RMS Calculator

The root-mean-square concept was introduced to AC electrical engineering by Charles Proteus Steinmetz at General Electric in the 1890s during his seminal work formalizing AC circuit analysis. The challenge: how do you give a single "voltage" figure for a waveform that\'s continuously changing? Peak, peak-to-peak, and average all fail to capture the crucial property of heating effect — the reason we care about AC power in the first place.

RMS solves this elegantly. Since resistive heating is proportional to V², averaging V² over one cycle and taking the square root gives the DC-equivalent amplitude that would produce the same heat. For a sine wave, this works out to Peak/√2 ≈ 0.707 × Peak — the familiar conversion factor every EE student memorizes. The 120 V AC in your wall is 120 V RMS, 170 V peak, 340 V peak-to-peak.

True-RMS measurement in meters became standard in the 1970s–80s. Early analog "average-responding" meters scaled their reading by 1.111 (the sine-wave form factor) to display RMS — correct only for pure sines. True-RMS meters electronically square the input, average it, and take the square root, giving correct readings for any waveform including switching-supply currents, audio, and noise. Modern digital DMMs almost universally implement true-RMS for AC modes.

Pick a waveform shape (sine, square, triangle, sawtooth, half-wave rectified, full-wave rectified) and enter any one amplitude quantity (peak, peak-to-peak, RMS, or average). The tool fills in the other three using the waveform-specific form factor and crest factor constants, and displays the waveform shape.

Use cases: reading an oscilloscope (Vpp shown) and converting to RMS for spec comparison; converting mains voltage between peak and RMS for dielectric stress calculation; sizing heating element wattage (always use RMS × RMS / R). For non-ideal or arbitrary waveforms, you\'ll need a true-RMS meter — none of the pre-set form factors apply. All math runs client-side.