Root Mean Square Calculator
This root mean square calculator finds the RMS of any list of numbers. Example: for 2, 4, 4, 4, 5, 5, 7, 9 the squares add up to 232, the mean square is 29 and the RMS is 5.38516.
Source: Wikipedia – Root mean square. Updated: .
How it is calculated
The root mean square is the square root of the mean of the squares of a set of numbers. It is abbreviated RMS; in electrical engineering it is called the effective value.
Formula and steps
The formula is RMS = √((x₁² + x₂² + … + xₙ²) / n). Square each value, add the squares, divide by the count n and finally take the square root. Because of the squaring, signs do not matter and large values count more than in an ordinary average.
Worked example
The numbers 2, 4, 4, 4, 5, 5, 7, 9 have squares 4, 16, 16, 16, 25, 25, 49 and 81 with a sum of 232. Divided by n = 8 that gives 29, whose root is ≈ 5.38516. The arithmetic mean of 5 lies below it. As a check, RMS² = mean² + variance: 25 + 4 = 29.
- For a sinusoidal voltage the effective value is the peak value divided by √2, about 0.7071 times the peak.
- The RMS equals the arithmetic mean when all values are equal, and is larger otherwise.
Frequently asked questions
How do you calculate the root mean square?
Square all values, add the squares, divide by the count and take the square root. For 2, 4, 4, 4, 5, 5, 7, 9 that is √(232 / 8) = √29 ≈ 5.38516.
How does it differ from the arithmetic mean?
The arithmetic mean adds the values directly. The RMS squares first and so weights large values more; 5.38516 instead of 5 in the example.
What is RMS used for?
For the effective value of alternating current and voltage, for error measures such as RMSE, and for vibration intensity. It captures the typical magnitude even when values change sign.
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