Quadratic Mean Calculator (RMS)
Calculate the quadratic mean or Root Mean Square (RMS), essential for electrical engineering, signal processing, and physics.
Enter Values
Example Data Sets:
Quadratic Mean (RMS)
5.196152
Arithmetic Mean
5.000000
Standard Deviation
1.414214
Sum of Squares
135.0000
Mean of Squares
27.000000
RMS Identity Verification:
RMS^2 = Mean^2 + Variance
sqrt(mean^2 + variance) = 5.196152
RMS = 5.196152
Number of Values
5
What is Quadratic Mean (RMS)?
The quadratic mean, also known as Root Mean Square (RMS), is calculated by taking the square root of the mean of squared values. It is especially useful for quantities that can be positive or negative (like AC voltage or velocity errors) because squaring eliminates negative signs. RMS is fundamental in electrical engineering for measuring AC voltage and current.
Formula
RMS = sqrt[(x1^2 + x2^2 + ... + xn^2) / n]
For sinusoidal AC: RMS = Peak / sqrt(2) ≈ 0.707 × Peak