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)