Quadratic Mean Calculator (Root Mean Square)
This calculator finds the quadratic mean, also known as the root mean square (RMS), of a set of numbers. It’s commonly used in physics, engineering, and statistics to measure the magnitude of varying quantities, especially when values can be both positive and negative.
Calculate the Root Mean Square of Any Data Set
Quadratic Mean (RMS) Formula
$$\text{Quadratic Mean} = \sqrt{\frac{x_1^2 + x_2^2 + \cdots + x_n^2}{n}}$$
Explanation:
To calculate the quadratic mean, square each value, find the average of those squares, then take the square root of the result. It always returns a non-negative value.
Quadratic Mean – Calculation Example
Values: 3, 4, 5
- Square each value → 9, 16, 25
- Average of squares → (9 + 16 + 25) / 3 = 50 / 3 ≈ 16.67
- Square root → √16.67 ≈ 4.08
Result: Quadratic Mean ≈ 4.08
Quadratic mean is most useful when measuring quantities with both direction and magnitude, such as AC voltage, velocity, or data dispersion. Unlike the arithmetic mean, it gives more weight to larger values. It is also used in machine learning and error analysis.