Root Mean Square Calculator

Calculate the root mean square of a set of values.

About Root Mean Square Calculator

The root mean square weights larger values more heavily because they are squared first. It is the measure that preserves energy content, which is why AC voltages and currents are quoted as RMS. RMS equals the arithmetic mean only when all values are identical; the gap grows with variability.

Formula

Root Mean Square

RMS = √(Σxᵢ² ÷ n)

RMS: Quadratic mean, always at least as large as the arithmetic mean

Worked example

With the default values below, Root Mean Square Calculator returns Root Mean Square of 4.636809. Change any input above and every figure here is recalculated in your browser.

Inputs used

Value 1: 3
Value 2: 4
Value 3: 5
Value 4: 6

Results

Root Mean Square: 4.636809
Arithmetic Mean: 4.500000
Sum of Squares: 86.0000
Mean Square: 21.500000
Ratio of Peak to RMS: 1.29399

Step by step

1Values used
2Root Mean Square
3Root Mean Square= 4.636809
4Arithmetic Mean= 4.500000
5Sum of Squares= 86.0000
6Mean Square= 21.500000
7Ratio of Peak to RMS= 1.29399

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Root Mean Square calculated?

RMS = √(Σxᵢ² ÷ n) The root mean square weights larger values more heavily because they are squared first. It is the measure that preserves energy content, which is why AC voltages and currents are quoted as RMS.

Why does Root Mean Square matter?

RMS equals the arithmetic mean only when all values are identical; the gap grows with variability.

What values do I need to enter?

This calculator takes 4 inputs: Value 1, Value 2, Value 3, Value 4. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.