均方根计算器 — 公式

How to Calculate the Root Mean Square

Formula

RMS = sqrt( (v1^2 + v2^2 + ... + vn^2) / n )

1. Square each value 2. Compute the arithmetic mean of the squares 3. Take the square root

The RMS is always greater than or equal to the absolute value of the arithmetic mean. In electrical engineering, RMS voltage represents the equivalent DC voltage that delivers the same power.

计算示例

Compute the RMS of 3, 4, 5.

  1. Squares: 9, 16, 25
  2. Mean of squares = (9 + 16 + 25) / 3 = 50 / 3 ≈ 16.6667
  3. RMS = sqrt(16.6667) ≈ 4.0825
  4. Compare: Arithmetic mean = (3 + 4 + 5) / 3 = 4