Calculate RMS voltage from peak voltage for sine, square, triangle, sawtooth, and rectified waveforms. Includes form factor, crest factor, and waveform comparison table.
The Root Mean Square (RMS) voltage is the equivalent DC voltage that would produce the same heating effect in a resistive load. For a pure sine wave, V_rms = V_peak / √2 ≈ 0.707 × V_peak. This is why US mains electricity is rated at 120V RMS even though the peak voltage is about 170V.
RMS values are essential because they represent the effective or "DC equivalent" voltage for power calculations. When you measure AC voltage with a multimeter, it typically displays the RMS value. Power dissipated in a resistor equals V²_rms / R, regardless of the waveform shape.
This calculator converts between peak and RMS voltage for six common waveforms: sine, square, triangle, sawtooth, half-wave rectified, and full-wave rectified. It also computes the average voltage, form factor (V_rms/V_avg), crest factor (V_peak/V_rms), current, and power dissipation. A comparison table shows how different waveforms produce different RMS values from the same peak voltage.
Different waveforms have different relationships between peak, RMS, and average values. The familiar 1/√2 factor only applies to sine waves. Square waves have V_rms = V_peak, while triangle waves have V_rms = V_peak/√3. This calculator handles all common waveforms and provides a side-by-side comparison, eliminating the need to look up individual conversion factors.
Sine wave: V_rms = V_peak / √2 ≈ 0.7071 × V_peak Square wave: V_rms = V_peak Triangle/Sawtooth: V_rms = V_peak / √3 ≈ 0.5774 × V_peak Half-wave rectified: V_rms = V_peak / 2 Full-wave rectified: V_rms = V_peak / √2 Form Factor = V_rms / V_avg Crest Factor = V_peak / V_rms Power: P = V²_rms / R
Result: V_rms = 120.0 V
For a sine wave with 169.7 V peak, V_rms = 169.7 / √2 ≈ 120.0 V. This is the standard US household voltage. With a 100 Ω load, the RMS current is 1.2 A and power dissipation is 144 W.
The key insight behind RMS is that a 120V RMS AC signal delivers exactly the same average power to a resistor as a 120V DC source. This equivalence holds regardless of waveform shape — the RMS calculation inherently accounts for the waveform. This is why power ratings for appliances, transformers, and generators are always specified in RMS values.
Different waveforms stress components differently. A square wave with the same RMS as a sine wave has no harmonic content at the fundamental frequency — all its energy is at odd harmonics. This means filters, transformers, and capacitors in square-wave circuits experience different losses and heating patterns than in sine-wave circuits. Triangle waves have harmonics that fall off as 1/n², making them gentler on components than square waves.
For sine waves, even simple average-responding meters give correct RMS readings because the form factor is constant. But for switched signals, PWM waveforms, or distorted mains, a true-RMS meter is essential. Thermal-type true-RMS meters use a heating element and thermocouple that directly measure the heating effect, while digital true-RMS meters compute the mathematical RMS over many samples per cycle.
RMS stands for Root Mean Square. It is calculated by squaring the instantaneous values, averaging them over one complete cycle, and taking the square root. It represents the DC equivalent voltage for heating purposes.
RMS is used because it directly relates to power dissipation. P = V²_rms/R works for any waveform, making RMS the most practical measure for electrical engineering calculations.
For a square wave oscillating between ±V_peak, the RMS equals V_peak because the signal is always at maximum magnitude. The form factor and crest factor are both 1.0.
A standard (average-responding) meter measures the average value and multiplies by 1.11 (the sine wave form factor) to display RMS. This is accurate only for sine waves. A true-RMS meter computes the actual RMS regardless of waveform shape.
Crest factor (peak/RMS) indicates how extreme the peaks are relative to the effective value. High crest factors require equipment (amplifiers, transformers, UPS) with higher peak capacity than the continuous RMS rating suggests.
Only if they are at different frequencies or are uncorrelated. For signals at the same frequency, you must add them as phasors (accounting for phase). For unrelated signals, V_total_rms = √(V²₁ + V²₂).