Last updated October 5, 2026 · Report an error
Root mean square (RMS) is a way of averaging a set of numbers that accounts for both positive and negative values equally, and gives more weight to larger-magnitude values than a simple average would. This tool calculates the RMS of any list of numbers.
How it works
Each number in the list is squared, the squares are averaged, and then the square root of that average is taken — giving the root mean square.
- Enter numbers (comma or space separated).
- Click Calculate to see your results.
Examples
A simple set of numbers
For 3, 4, 5, 6: squares are 9, 16, 25, 36, averaging to 21.5, and the square root of 21.5 is approximately 4.637.
Who should use it
- Calculating RMS voltage or current in electrical engineering.
- Measuring the typical magnitude of a signal or error set in statistics.
Industry applications
- Electrical engineering
- Signal processing
- Statistics and data analysis
Advantages
- Accepts any list of numbers, including negative values.
- Shows the full squaring, averaging, and square-root steps.
Limitations
- Not the appropriate statistic when you specifically need a plain arithmetic mean.
Common mistakes to avoid
- Using a plain average when RMS is actually required, especially for AC electrical quantities where the two give meaningfully different answers.
Best practices
- Use RMS whenever the sign of individual values doesn't matter but their magnitude does — such as measuring signal or error magnitude.
Tips
- RMS is always greater than or equal to the plain arithmetic mean of the absolute values, since squaring emphasizes larger values more heavily.
Frequently asked questions
Because RMS squares each value first, larger-magnitude values (whether positive or negative) have a bigger influence on the result than they would in a plain average — and negative values contribute the same as their positive counterparts, since squaring removes the sign.
RMS is standard in electrical engineering for describing AC voltage/current (since it represents the equivalent steady DC value for power purposes), and in statistics/signal processing for measuring the typical magnitude of a varying quantity.