# Vrms to Vpp Calculator

This calculator converts V RMS (Root-mean-square) to V peak-to-peak.

## Formula

Vpp = (2√2)*VRMS

To find the peak to peak voltage multiply the RMS value by 2√2 or 2.828.

This formula applies for a sine wave.

## Background

### What is Volts RMS?

To understand this, let’s start with a basic definition. In electronics, the Root-mean-square current value is defined as the “value of direct current that dissipates the same amount of power in a resistor.” 

For a DC current I, through a resistor R, the power is given by

P = I2R

However, if the current I varies with time it’s referred to as an alternating current. This is represented as I(t). The average power can be written as

Pavg = (I(t)2R)avg

Since the resistance value R does not change with time, this can simply be written as

Pavg = (I(t)2)avg*R

I(t) can be represented as a sequence of numbers that represent current measurements in time I1, I2, … In. The average of the sum of squares is

(I(t)2)avg = IRMS = √(1/n)(I12 +I22 + … + In2)

where IRMS is the RMS value of current

IRMS = √(1/n)(I12 +I22 + … + In2)

The RMS value of the corresponding alternating voltage that causes this time varying current is

VRMS = IRMS * R

It is similarly defined as

VRMS = √(1/n)(V12 +V22 + … + Vn2)

where V1, V2, … Vn are the corresponding values of voltage.

### How to calculate VRMS?

The RMS voltage depends on the waveform type (e.g. sine wave, square wave, etc.) and can be calculated from the peak or average voltage. Alternatively, the data sequence associated with any waveform can also be used to compute VRMS.

### What is the difference between RMS and Peak to peak voltage?

Peak to peak voltage is the difference between the maximum and minimum voltage levels of a waveform. The picture below shows a sine wave, with max value = a and min value = -a.

In this case,

Vpp = a-(-a) = 2a 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 the peak voltage important?

Peak voltage provides the maximum value of the voltage that varies with time. Many devices are specified to have maximum and minimum voltage levels and it’s important that the peak voltage falls within these limits.

### Why is the RMS voltage important?

RMS voltage of an AC waveform is used to calculate the power dissipation across a resistive circuit element or a load. (In this case, it’s not the peak or the average voltage).

### Does RMS or Peak Voltage change with Frequency?

Neither RMS nor Peak Voltage should change with frequency. However if a sine wave measurement is made on an oscilloscope then care must be taken that the bandwidth of the oscilloscope exceeds that of the sine wave by at least a factor of 2. Using the Nyquist rate calculator.

### What is the peak to peak value for 120 V?

The peak to peak voltage for 120 V AC is 340 V. The peak voltage is 170 V.

### What is the peak to peak value for 240 V?

The peak to peak voltage for 240 V AC is 680 V. The peak voltage is 340 V.