Convert sine-wave peak, peak-to-peak, or rectified average voltage into RMS voltage.
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RMS voltage calculator Convert sine-wave peak, peak-to-peak, or full-wave rectified average voltage into RMS voltage, with the supporting waveform values shown beside the result. This page now covers rms voltage calculator, peak to rms calculator, peak-to-peak voltage calculator, and average voltage to rms intent while keeping waveform-specific caveats visible.
Starting value
Start with sine-wave peak voltage and derive RMS and peak-to-peak values.
Common sine-wave checkpoints
How to use this result
Peak to RMS: use it when the source gives crest voltage, oscilloscope amplitude, or generator peak output.
Peak-to-peak to RMS: use it when the source gives a full swing value from top crest to bottom crest.
Rectified average to RMS: use it when an average-responding meter or worksheet gives the full-wave rectified average for a clean sine wave.
Scope: this is a sine-wave conversion only, not a general distorted-waveform RMS solver or signed full-cycle average converter.
Choose a starting voltage Select the peak to rms workflow above, then enter the known sine-wave voltage to calculate RMS voltage.
RMS voltage calculator: convert peak or peak-to-peak voltage for sine waves
An RMS voltage calculator converts sine-wave peak voltage, peak-to-peak voltage, or full-wave rectified average voltage into RMS voltage and shows the related waveform values alongside the main result.
What this RMS voltage calculator solves
This page starts from the three waveform values users most often have on hand: peak voltage, peak-to-peak voltage, and the full-wave rectified average used by average-responding meter shortcuts. In peak mode it divides by the square root of two to produce RMS voltage. In peak-to-peak mode it first derives the peak value and then applies the same RMS relationship. In rectified-average mode it uses the standard sine-wave 1.11 form-factor relationship to recover RMS voltage.
Showing the supporting peak, peak-to-peak, and rectified-average figures beside the answer keeps the conversion auditable. That matters when you are checking whether a measured waveform lines up with a datasheet rating, translating a bench measurement into the RMS value used by other equipment, or reconciling a true-RMS reading against an average-responding meter on a clean sine wave.
The page is built for rms voltage calculator, peak voltage calculator, peak-to-peak voltage calculator, average voltage to rms calculator, and Vrms intent, while keeping the waveform assumption visible for anyone who is comparing a sine wave to an instrument reading.
The sine-wave formulas behind the result
For an ideal sinusoidal waveform, RMS voltage equals peak voltage divided by the square root of two. Peak-to-peak voltage is twice the peak voltage, so dividing peak-to-peak voltage by two times the square root of two gives the same RMS result directly.
For a full-wave rectified sine wave, the rectified average is two times the peak voltage divided by pi. Rearranging that relationship gives the common average-to-RMS shortcut used by average-responding meters: multiply the rectified average by about 1.1107 to estimate RMS for a clean sine wave.
Those relationships are specific to sine waves. The calculator keeps the conversion modes separate so you can start from the quantity you actually know without having to work through the intermediate step manually.
Vrms = Vpeak / √2
Converts sine-wave peak voltage into RMS voltage.
Vpeak = Vpp / 2
Converts peak-to-peak voltage into peak voltage.
Vrms = Vpp / (2 × √2)
Direct sine-wave conversion from peak-to-peak voltage to RMS voltage.
Vavg(rectified) = 2 × Vpeak / π
Full-wave rectified average for a sine wave.
Vrms = Vavg(rectified) × π / (2 × √2)
Sine-wave conversion from rectified average voltage to RMS voltage.
Peak voltage, RMS voltage, and peak-to-peak voltage
The three values stay connected by a simple ratio for a sine wave: peak-to-peak is twice peak, and RMS is peak divided by √2. That is why 170 V peak maps to about 120.2 V RMS and 340 V peak-to-peak, while 325 V peak maps to about 230 V RMS and 650 V peak-to-peak.
The rectified average adds one more useful checkpoint: a 170 V peak sine wave also corresponds to about 108.2 V full-wave rectified average. That is the average value an average-responding meter effectively scales by about 1.11 when it is assuming a clean sine wave.
That ratio set is the reason many searchers switch between rms voltage calculator, peak voltage calculator, peak-to-peak voltage calculator, and average voltage to rms intent. The underlying waveform is the same; only the starting value changes.
170 V peak = about 120.2 V RMS = 340 V peak-to-peak
325 V peak = about 230 V RMS = 650 V peak-to-peak
108.2 V rectified average = about 120.2 V RMS = 170 V peak = 340 V peak-to-peak
5 V peak = about 3.536 V RMS = 10 V peak-to-peak
Worked examples: 170 V peak, 340 Vpp, 108.2 V rectified average, 230 V RMS
Worked examples make the conversion easier to sanity-check. A 170 V peak sine wave is the familiar bench example because it lands right around 120 V RMS, 340 V peak-to-peak, and 108.2 V full-wave rectified average. A 340 V peak-to-peak sine wave gives the same answer from the other direction, and 108.2 V rectified average lands on the same waveform if the source really is a clean sine wave.
The same logic applies to 230 V RMS mains-style signals. That corresponds to about 325 V peak, about 650 V peak-to-peak, and about 206.9 V rectified average. On the other end of the scale, a 5 V peak test signal corresponds to about 3.536 V RMS, 10 V peak-to-peak, and about 3.183 V rectified average.
170 V peak -> 120.208 V RMS -> 340 V peak-to-peak -> 108.225 V rectified average
340 V peak-to-peak -> 170 V peak -> 120.208 V RMS -> 108.225 V rectified average
108.225 V rectified average -> 120.208 V RMS -> 170 V peak -> 340 V peak-to-peak
325 V peak -> 229.810 V RMS -> 650 V peak-to-peak -> 206.901 V rectified average
5 V peak -> 3.536 V RMS -> 10 V peak-to-peak -> 3.183 V rectified average
Average-responding meters versus true-RMS meters
Average-responding meters do not calculate the true heating value from the waveform itself. Instead, they measure a rectified average and multiply by about 1.11 under the assumption that the waveform is a pure sine wave. For standard sinusoidal AC that shortcut is usually close enough, which is why average voltage to RMS searches often sit next to classic Vrms searches.
The shortcut breaks down once the waveform is distorted, clipped, heavily harmonic, PWM-shaped, or otherwise non-sinusoidal. In those cases a true-RMS meter or waveform-specific analysis is the safer choice, because the same rectified average can correspond to a different RMS value on a different waveform.
Why waveform shape matters
This calculator assumes an ideal sine wave only. That is the right assumption for standard AC measurements, but it is not the same as a clipped, square, triangle, PWM, or otherwise distorted waveform.
Once the waveform is no longer sinusoidal, the simple √2 and 1.11 relationships may no longer describe the true RMS value. In those cases, measure RMS directly or use a waveform-specific method instead of treating the result as a general-purpose converter.
How to use the result with meters and signal generators
RMS voltage is the effective value most often used for AC power discussions, multimeter readings, and equipment ratings. Peak and peak-to-peak values are more common on oscilloscopes, signal generators, and waveform descriptions.
Rectified-average values show up when a worksheet, meter, or service note is using an average-responding convention for clean sine waves. Seeing all four quantities together helps prevent two common mistakes: treating a measured crest value as though it were already an RMS rating, and treating a rectified average as though it were the signed average over a full AC cycle.
If your source data starts in peak, peak-to-peak, or rectified-average form, the calculator gives you the corresponding RMS value immediately and exposes the other waveform checkpoints you may need for cross-checking.
What this page does not replace
This calculator does not model clipped, distorted, offset, or non-sinusoidal signals. It does not replace waveform analysis, lab-grade RMS measurement, or a bench instrument's own conversion algorithms.
It also does not use the signed average over a full AC cycle, which is zero for an ideal sine wave. The average-input path on this page is the full-wave rectified average only.
Use it as a planning and educational aid when the waveform is approximately sinusoidal. If the signal shape is intentionally non-sinusoidal or visibly distorted, calculate or measure RMS from the actual waveform instead.
RMS voltage is the effective heating-equivalent value of an AC waveform. For a sine wave, it is the peak voltage divided by the square root of two.
Why can I not use this for square or triangle waves?
Because the conversion factors on this page are specific to sine waves. Other waveform shapes have different relationships among RMS, peak, and peak-to-peak voltage.
Why does the result also show peak and peak-to-peak voltage?
Those supporting values make it easier to compare the answer with oscilloscope readings, signal-generator settings, and equipment limits that may use a different voltage convention.
What is the formula for RMS voltage from peak voltage?
For an ideal sine wave, Vrms equals Vpeak divided by the square root of two. That is the standard peak-to-RMS relationship this calculator uses.
What is the formula for RMS voltage from peak-to-peak voltage?
For an ideal sine wave, Vrms equals Vpp divided by two times the square root of two. The calculator uses that shortcut when you start from peak-to-peak voltage.
Is RMS the same as average voltage?
No. RMS is an effective value used for power and equipment comparisons, while average voltage depends on the waveform and how it is measured. For a sine wave, those numbers are not the same.
Can I convert average voltage to RMS with this calculator?
Yes, if the value you have is the full-wave rectified average of a clean sine wave. In that specific case the calculator applies the standard sine-wave relationship and multiplies by about 1.1107 to estimate RMS.
What kind of average does this page use?
It uses the full-wave rectified average, not the signed average over a full AC cycle. The signed average of an ideal sine wave over one complete cycle is zero, which is not the value average-responding meter shortcuts rely on.
What is the difference between peak and peak-to-peak voltage?
Peak voltage is measured from the zero line to the crest. Peak-to-peak voltage is measured from the positive crest to the negative crest, so it is twice the peak voltage on a sine wave.
What does 170 V peak mean in RMS terms?
A 170 V peak sine wave corresponds to about 120.2 V RMS and about 340 V peak-to-peak. That is the classic conversion example for a sine wave.
Can I use this for distorted or clipped signals?
Not safely. The square-root-of-two conversion only describes ideal sine waves. Distorted or clipped waveforms need a waveform-specific RMS measurement.
Why does the calculator mention average-responding meters?
Because many meters estimate RMS on a clean sine wave by measuring the rectified average and scaling it by about 1.11. That shortcut is accurate for a pure sine wave, but it can be misleading for distorted signals.
When should I use the peak voltage calculator instead?
Use the peak voltage calculator when you already know RMS or peak-to-peak voltage and need crest voltage instead of RMS.
What if my waveform is clipped or distorted?
The sine-wave square-root-of-two shortcut may no longer be accurate. Measure RMS directly or use a waveform-specific method when the signal is not a clean sine wave.
