RMS Voltage Calculator
Calculate Root Mean Square (RMS) voltage for various waveforms with DC offset support
Calculate RMS Voltage
Sinusoidal waveform - most common AC waveform
The reference voltage measurement for the waveform
The peak voltage of the waveform
DC component added to the AC waveform (can be negative)
RMS Voltage Results
Formula used: VRMS = √(VAC_RMS² + V0²)
AC RMS: 0.000V, DC Offset: 0.000V
Meaning: This AC voltage has the same power as 0.000V DC
Voltage Analysis
Example Calculation
Household AC Power Example
Waveform: Sine wave (typical AC power)
Peak voltage: 170V (US household)
DC offset: 0V (pure AC)
Characteristic type: Peak voltage
Calculation
For sine wave: VRMS = Vpeak / √2
VRMS = 170V / √2 = 170V / 1.414
VRMS = 120.2V
This matches the standard US household voltage rating of 120V RMS.
RMS Formulas by Waveform
Sine Wave
VRMS = Vp / √2
Most common AC waveform
Square Wave
VRMS = Vp
Digital signals
Triangle Wave
VRMS = Vp / √3
Audio synthesis
Sawtooth Wave
VRMS = Vp / √3
Oscilloscope time base
Half-Wave Rectified
VRMS = Vp / 2
Simple rectifier
Full-Wave Rectified
VRMS = Vp / √2
Bridge rectifier
RMS Tips
RMS represents equivalent DC power dissipation
DC offset adds to RMS using Pythagorean theorem
Square waves have highest RMS for given peak
Triangle/sawtooth waves have lowest RMS
RMS is always ≥ average for AC signals
Understanding RMS Voltage
What is RMS Voltage?
Root Mean Square (RMS) voltage is the effective value of an alternating voltage. It represents the equivalent DC voltage that would dissipate the same amount of power in a resistive load as the AC voltage.
Why is RMS Important?
- •Determines actual power dissipation in AC circuits
- •Standard for rating AC voltage systems
- •Essential for power calculations and safety
- •Enables comparison between different waveforms
Mathematical Definition
VRMS = √(1/T ∫₀ᵀ v²(t) dt)
For continuous periodic functions
With DC Offset
Vtotal = √(VAC_RMS² + V₀²)
Pythagorean combination
Note: RMS is also called "quadratic mean" and represents the square root of the mean of the squares of the values.