Calculators
RMS Calculator
Convert RMS, peak, and peak-to-peak waveform values or find RMS from samples.
Convert RMS, peak, and peak-to-peak values for ideal symmetric waveforms, or calculate RMS directly from a list of measured samples. Everything runs locally in your browser.
230
325.26912
650.53824
207.07275
Crest factor: 1.4142136 · Form factor: 1.1107207
Preset waveform conversions assume ideal symmetric waveforms with zero DC offset. For distorted or offset signals, use actual samples or a true-RMS measurement instead of applying a preset conversion factor.
About This Tool
Root mean square (RMS) describes the effective magnitude of a changing quantity. In electrical work it is especially useful because an RMS voltage or current can be compared with the DC value that would produce the same heating in a resistive load. This calculator supports two distinct tasks: converting amplitude measures for ideal symmetric waveforms and computing RMS directly from numeric samples.
How To Use It
- For waveform conversion, choose sine, square, triangle, or sawtooth and identify whether your known value is RMS, peak, or peak-to-peak.
- Enter the known amplitude using any consistent unit such as volts or amps. The results use that same unit.
- For measured or arbitrary data, switch to RMS of samples and paste signed values separated by spaces, commas, semicolons, or new lines.
- Use preset conversions only when the waveform matches the stated ideal shape and has no DC offset.
Examples
230 V RMS sine wave
An ideal 230 V RMS sine wave has a peak of about 325.27 V and a peak-to-peak value of about 650.54 V.
10 V peak square wave
A symmetric ideal square wave with 10 V peak has 10 V RMS because its magnitude remains at the peak level throughout each half-cycle.
Signed samples
Samples -1, 1, -1, 1 have an RMS value of 1. Squaring removes the sign before the mean and square root are taken.
Useful Notes
The RMS definition
For N discrete samples x₁ through xₙ, RMS = √[(x₁² + x₂² + … + xₙ²) / N]. For a continuous periodic waveform, the same idea is expressed by integrating the squared waveform over one period, taking its mean, and then the square root.
Sine-wave relationships
For an ideal zero-offset sine wave, RMS = peak/√2, peak-to-peak = 2 × peak, and the full-wave rectified average magnitude is 2 × peak/π. A 230 V RMS sine therefore reaches about 325 V at each crest.
Square, triangle, and sawtooth waves
A symmetric square wave has RMS equal to its peak magnitude. Ideal symmetric triangle and sawtooth waveforms have RMS = peak/√3. These factors are shape-specific and should not be applied to clipped, pulsed, distorted, or offset signals.
Crest factor and form factor
Crest factor is peak divided by RMS and indicates how large the crest is relative to effective magnitude. Form factor here is RMS divided by the full-wave rectified average magnitude. Both depend on waveform shape.
Why RMS of samples is different
When you have actual sampled data, computing √mean(x²) avoids assuming a waveform shape. The samples should adequately represent the signal interval you care about; biased or incomplete sampling can produce a misleading result.
Limitations
Preset conversions assume ideal symmetric periodic waveforms centered on zero. Real signals may include DC offset, harmonics, noise, clipping, transients, changing duty cycle, or measurement error. Use representative samples or an appropriate true-RMS instrument when those effects matter.
FAQ
Is RMS the same as average?
No. A symmetric AC waveform can have a signed full-cycle average of zero while still having a nonzero RMS value. RMS squares the instantaneous values before averaging.
How do I convert RMS to peak for a sine wave?
Multiply RMS by √2. For example, 120 V RMS is about 169.7 V peak for an ideal sine wave.
Can I use the sine-wave factor for a square wave?
No. A symmetric ideal square wave has RMS equal to its peak, while a sine wave has RMS equal to peak/√2.
What does peak-to-peak mean?
For a symmetric zero-offset waveform, peak-to-peak is the full excursion from the negative peak to the positive peak, equal to twice the peak magnitude.
Does frequency change these RMS conversion ratios?
Not for the ideal waveform shapes used here. Frequency changes how quickly the waveform repeats, but not the shape-specific ratio between peak and RMS.
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