Root Mean Square Calculator
Calculate the RMS magnitude of a list, including positive and negative values.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Numbers | Separate values with commas, spaces or line breaks. Use dots for decimals; at most 10,000 values. |
Understanding your result
These are descriptive results for the observations you entered, not proof of causation, significance or a particular population distribution.
Common mistakes
- Confusing a descriptive statistic with a population inference or ignoring repeated values.
Check your calculation
- Try a small hand-checkable list; confirm the stated quartile/rank/denominator convention before comparing with another application.
Calculation checks, sources and review limits
What is the RMS magnitude of these values?
Calculate the RMS magnitude of a list, including positive and negative values.
Common uses
- Calculate the RMS magnitude of a list, including positive and negative values.
How it works
sqrt(sum(x²)/n) Lists accept commas, semicolons, spaces or line breaks as separators; use a dot for decimals. At most 10,000 observations are supported. Calculations use floating-point arithmetic; displayed numeric results have up to 12 significant digits.
Worked example
Enter Numbers: 3, 4. The result is Rms: 3.5355339059327378.
FAQ
What is the RMS magnitude of these values?
sqrt(sum(x²)/n) Lists accept commas, semicolons, spaces or line breaks as separators; use a dot for decimals. At most 10,000 observations are supported. Calculations use floating-point arithmetic; displayed numeric results have up to 12 significant digits.
What assumptions and limits apply?
RMS is distinct from sample standard deviation; use scaled accumulation to avoid overflow.