# RMS Average Calculator and Formula

The Root mean square (RMS) average of a set of values is the square root of the arithmetic mean of the squares of the values.

Use the calculator below to calculate the RMS average.

Enter the numbers x1, x2, x3, … each separated by a comma.

## Example Calculation

The RMS average of two numbers 1 and 4 is 2.915

## RMS Average Formula

The formula for this is

xRMS = √(1/n)(x12 + x22 + … + xn2)

## Applications of RMS

1. Electrical Engineering:
• AC Voltage and Current: The RMS value is used to describe the effective voltage or current of an AC waveform. For example, the RMS value of a sinusoidal AC waveform is approximately 0.707 times its peak value.
• Power Calculation: The power consumed by a resistive load with an AC supply can be calculated using the RMS values of voltage and current.
2. Signal Processing:
• Audio Engineering: RMS values are used to measure the power of audio signals, giving an indication of perceived loudness.
• Vibration Analysis: RMS values are used to quantify the average level of vibration over time.
3. Mechanical Engineering:
• Stress Analysis: RMS values can be used to assess the average stress experienced by a material under cyclic loading conditions.