<Dd> R M S (x (n)) = 1 N ∑ n x 2 (n) = 1 N 2 ∑ m X (m) 2 = ∑ m X (m) N 2 . (\ displaystyle \ mathrm (RMS) \ (x (n) \) = (\ sqrt ((\ frac (1) (N)) \ sum _ (n) (x ^ (2) (n)))) = (\ sqrt ((\ frac (1) (N ^ (2))) \ sum _ (m) ((\ bigl) X (m) (\ bigr)) ^ (2))) = (\ sqrt (\ sum _ (m) (\ left (\ frac (X (m)) (N)) \ right ^ (2)))).) </Dd> <P> If x _̄ (\ displaystyle (\ bar (x))) is the arithmetic mean and σ x (\ displaystyle \ sigma _ (x)) is the standard deviation of a population or a waveform then: </P> <Dl> <Dd> x r m s 2 = x _̄ 2 + σ x 2 = x 2 _̄ . (\ displaystyle x_ (\ mathrm (rms)) ^ (2) = (\ overline (x)) ^ (2) + \ sigma _ (x) ^ (2) = (\ overline (x ^ (2))).) </Dd> </Dl> <Dd> x r m s 2 = x _̄ 2 + σ x 2 = x 2 _̄ . (\ displaystyle x_ (\ mathrm (rms)) ^ (2) = (\ overline (x)) ^ (2) + \ sigma _ (x) ^ (2) = (\ overline (x ^ (2))).) </Dd>

How to find rms value of sine wave