How this calculation works
RMS is zero only when every input is zero. Opposite signs cannot cancel after squaring.
THE FORMULA
RMS = √[(a²+b²+c²)/3]A worked example
The mean of the squares of −3, 0, and 3 is 6, so the RMS is √6.
Good to know
The three observations have equal weight.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Measure the magnitude of signed values without cancellation between positive and negative observations.
The primary result is labeled “Root mean square”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The three observations have equal weight.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
The mean of the squares of −3, 0, and 3 is 6, so the RMS is √6.
Which rule does this calculator apply?
RMS = √[(a²+b²+c²)/3]