RMS Value Calculator

RMS Value Formula

Worked Example

A sine wave with a 325 V peak (230 V mains):

1. Sine: V_rms = V_p/√2
2. V_rms = 229.8097039
3. Rectified average = 2V_p/π (over a half cycle) = 206.901426

Average of |v| (rectified average): 206.901426 · Form factor RMS ÷ rectified average: 1.110720735 · Crest factor peak ÷ RMS: 1.414213562 · Peak-to-peak: 650

GATE tip

For a waveform made of a DC part and AC parts at different frequencies, V_rms = √(V_dc² + V₁,rms² + V₂,rms² + …). GATE uses this for signals like 10 + 5 sin ωt: √(100 + 12.5) = 10.61.

More Electric Circuits Calculators

• Impedance Calculator

  Z = R + j(ωL − 1/ωC) (series)

  parallel: 1/Z = 1/R + j(ωC − 1/ωL); ω = 2πf; φ = arctan(X/R)

  Example: R = 10 Ω, L = 100 mH and C = 200 µF in series at 50 Hz: Impedance |Z| = 18.4462 Ω.

  Open the impedance calculator →

• AC Power Calculator

  S = VI (√3 V_L I_L), P = S cos φ, Q = S sin φ

  P real power (W), Q reactive (VAR), S apparent (VA), cos φ the power factor

  Example: A single-phase load drawing 10 A at 230 V with 0.8 power factor lagging: Real power P = 1.84 kW.

  Open the ac power calculator →

• RC & RL Time Constant Calculator

  τ = RC, v_C(t) = V(1 − e^(−t/τ))

  RL circuit: τ = L/R, i(t) = (V/R)(1 − e^(−t/τ)); discharging uses e^(−t/τ)

  Example: A 10 kΩ resistor charging a 100 µF capacitor from 10 V, after 1 s: Time constant τ = 1 s.

  Open the rc & rl time constant calculator →

• RLC Resonance Calculator

  f₀ = 1 / (2π√(LC)), Q = (1/R)√(L/C) (series)

  parallel: Q = R√(C/L); bandwidth = f₀/Q; ζ = 1/(2Q)

  Example: A series circuit with R = 10 Ω, L = 10 mH and C = 1 µF: Resonant frequency f₀ = 1591.55 Hz.

  Open the rlc resonance calculator →

Frequently asked questions

Sources

• The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.