Parameters of Alternating Voltage

Calculator and formulas for calculating RMS and average values for AC voltage

Calculate Sine Parameters

AC Voltage Parameters

This function calculates the sine parameters for RMS voltage, peak voltage, peak-to-peak voltage, and rectified voltage from the specified voltage. RMS voltage is preset for input.

V
Results
RMS voltage:
Peak voltage:
Peak-to-peak voltage:
Rectified voltage:

Sine Parameters

Sine voltage parameters

Sine voltage parameters

Parameters
\(\displaystyle U_{eff}\) = RMS voltage [V]
\(\displaystyle U_s\) = Peak voltage [V]
\(\displaystyle U_{ss}\) = Peak-to-peak voltage [V]
\(\displaystyle U_g\) = Rectified voltage [V]
Basic formulas
\[U_{eff} = \frac{U_s}{\sqrt{2}}\]
\[U_s = U_{eff} \cdot \sqrt{2}\]
\[U_{ss} = 2 \cdot U_s\]

Conversion factors

Factors between the parameters

From RMS value to:
Peak voltage:
× √2 ≈ × 1.414
Peak-to-peak:
× 2√2 ≈ × 2.828
Rectified value:
÷ 1.11 ≈ × 0.9
To RMS value from:
Peak voltage:
÷ √2 ≈ × 0.707
Peak-to-peak:
÷ 2√2 ≈ × 0.354
Rectified value:
× 1.11

Example calculations

Practical calculation examples

Example 1: Mains voltage (230V RMS)

Given: Urms = 230V (European mains voltage)

\[U_s = 230V \times \sqrt{2} = 325.3V\]
\[U_{ss} = 2 \times 325.3V = 650.5V\]
\[U_g = \frac{230V}{1.11} = 207.2V\]
Typical household AC voltage
Example 2: Low voltage (12V RMS)

Given: Urms = 12V (low voltage)

\[U_s = 12V \times \sqrt{2} = 17.0V\]
\[U_{ss} = 2 \times 17.0V = 33.9V\]
\[U_g = \frac{12V}{1.11} = 10.8V\]
Typical low voltage application
Example 3: Signal voltage (1V peak)

Given: Us = 1V (peak voltage)

\[U_{eff} = \frac{1V}{\sqrt{2}} = 0.707V\]
\[U_{ss} = 2 \times 1V = 2.0V\]
\[U_g = \frac{0.707V}{1.11} = 0.637V\]
Typical signal processing level
Parameter ratios
Crest factor:
Us / Urms: √2 ≈ 1.414
Crest Factor
Form factor:
Urms / Ug: 1.11
Form Factor
Peak-to-peak:
Uss / Us: 2
Peak-to-Peak
Rectified value:
Ug / Us: 2/π ≈ 0.637
Average Value

Parameters and Formulas

AC Voltage Generation

When generating voltage in a rotating generator, a time-varying sinusoidal and periodically repeating AC voltage is produced.

Nominal value and RMS value

The RMS value of an AC voltage Urms is the value that produces the same heat in a resistor as an equal DC voltage. When "230 V" is mentioned for household AC voltage, it refers to the RMS value.

If the peak value is known, the RMS value can be calculated using the following formula:

RMS value formula
\[U_{eff} = \frac{U_s}{\sqrt{2}}\]

The RMS value corresponds to the Root Mean Square (RMS).

Maximum value, peak value, amplitude

The peak value is the highest voltage reached in a sinusoidal waveform. If the RMS value is given, the peak value can be calculated as follows:

Peak value formula
\[U_s = U_{eff} \cdot \sqrt{2}\]

The peak value is √2 times greater than the RMS value.

Peak-to-peak voltage

The peak-to-peak voltage Uss is the difference between the positive and negative peak values, i.e., twice the peak value.

Peak-to-peak formula
\[U_{ss} = 2 \cdot U_s\]

The peak-to-peak voltage covers the entire voltage range.

Rectified value

The rectified value is the arithmetic mean of the rectified AC voltage. For pure sine voltages, it can be calculated simply by dividing the RMS voltage by 1.111.

Rectified value formula
\[U_g = \frac{U_{eff}}{1.11}\]

The rectified value corresponds to the arithmetic mean after full-wave rectification.

Important factors

Form factor

The form factor is the ratio of the RMS value to the rectified value. For sinusoidal AC voltage, it is 1.111 (exactly π/√8).

\[F = \frac{U_{eff}}{U_g} = 1.111\]
Crest factor

The crest factor is the ratio of the peak value to the RMS value. For a sine wave, the crest factor is 1.414 (exactly √2).

\[C = \frac{U_s}{U_{eff}} = \sqrt{2}\]

Practical applications

Electrical engineering
  • Mains voltage specifications
  • Transformer design
  • Insulation coordination
  • Power calculations
Measurement technology
  • Oscilloscope measurements
  • Multimeter displays
  • Signal analysis
  • Calibration
Electronics
  • Amplifier drive
  • ADC range setting
  • Voltage regulator design
  • EMC considerations

Design notes

Practical considerations
  • Voltage withstand: Components must be rated for peak voltage
  • Power calculation: Use RMS values for thermal calculations
  • Measuring instruments: Distinguish between true-RMS and average-detecting multimeters
  • Safety: Consider peak voltages for insulation distances
  • Transformers: Core design is based on RMS values
  • Capacitors: Voltage rating must be at least for peak voltage

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AC functions

Alternating voltage values  •  Alternating voltage and time  •  Frequency and wavelength  •  Alternating voltage value and angle  •  Frequency and periodic time  •  RMS value of a sinusoidal oscillation  •  RMS value of a sinusoidal oscillation with offset  •  RMS value of a sine pulse (half-wave rectification)  •  RMS value of a sine pulse (full-wave rectification)  •  RMS value of a square wave voltage  •  RMS value of a square pulse  •  RMS value of a triangle voltage  •  RMS value of a triangular pulse  •  RMS value of a sawtooth voltage  •  RMS value of a sawtooth pulse  •