RMS ⇄ Peak ⇄ Peak-to-Peak
Sine-wave conversions between RMS, peak, and peak-to-peak.
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The engineering
These ratios are for clean sines only — 120 Vrms mains is 170 V peak, 340 V peak-to-peak. For anything distorted, a 'true-RMS' meter integrates the actual waveform while an average-responding meter just scales by 1.11 and hopes.
The rectified-average row is why cheap meters read squarewaves ~11% high and triangles low.
Where this math comes from
RMS is the heating value of a waveform — the DC equivalent that dissipates the same power, rooted in James Joule's 1840s heating law. The AC-era fight over how to even state 'the voltage' was settled by the 1890s power engineers, with Charles Steinmetz's complex-number method making sinusoidal arithmetic routine.
The √2 on this card is, quietly, why 115 V equipment carries 163 V peak stress — a distinction that has been biting insulation designers since Niagara Falls first sent AC to Buffalo in 1896.
- 1841James Prescott JouleI²R heating — the physical meaning of RMS.
- 1893Charles SteinmetzComplex/phasor method tames AC calculation.
- 1896Niagara Falls plantAC power transmission wins; RMS becomes the lingua franca.
See the full timeline of the math behind every calculator →
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