# Peak AC Voltage and RMS Voltage ?

#### jethro99

Joined Oct 31, 2020
15
Took some measurements. First one from a wall outlet and then several from a permanent magnet generator being turned by an electric motor at varying RPM's.

Used the measurements to calculate from peak volts to RMS volts and from RMS volts to peak volts.

Results are somewhat close but not spot on. Any ideas as to what is going on?

#### crutschow

Joined Mar 14, 2008
28,155
How did you take your "Measured" values, and how can that be different from the "Calculated" values?
Calculated from what?

Difference between the calculated Vrms and Vp can be due to distortion or noise in the sinewave.

#### dcbingaman

Joined Jun 30, 2021
493
What type of meter did you use to take the measurements? There are 'true RMS' meters and there are meters that simply approximate true RMS. The more expensive ones tend to be 'true RMS'.

#### AnalogKid

Joined Aug 1, 2013
9,471
And (piling on) look at the generator output waveform with a scope. The classic equation to convert peak to RMS is valid **only** for a pure sine wave.

Also - loading. The generator's output will sag under load more than will the output from a wall outlet.

ak

#### jethro99

Joined Oct 31, 2020
15
RMS voltage was measured using a voltmeter set on the AC scale. Peak voltage was measured using a peak voltage reading adapter with the voltmeter set on the DC scale.

Wall outlet measured first which indicated ~ 123.7 volts. Which according to all that I can find is RMS voltage.

Using standard formulas for converting RMS volts to peak volts, and peak volts to RMS volts, I then let an excel spreadsheet do the calculations for me.

VP = VRMS × √2,

VRMS = VP / √2

#### AlbertHall

Joined Jun 4, 2014
11,587
Difference between the calculated Vrms and Vp can be due to distortion or noise in the sinewave.
Not to mention measurement error.
Look up the specified accuracy of AC measurements for your meter.

#### jethro99

Joined Oct 31, 2020
15
The generator was unloaded. No load applied.

#### dcbingaman

Joined Jun 30, 2021
493
RMS voltage was measured using a voltmeter set on the AC scale. Peak voltage was measured using a peak voltage reading adapter with the voltmeter set on the DC scale.

Wall outlet measured first which indicated ~ 123.7 volts. Which according to all that I can find is RMS voltage.

Using standard formulas for converting RMS volts to peak volts, and peak volts to RMS volts, I then let an excel spreadsheet do the calculations for me.

VP = VRMS × √2,

VRMS = VP / √2
As AnalogKid stated, these equations are only valid for a 'pure' non distorted sine wave.

#### crutschow

Joined Mar 14, 2008
28,155
The discrepancies are likely do to error in the meter readings between the RMS and PK measurements (especially if you meter doe not measure "True" RMS, and distortion in the waveform from the generator.

Do you have an oscilloscope to look at the waveform?

#### jethro99

Joined Oct 31, 2020
15
No oscilloscope. Have always wanted one.

Is the wall outlet AC voltage not a pure sign wave?

#### crutschow

Joined Mar 14, 2008
28,155
Is the wall outlet AC voltage not a pure sign wave?
Usually it's pretty close, but large low power-factor loads on the line can distort it.

#### Alec_t

Joined Sep 17, 2013
12,309
Is the wall outlet AC voltage not a pure sign wave?
Generally far from pure. There is a lot of electrical noise superimposed on the mains supply; increasingly so with all the switch-mode power supplies used by modern electronic gadgets.

#### AlbertHall

Joined Jun 4, 2014
11,587
Peak voltage was measured using a peak voltage reading adapter with the voltmeter set on the DC scale
There is also the accuracy of this adaptor to take into account.