RMS Calculator
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 + x₂² + ... + xₙ²) / n]
AC Signals: RMS = Peak / √2 ≈ Peak × 0.707
Quick Facts
RMS vs Mean: RMS is always ≥ arithmetic mean
AC Power: P = VRMS × IRMS (for resistive loads)
Conversion: RMS = Peak / √2 ≈ Peak × 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 ≥ Arithmetic mean (equality only if all values equal)
Applications
Electrical Engineering:
- AC voltage and current measurements
- Power calculations (P = VRMS × 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 × √2
- Peak-to-Peak = 2 × Peak
- Average = (2 × Peak) / π
Factors:
- Form Factor = RMS / Average
- Crest Factor = Peak / RMS
- For sine wave: FF ≈ 1.11
- For sine wave: CF ≈ 1.414 (√2)
Power:
- P = VRMS × IRMS (resistive)
- P = VRMS × IRMS × cos(φ) (reactive)
- Energy = Power × Time
- 1 kWh = 3.6 MJ
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