Quadratic Mean Calculator

About Quadratic Mean (RMS)

The quadratic mean, also known as the root mean square (RMS), is calculated by: 1) squaring all numbers 2) finding their arithmetic mean 3) taking the square root of the result

Formula:

For numbers x₁, x₂, ..., xₙ:
RMS = √[(x₁² + x₂² + ... + xₙ²)/n]

Properties:

• Always greater than or equal to the arithmetic mean
• Particularly useful for varying quantities
• Gives greater weight to larger values
• Common in electrical engineering and statistics

Applications:

• AC voltage and current measurements
• Sound pressure level calculations
• Statistical dispersion analysis
• Signal processing

Example:

For AC voltage that varies sinusoidally between +120V and -120V, the RMS value is approximately 85V, which represents the equivalent DC voltage that would produce the same heating effect.