Peak, RMS and average: the measures of a sine wave
A sine wave has several values that can be called its amplitude, and they differ. When a datasheet says "1 V", it matters which one is meant.
The three values
- Peak value (û): the maximum distance from zero.
- Peak-to-peak value: from the positive peak to the negative peak. For a sine it is twice the peak value.
- RMS value (root mean square): the square root of the mean of the squared signal. This value gives the same heating power in a resistor as a direct voltage of that size.
- Rectified average: the mean of the absolute value.
For a sine wave with peak value 1:
| Measure | Value |
|---|---|
| Peak | 1 |
| Peak-to-peak | 2 |
| RMS | 0.707 (1/√2) |
| Rectified average | 0.637 (2/π) |
The crest factor is peak divided by RMS: 1.414 for a sine, or 3.01 dB. The form factor is RMS divided by the rectified average: 1.11.
Other waveforms
| Waveform | RMS (peak 1) | Average (peak 1) | Crest factor |
|---|---|---|---|
| Sine | 0.707 | 0.637 | 1.414 (3.0 dB) |
| Square | 1 | 1 | 1 (0 dB) |
| Triangle | 0.577 | 0.5 | 1.73 (4.8 dB) |
Music and speech have much higher crest factors, often 10 to 20 dB, because they are made of occasional peaks on a lower average level. That is why peak headroom matters, see Headroom and gain staging.
Examples with audio levels
A line level of +4 dBu is 1.228 V RMS. As a sine wave, it has a peak value of 1.737 V and a peak-to-peak value of 3.47 V. An oscilloscope shows the peak-to-peak value, a multimeter the RMS.
Why meters can mislead
Many cheap meters measure the rectified average and then scale it by the form factor of a sine so that it displays the RMS value. This is correct only for sine waves. For other waveforms the reading is wrong, by about 11 % for a square wave. A true-RMS meter computes the real RMS value and is accurate for any waveform within its bandwidth.
Which one is used where
- Voltage in audio levels (dBu, dBV) is RMS.
- Amplifier power ratings use RMS voltage and the load resistance: 100 W into 8 Ω needs 28.3 V RMS, which is 40 V peak.
- Digital level (dBFS) refers to the peak value of the largest sample, with a full-scale sine reading −3 dBFS RMS.
Try it
Use the peak, RMS and average tool to convert between these measures for sine, square and triangle waves.
Draft: written by an AI assistant, awaiting technical review.
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