Free · Ideal mechanics
Ideal Waveform RMS Amplitude and Offset
Find RMS voltage for six ideal waveforms using peak, original peak-to-peak or mean-absolute/rectified amplitude conventions.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
Root-mean-square voltage is the square root of the waveform mean square, including its added DC offset and any rectified-wave mean.
Vrms=√mean(v²); for zero-mean AC plus offset, Vrms²=Voffset²+mean(vAC²).
Worked example
Enter these known values and leave the other values blank.
- Waveform shape
- Sine wave
- Characteristic voltage
- Peak AC amplitude
- Voltage
- 10 V
- Wave offset (V==0==)
- -3 V
- RMS voltage
- 7.681 V
Assumptions and limitations
- Voltages describe ideal periodic waves and uniform averaging over a complete cycle. RMS is the square root of mean squared voltage.
- For balanced sine, square, triangle and sawtooth waves, Vavg means the mean absolute amplitude of the zero-mean AC component before the added DC offset, not the signed cycle mean.
- For rectified sine waves, Vavg is the rectified cycle mean, and Vpp means the original unrectified sine peak-to-peak amplitude. It is not the post-rectification peak-to-peak excursion.
- This waveform model does not establish safe voltage levels or substitute for measurement of a real distorted signal.
- Signed added DC offset is supported in every waveform. Rectified-wave RMS includes twice the offset times the waveform mean, as well as AC mean square and offset square.
- Inverse quadratic branches choose the larger real amplitude or offset root. With a rectified waveform, two different signed offsets can give the same RMS; a sufficiently negative known offset can also allow two nonnegative amplitudes. RMS alone does not select between those solutions. Inverse amplitudes must remain nonnegative.
Common questions
Can RMS recover a unique signed offset?
No. A quadratic can have two real offset roots. The retained inverse chooses the larger root; its companion gives the same RMS and may have a different sign.
References
Replace explanatory external images with original accessible descriptions preserving each scenario, rope or machine arrangement and every variant condition. Require nonnegative AC amplitude and nonnegative RMS voltage; signed DC offset remains supported for all six waveform families. Include the waveform-mean cross term when adding signed DC offset to half-wave and full-wave rectified sine signals. Retain all amplitude controls and solve inverse quadratics using their larger real root, with branch ambiguity disclosed.