RMS Value Calculator
Enter the peak value to compute the RMS (sine: Vrms=Vmax/√2=Vpp/(2√2)), peak-to-peak and form factor. HK mains 311 V peak → 220 V RMS; sine form factor 1.1107.
Input Data
Results
At a glance:RMS (root mean square) Vrms=√(Σx²/n): the square root of the mean of the squared signal over one period. It represents the DC-equivalent value (same power). For a sine wave Vrms=Vmax/√2=Vpp/(2√2). Form factor FF=RMS/mean=π/(2√2)≈1.1107 for a sine. Properties: (1) RMS dissipates the same power as DC (thermal equivalence); (2) HK mains 220 V is RMS with a 311 V peak; (3) triangle wave Vrms=Vmax/√3; (4) square wave Vrms=Vmax. Applications: (1) AC voltage/current (multimeter reads RMS); (2) audio power; (3) vibration acceleration; (4) signal processing; (5) electricity billing.
Formula
RMS: Vrms = √(Σx²/n)
Sine: Vrms = Vmax/√2 = Vpp/(2√2)
Peak-to-peak: Vpp = 2·Vmax
Form factor: FF = RMS/mean = sine π/(2√2) ≈ 1.1107
$$V_{rms} = \sqrt{\frac{1}{n}\sum_{i=1}^{n} x_i^2} = \frac{V_{max}}{\sqrt{2}}\ \text{(sine)}, \quad FF = \frac{\pi}{2\sqrt{2}} \approx 1.1107$$How to Use
- Enter the peak value Vmax (V).
- The tool gives the sine RMS, peak-to-peak and form factor.
Case Studies
Mains power and billing
HK mains: 220 V RMS, 311 V peak, 50 Hz, 20 ms period. Meters read RMS; appliance power is RMS-based.
Billing: P=Vrms²/R; a 100 W bulb consumes 100 W (RMS).
Three-phase: industrial 380 V RMS line voltage, 50 Hz in HK factories.
Audio and vibration
Audio power: an amplifier's RMS output drives the speaker; 100 W RMS is sustained, peak power is not.
Vibration analysis: RMS acceleration assesses fatigue (HK rail carriage monitoring).
Sound pressure: SPL=20log(p_rms/p_ref), p_ref=20 μPa — HK noise control uses SPL.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.