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 **x _{1}, x_{2}, x_{3},** … 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

**x _{RMS} = √(1/n)(x_{1}^{2} + x_{2}^{2} + … + x_{n}^{2})**

## Applications of RMS

**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.

**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.

**Mechanical Engineering:****Stress Analysis:**RMS values can be used to assess the average stress experienced by a material under cyclic loading conditions.