Calculating your root mean square (rms) is straightforward once you know the Root Mean Square formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Root Mean Square Calculator.
What is Root Mean Square?
The Root Mean Square calculation tells you your root mean square (rms) from a few simple inputs. The figure you are solving for here is the root mean square (rms).
The Root Mean Square formula
The core formula is:
Root mean square (RMS) = √((Value 1 ^ 2 + Value 2 ^ 2 + Value 3 ^ 2) ÷ 3)Here is what each input means:
- Value 1 — a number. Example: 3.
- Value 2 — a number. Example: 4.
- Value 3 — a number. Example: 5.
How to calculate it step by step
- Write down the value 1 (for example, 3).
- Write down the value 2 (for example, 4).
- Write down the value 3 (for example, 5).
- Apply the formula above to get your root mean square (rms).
- Double-check the result with the Root Mean Square Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Value 1 | 3 |
| Value 2 | 4 |
| Value 3 | 5 |
| Root mean square (RMS) | 4.0825 |
With value 1 of 3, value 2 of 4 and value 3 of 5, the root mean square (rms) works out to 4.0825.
Example 2
With value 1 of 6, value 2 of 4 and value 3 of 5, the root mean square (rms) works out to 5.0662.
| Result | Value |
|---|---|
| Root mean square (RMS) | 5.0662 |
Example 3
With value 1 of 1.5, value 2 of 4 and value 3 of 5, the root mean square (rms) works out to 3.7969.
| Result | Value |
|---|---|
| Root mean square (RMS) | 3.7969 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Root Mean Square Calculator does it instantly, for free, with the formula and a worked example built in.
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