How this calculator works
RMS is the square root of the cycle average of voltage squared, so it predicts resistor heating. Symmetric waves have zero mean before offset, allowing DC and AC RMS components to combine in quadrature. Rectified waves already have a nonzero mean, so their offset creates an additional cross term. Signed average cannot recover the amplitude of a symmetric waveform; average-rectified magnitude is a different measurement.
Formula
Vrms² = A² mean(w²) + 2 V0 A mean(w) + V0². For sine, square, triangle and sawtooth, mean(w)=0 and mean(w²)=1/2, 1, 1/3, 1/3. Half-wave: mean=1/pi, mean-square=1/4. Full-wave: mean=2/pi, mean-square=1/2.
Worked example
A 10 V peak sine with no offset has 7.07106781 V RMS. A bipolar square wave with 8 V peak-to-peak and 3 V offset has sqrt(4²+3²) = 5 V RMS.
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Frequently asked questions
Does a multimeter always measure true RMS?
No. Some meters infer RMS from average-rectified readings and assume a sine wave; check the meter specification.
Is peak-to-peak always twice the peak?
For these symmetric bipolar waves it is. A rectified sine ranges from zero to its positive peak, so its peak-to-peak span equals that peak.
Why is offset treated differently for rectified waves?
Their unshifted cycle average is nonzero, producing a cross term when voltage is squared.