Vpp to Vrms calculator (with Examples)

This tool converts peak to peak voltage V_PP to its root-mean-square (RMS) voltage equivalent V_RMS.

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Calculator

How to use this calculator

Enter the peak-to-peak voltage value. Units can be volt/millivolt/microvolt/nanovolt. The tool will calculate the RMS voltage value.

? Volt RMS to Volt peak-to-peak

Formula

V_RMS = V_pp/(2√2)

This formula applies to a sine wave. Here’s a list of V_pp to V_RMS calculators for other common waveforms such as triangle, square and pulse.

Example Calculation

A peak to peak voltage of 2 V is equivalent to an RMS voltage of 0.707 V.

What is Volt Peak to Peak?

Volt peak-to-peak (abbreviated Vpp) as the name suggests, is the difference between the peaks or maximum and minimum voltage level of an AC waveform.

The maximum value is also sometimes called the crest, while the minimum value is called the trough.

The picture below shows a sine wave, with max value = a and min value = -a.

In this case,

Vpp = a-(-a) = 2a

Sine wave voltages

The sine wave in the picture above has a DC value of zero. Vpp is independent of the DC value. In other words it doesn’t change for a non zero DC value.

The RMS value is lower than the peak value. It is equivalent to the DC voltage that would produce the same power in a resistor.

Why is Peak-to-Peak Voltage Important?

The input to certain circuits specify a max or min voltage level (for instance + 5V). Input levels that exceed this limit can damage the circuit.

In this situation it’s therefore important to understand the peak values. In the event that the input is specified in terms of voltage or RMS voltage, it becomes necessary to make the conversion from Vpp to VRMS.

How to find VRMS for a signal?

Older analog oscilloscopes don’t provide V_RMSso you have to measure the min and max levels Vp and -Vp using horizontal markers and then calculate VRMS using the calculator on this page. However, this conversion only applies to sinusoidal waveforms.

In some cases, there’s no closed form expression for Vpp to VRMS and in that case, the only way to compute VRMS is from a sequence of data samples.

V_RMS = √(1/n)(V₁² +V₂² + … + V_n²)

Modern digital oscilloscopes use Analog-to-Digital Converters to collect data samples from which the RMS voltage can be computed. This method is independent of the type of waveform. The only requirement is that the sampling rate of the oscilloscope be at least twice the maximum frequency of the measured input signal.

Video Explanation

Here is a video that explains how to convert between peak and RMS voltages

Related Calculators

The RMS voltage can be converted to Watt or dBm. This is useful for Radio Frequency applications.
For very large and very small numbers, it’s convenient to work in the dB scale. Use this calculator to convert from Volt to dBV.

V_pp to V_RMS Table

V_pp	V_RMS
0.25	0.09
0.50	0.18
0.75	0.27
1.00	0.35
1.25	0.44
1.50	0.53
1.75	0.62
2.00	0.71
2.25	0.80
2.50	0.88
2.75	0.97
3.00	1.06
3.25	1.15
3.50	1.24
3.75	1.33
4.00	1.41
4.25	1.50
4.50	1.59
4.75	1.68
5.00	1.77
5.25	1.86
5.50	1.94
5.75	2.03
6.00	2.12
6.25	2.21
6.50	2.30
6.75	2.39
7.00	2.47
7.25	2.56
7.50	2.65
7.75	2.74
8.00	2.83
8.25	2.92
8.50	3.01
8.75	3.09
9.00	3.18
9.25	3.27
9.50	3.36
9.75	3.45
10.00	3.54
10.25	3.62
10.50	3.71
10.75	3.80
11.00	3.89
11.25	3.98
11.50	4.07
11.75	4.15
12.00	4.24
12.25	4.33
12.50	4.42
12.75	4.51
13.00	4.60
13.25	4.68
13.50	4.77
13.75	4.86
14.00	4.95
14.25	5.04
14.50	5.13
14.75	5.21
15.00	5.30
15.25	5.39
15.50	5.48
15.75	5.57
16.00	5.66
16.25	5.75
16.50	5.83
16.75	5.92
17.00	6.01
17.25	6.10
17.50	6.19
17.75	6.28
18.00	6.36
18.25	6.45
18.50	6.54
18.75	6.63
19.00	6.72
19.25	6.81
19.50	6.89
19.75	6.98
20.00	7.07
20.25	7.16
20.50	7.25
20.75	7.34
21.00	7.42
21.25	7.51
21.50	7.60
21.75	7.69
22.00	7.78
22.25	7.87
22.50	7.95
22.75	8.04
23.00	8.13
23.25	8.22
23.50	8.31
23.75	8.40
24.00	8.49
24.25	8.57
24.50	8.66
24.75	8.75
25.00	8.84
25.25	8.93
25.50	9.02
25.75	9.10
26.00	9.19
26.25	9.28
26.50	9.37
26.75	9.46
27.00	9.55
27.25	9.63
27.50	9.72
27.75	9.81
28.00	9.90
28.25	9.99
28.50	10.08
28.75	10.16
29.00	10.25
29.25	10.34
29.50	10.43
29.75	10.52
30.00	10.61
30.25	10.69
30.50	10.78
30.75	10.87
31.00	10.96
31.25	11.05
31.50	11.14
31.75	11.23
32.00	11.31
32.25	11.40
32.50	11.49
32.75	11.58
33.00	11.67
33.25	11.76
33.50	11.84
33.75	11.93
34.00	12.02
34.25	12.11
34.50	12.20
34.75	12.29
35.00	12.37
35.25	12.46
35.50	12.55
35.75	12.64
36.00	12.73
36.25	12.82
36.50	12.90
36.75	12.99
37.00	13.08
37.25	13.17
37.50	13.26
37.75	13.35
38.00	13.44
38.25	13.52
38.50	13.61
38.75	13.70
39.00	13.79
39.25	13.88
39.50	13.97
39.75	14.05
40.00	14.14
40.25	14.23
40.50	14.32
40.75	14.41
41.00	14.50
41.25	14.58
41.50	14.67
41.75	14.76
42.00	14.85
42.25	14.94
42.50	15.03
42.75	15.11
43.00	15.20
43.25	15.29
43.50	15.38
43.75	15.47
44.00	15.56
44.25	15.64
44.50	15.73
44.75	15.82
45.00	15.91
45.25	16.00
45.50	16.09
45.75	16.18
46.00	16.26
46.25	16.35
46.50	16.44
46.75	16.53
47.00	16.62
47.25	16.71
47.50	16.79
47.75	16.88
48.00	16.97
48.25	17.06
48.50	17.15
48.75	17.24
49.00	17.32
49.25	17.41
49.50	17.50
49.75	17.59
50.00	17.68
50.25	17.77
50.50	17.85
50.75	17.94
51.00	18.03
51.25	18.12
51.50	18.21
51.75	18.30
52.00	18.38
52.25	18.47
52.50	18.56
52.75	18.65
53.00	18.74
53.25	18.83
53.50	18.92
53.75	19.00
54.00	19.09
54.25	19.18
54.50	19.27
54.75	19.36
55.00	19.45
55.25	19.53
55.50	19.62
55.75	19.71
56.00	19.80
56.25	19.89
56.50	19.98
56.75	20.06
57.00	20.15
57.25	20.24
57.50	20.33
57.75	20.42
58.00	20.51
58.25	20.59
58.50	20.68
58.75	20.77
59.00	20.86
59.25	20.95
59.50	21.04
59.75	21.12
60.00	21.21
60.25	21.30
60.50	21.39
60.75	21.48
61.00	21.57
61.25	21.66
61.50	21.74
61.75	21.83
62.00	21.92
62.25	22.01
62.50	22.10
62.75	22.19
63.00	22.27
63.25	22.36
63.50	22.45
63.75	22.54
64.00	22.63
64.25	22.72
64.50	22.80
64.75	22.89
65.00	22.98
65.25	23.07
65.50	23.16
65.75	23.25
66.00	23.33
66.25	23.42
66.50	23.51
66.75	23.60
67.00	23.69
67.25	23.78
67.50	23.86
67.75	23.95
68.00	24.04
68.25	24.13
68.50	24.22
68.75	24.31
69.00	24.40
69.25	24.48
69.50	24.57
69.75	24.66
70.00	24.75
70.25	24.84
70.50	24.93
70.75	25.01
71.00	25.10
71.25	25.19
71.50	25.28
71.75	25.37
72.00	25.46
72.25	25.54
72.50	25.63
72.75	25.72
73.00	25.81
73.25	25.90
73.50	25.99
73.75	26.07
74.00	26.16
74.25	26.25
74.50	26.34
74.75	26.43
75.00	26.52
75.25	26.60