burden check.PV = PVlo + (I − 4 mA)/16 mA · span
- Shunt ResistorDrop, dissipation, and required rating for a current-sense shunt.V = I·R P = I²·R
- SNR ⇄ ENOBConvert between signal-to-noise ratio and effective number of bits.ENOB = (SINAD − 1.76) / 6.02
- Crest FactorPeak-to-RMS ratio — the number that clips amplifiers and fools meters.CF = |V|peak / Vrms
- LED Series ResistorThe resistor between your supply and the LED, plus its dissipation.R = (Vs − Vf) / I
- Capacitor Energy & ChargeStored energy and charge at a given voltage.E = ½CV² Q = CV
- Battery LifeRuntime from capacity and load, with a usable-capacity derating.t = (capacity × derating) / load
- dB Voltage RatioGain in dB from two voltages — the 20·log flavor.dB = 20 · log₁₀(V2 / V1)
- Thermal Noise FloorkTB noise power for a bandwidth — the −174 dBm/Hz line.P = kTB (−173.98 dBm/Hz at 290 K)
- Cascade Noise FigureTwo-stage Friis cascade — why the LNA wins.F = F1 + (F2 − 1) / G1
- Reactance (XL / XC)Inductive or capacitive reactance at frequency.XL = 2πfL XC = 1 / (2πfC)
- PCB Trace WidthIPC-2221 trace width for a current and temperature rise.I = k · ΔT^0.44 · A^0.725 (IPC-2221; k = 0.048 ext / 0.024 int)
- dBm ⇄ dBµV (50 Ω)Convert between the RF power and EMC voltage dialects.dBµV = dBm + 107 (in 50 Ω)
- Frequency ⇄ Periodf to T and back, with the angular frequency thrown in.T = 1/f ω = 2πf
- Transformer Turns RatioVoltage, current, and impedance transformation from the turns ratio.Vs = Vp·Ns/Np Zp = Zs·(Np/Ns)²
- RC Charge TimeTime for a capacitor to reach a target percentage of the supply.t = −RC · ln(1 − target)
- Inductor EnergyStored energy in a current-carrying inductance.E = ½LI²
- Natural Frequency (Spring–Mass)f = (1/2π)√(k/m) — the fundamental note of any stiffness and mass.fn = (1/2π) · √(k/m)
- Pendulum PeriodT = 2π√(L/g) — small-swing period of a simple pendulum.T = 2π · √(L/g)
- Speed of Sound in MaterialsLongitudinal bar velocity c = √(E/ρ) for common engineering solids.c = √(E / ρ)
- Orifice FlowFlow through a sharp-edged orifice from a pressure differential — Q = C_d·A·√(2ΔP/ρ).Q = C_d · A · √(2·ΔP/ρ)
- Temperature Converter°C, °F, K, and °R — the one conversion with offsets, done right.K = °C + 273.15 °F = 1.8·°C + 32 °R = 1.8·K
- Half-Life DecayFraction remaining after any elapsed time, from the half-life.N/N₀ = 2^(−t/t½) = e^(−λt), λ = ln 2 / t½
- Dew Point & Absolute HumidityDew point from temperature and relative humidity — Magnus formula, plus g/m³ of water.Td = b·γ / (a − γ), γ = ln(RH/100) + a·T/(b+T) (a = 17.625, b = 243.04)
- 555 Timer — AstableR1, R2, C → frequency, duty cycle, and high/low times for the classic astable hookup.f ≈ 1.44 / ((R1 + 2·R2)·C) t_hi = 0.693·(R1+R2)·C t_lo = 0.693·R2·C
- 555 Timer — MonostableOne-shot pulse width from R and C: t = 1.1·R·C.t = ln(3)·R·C ≈ 1.1·R·C
- Zener Shunt RegulatorSeries resistor window and worst-case zener dissipation for a simple shunt regulator.R ≤ (Vin_min − Vz)/(I_load + Iz_min) Pz_max = Vz·(Vin_max − Vz)/R
- Wire Gauge (AWG) PropertiesPick an AWG size — diameter, area, resistance, and rule-of-thumb ampacity for copper.d(mm) = 0.127 · 92^((36−AWG)/39) R = ρ/A, ρ_Cu = 1.724×10⁻⁸ Ω·m
- Wire Voltage DropRound-trip drop over a copper pair: AWG size, one-way length, and load current.V_drop = I · ρ/A · 2L (out and back; Cu at 20 °C)
- Power Sum in dBmAdd two incoherent powers expressed in dBm — the right way.P_total = 10·log₁₀(10^(P1/10) + 10^(P2/10))
- Series RLC Impedance|Z| and phase of a series R-L-C at frequency, plus where it resonates.|Z| = √(R² + (XL − XC)²) φ = atan((XL−XC)/R) f₀ = 1/(2π√LC)
- Battery Pack ConfigurationSeries × parallel cells → pack voltage, capacity, and watt-hours.V = S·V_cell Capacity = P·C_cell E = V × Ah
- Hold-Up Capacitor SizingBulk capacitance to ride through a dropout: C = 2·P·t / (V₁² − V₂²).C = 2·P·t / (V₁² − V₂²) (from ½CV₁² − ½CV₂² = P·t)
- Nearest E-Series ValueSnap a target resistance to the nearest E12 / E24 / E96 standard value.E-series: mantissas ≈ 10^(i/N), i = 0…N−1 (IEC 60063)
- LED Array / String DesignerSupply, Vf, and current → LEDs per string, string count, and the ballast resistor.n ≤ (Vs − V_headroom)/Vf R = (Vs − n·Vf)/I
- RC Snubber (Ring Killer)Size R and C from the measured ringing frequency and estimated parasitic capacitance.R = 1/(2π·f_ring·C_par) C_snub ≈ 4·C_par P_R = C_snub·V²·f_sw
- Inrush Limiter (NTC) SizingCold resistance to cap the surge into a capacitor bank, and the joules the NTC must swallow.R_cold ≥ V_peak / I_max E = ½·C·V² (energy the limiter absorbs at turn-on)
- X̄ / R Control Chart LimitsCompute control limits and process capability from subgroup average and range data using AIAG SPC constants.UCLₓ = X̄̄ + A₂·R̄ , LCLₓ = X̄̄ − A₂·R̄ , UCL_R = D₄·R̄ , LCL_R = D₃·R̄ , σ̂ = R̄/d₂ , Cpk = min[(USL−X̄̄), (X̄̄−LSL)] / 3σ̂
- 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.n = ( z(α/2) · σ / E )² , rounded up
- χ² Goodness-of-FitCompare observed counts against expected counts and get the χ² statistic, degrees of freedom, and p-value.χ² = Σ (Oᵢ − Eᵢ)² / Eᵢ , df = k − 1 − m , p = Q(df/2, χ²/2)
- 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.F = MSB / MSW, MSB = Σ nᵢ(x̄ᵢ − x̄)² / (k − 1), MSW = Σ (nᵢ − 1)sᵢ² / (N − k)
- Gage R&R (%P/T)Turn repeatability and reproducibility standard deviations into %Tolerance and %Study measurement-system metrics.GRR = √(EV² + AV²) , %P/T = k·GRR / (USL−LSL) × 100 , %GRR = GRR/√(GRR²+PV²) × 100 , ndc = ⌊√2 · PV/GRR⌋
- Combined Uncertainty (GUM)Root-sum-square of up to five uncertainty components, with coverage factor for an expanded uncertainty.uₙ = √(u₁² + u₂² + … + uₙ²) , U = k · uₙ
- 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.u_A = s/√n u_B = a/√3 (rect), a/√6 (tri), a/√2 (U), a (normal 1σ) u_c = √(u_A² + u_B²) U = k·u_c ν_eff = u_c⁴ / (u_A⁴/(n−1))
- 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.u_ref = U_ref/2 u_rep = s/√n u_res = r/(2√3) , u_c = √(u_ref² + u_rep² + u_res² + u_other²) CMC = k · u_c
- Nyquist Rate & AliasingCheck whether your sample rate clears Nyquist and find the alias frequency a tone folds down to.f_N = f_s / 2 , Nyquist rate = 2·f_sig , f_alias = |f_sig − f_s·round(f_sig/f_s)|
- FFT Bin Width & ResolutionGet frequency resolution, capture time, and bin count from sample rate and FFT size before you set up a spectrum capture.Δf = fs / N , T_capture = N / fs = 1 / Δf , f_Nyquist = fs / 2
- DAQ Offset + Gain ErrorTurn a two-point calibration into offset and gain-error terms, then correct any raw DAQ reading.measured = gain·applied + offset , gain = (Hₘ − Lₘ)/(Hᵣ − Lᵣ) , offset = Lₘ − gain·Lᵣ , corrected = (raw − offset)/gain
- LSB Dither RMSRMS amplitude and quantization-noise floor for uniform (flat-PDF) dither in an ADC or DAC LSB.RPDF: σ = V_pp / √12 , TPDF: σ = V_pp / √24 , σ_total = √(σ_dither² + σ_q²) , σ_q = LSB/√12
- SNR Loss from Sample JitterFind the jitter-limited SNR ceiling of a sampled sine — the number that kills your high-IF ADC's ENOB.SNR_jitter = −20 · log₁₀( 2π · f_in · t_j ) , ENOB = (SNR − 1.76) / 6.02
- Cross-Correlation Peak LagFind the time delay between two sampled signals from the lag of their cross-correlation peak.τ = k* / fₛ , k* = argmaxₖ Rₓᵧ(k) Δd = c · τ
- Optical Power Budget (dBm)Check whether a fiber link closes: subtract fiber, connector, and splice losses from Tx power and compare against receiver sensitivity.Loss = L·α + N_conn·L_conn + N_splice·L_splice , Margin = (P_tx − P_rx,sens) − Loss
- Pt100 RTD (Callendar–Van Dusen)Convert Pt100/Pt1000 resistance to temperature and back using the IEC 60751 Callendar–Van Dusen coefficients.t ≥ 0: R(t) = R₀·(1 + A·t + B·t²) , t < 0: R(t) = R₀·(1 + A·t + B·t² + C·(t−100)·t³) , A = 3.9083×10⁻³, B = −5.775×10⁻⁷, C = −4.183×10⁻¹²
- Thermistor Steinhart-HartConvert a measured NTC thermistor resistance to temperature with the Steinhart-Hart equation.1/T = A + B·ln(R) + C·ln(R)³ , T in K
- 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.±E = (class% / 100) · FS , %reading = E / reading · 100
- Flow-Meter Turndown RatioTurndown (rangeability) from max/min accurate flow, plus a quick accuracy-band check at the low end.Turndown = Q_max / Q_min (both at rated accuracy)
- Valve Sizing (Cv) — LiquidSize a control valve for liquid service: get required Cv from flow, pressure drop, and specific gravity.Cv = Q · √(SG / ΔP) , Kv ≈ 0.865 · Cv (Q in gpm, ΔP in psi)
- Calibration Drift ProjectionProject when an instrument's linear drift will breach tolerance and recommend the next cal interval.rate = (E_found − E_left) / Δt , t_breach = (±Tol − E_left) / rate , interval = (guard·Tol − E_left) / rate
- Pyrometer Emissivity CorrectionCorrect a radiation pyrometer reading when the target emissivity differs from the value the instrument assumed.1/T_true = 1/T_ind + (λ / c₂) · ln(ε_true / ε_set) , c₂ = 1.4388×10⁻² m·K
- Orifice β-Ratio Sizing (ISO 5167)Size a concentric square-edged orifice plate for a target flow — solves bore diameter, β, and differential pressure.qₘ = C·E·ε·(π/4)·d²·√(2·ρ·ΔP) , E = 1/√(1−β⁴) , β = d/D , C = Reader–Harris/Gallagher(β, Re_D)