Statistics
Root Mean Square Calculator
Use this root mean square calculator when squared magnitude matters more than signed average.
Separate values with commas, spaces, or semicolons.
Try an example
Result
Root mean square
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- Count
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- Mean
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- Minimum
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- Maximum
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- Range
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- Sum of squares
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More details (2 more)
- Mean square
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- Root mean square
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the root mean square calculator solves
Use this root mean square calculator when squared The length or size of a vector, ignoring which way it points. matters more than signed average.
Formula
How to use it
- Enter a dataset as numbers separated by commas, spaces, or semicolons.
- Choose A smaller group taken from a population, used to estimate facts about the whole group. or Every member of the group you actually care about, not just the ones measured. when the statistic uses a different The bottom number of a fraction; it says how many equal parts make one whole..
- Use the sorted data, count, mean, and work lines to check the result.
How to read the answer
RMS keeps signs from canceling out because it squares each value first, then takes the square root.
Common mistakes and edge cases
- Do not use RMS when you want an ordinary signed average.
- Square each value before adding.
- RMS is always nonnegative.
Worked examples
Mixed signs
Root mean square
Root mean square = 4.6368
All positive
Root mean square
Root mean square = 5.4772
Frequently asked questions
Why is RMS useful?+
It measures typical magnitude when positive and negative signs should not cancel, such as with oscillating values.
Is RMS always larger than the arithmetic mean?+
For nonnegative values, RMS is at least as large as the arithmetic mean. With mixed signs, compare it to magnitude rather than signed average.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- May 15, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: May 15, 2026