How it works
RMS = √[Σ(x²)/n]. Scale by the largest absolute sample first to avoid overflow in the sum of squares.
Input definitions
- Numeric samples
- Plain text; maximum 200,000 characters.
A worked example
- Numeric samples
- 3, 4
Assumptions & limits
Discrete equally weighted samples; do not subtract the mean. RMS includes any DC offset and differs from standard deviation.
Sources & review
Maintained by AnsRio. Methods and examples use automated checks; this does not imply independent professional certification.
Method updated 2026-10-17. Content checked against the stated method and examples. Our verification approach.
Common questions
Is RMS the same as standard deviation?
No. RMS squares the raw values; standard deviation measures deviations from their mean. RMS includes a constant DC offset and equals population standard deviation only when the mean is zero.
Why can statistical results differ between tools?
Denominator, interpolation and boundary conventions can differ. Use the method and assumptions on this page to compare the same definition; displayed decimals may also be rounded.
How does the Root mean square (RMS) tool work?
RMS = √[Σ(x²)/n]. Scale by the largest absolute sample first to avoid overflow in the sum of squares.
What are the assumptions and limits of Root mean square (RMS)?
Discrete equally weighted samples; do not subtract the mean. RMS includes any DC offset and differs from standard deviation.