Math

Root Mean Square Calculator

RMS value of any dataset, waveform or error list.

Enter your values

Enter the values you are working with.

Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.

Results
Root mean square
4.24264
Mean of squares
18
Peak magnitude
6
Crest factor
1.4142
Count
5
Sine-wave equivalent peak
6

Quick answer

RMS is the square root of the mean of the squares — the effective magnitude of a set of values regardless of sign, used for AC voltage and error metrics.

RMS = √(Σxᵢ² ÷ n)

At a glance

What it doesRMS value of any dataset, waveform or error list.
CategoryMath
Inputs neededValues
Main outputRoot mean square
FormulaRMS = √(Σxᵢ² ÷ n)
CostFree — no sign-up, no download

How to use the Root Mean Square Calculator

  1. 1Enter your values — signs are fine, they get squared away.
  2. 2Read the RMS as the effective magnitude.
  3. 3Use the crest factor to see how spiky the data is compared with a pure sine wave (1.414).

Inputs explained

Values
Enter the values you are working with.

Worked example

Using the values the calculator loads with:

Inputs

  • Values3, -4, 5, -6, 2

Results

  • Root mean square4.24264
  • Mean of squares18
  • Peak magnitude6
  • Crest factor1.4142
  • Count5
  • Sine-wave equivalent peak6

Frequently asked questions

Is RMS the same as standard deviation?

Only when the mean is zero. Standard deviation is the RMS of the deviations from the mean.

Why is mains voltage quoted as RMS?

Because RMS voltage delivers the same heating power as an equal DC voltage, which is the number that matters for equipment.

What do I need to enter into the Root Mean Square Calculator?

Just 1 value: values. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.

How does the Root Mean Square Calculator work out the answer?

RMS is the square root of the mean of the squares — the effective magnitude of a set of values regardless of sign, used for AC voltage and error metrics. It applies the formula RMS = √(Σxᵢ² ÷ n) and shows the working so you can check each step by hand.

Is the Root Mean Square Calculator free, and do I need an account?

It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.

Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.