RMS Calculator

Root Mean Square Calculator with Statistics

Calculate Root Mean Square (RMS) for datasets, AC voltage, and current with comprehensive statistics and analysis.

Calculator Mode

Enter numbers to calculate RMS and statistics (max 10,000 values)

What is RMS?

Root Mean Square (RMS) is the square root of the arithmetic mean of the squares of values.

Formula: RMS = √[(x₁² + xβ‚‚Β² + ... + xβ‚™Β²) / n]

AC Signals: RMS = Peak / √2 β‰ˆ Peak Γ— 0.707

Quick Facts

RMS vs Mean: RMS is always β‰₯ arithmetic mean

AC Power: P = VRMS Γ— IRMS (for resistive loads)

Conversion: RMS = Peak / √2 β‰ˆ Peak Γ— 0.707

Standard: 120V AC (US) means 120V RMS

Understanding RMS

RMS (Root Mean Square) is a statistical measure that represents the magnitude of a varying quantity. It's especially important in AC circuits and signal processing.

Key Properties:

  • RMS value is always positive
  • For AC sine waves: RMS = Peak / √2
  • RMS represents equivalent DC value for power
  • Used to calculate average power in AC circuits
  • RMS β‰₯ Arithmetic mean (equality only if all values equal)

Applications

Electrical Engineering:

  • AC voltage and current measurements
  • Power calculations (P = VRMS Γ— IRMS)
  • Effective voltage ratings
  • Signal analysis and processing

Other Fields:

  • Statistics and data analysis
  • Audio signal processing
  • Vibration analysis
  • Quality control measurements

AC Signal Relationships

Voltage/Current:

  • RMS = Peak / √2
  • Peak = RMS Γ— √2
  • Peak-to-Peak = 2 Γ— Peak
  • Average = (2 Γ— Peak) / Ο€

Factors:

  • Form Factor = RMS / Average
  • Crest Factor = Peak / RMS
  • For sine wave: FF β‰ˆ 1.11
  • For sine wave: CF β‰ˆ 1.414 (√2)

Power:

  • P = VRMS Γ— IRMS (resistive)
  • P = VRMS Γ— IRMS Γ— cos(Ο†) (reactive)
  • Energy = Power Γ— Time
  • 1 kWh = 3.6 MJ