About RMS Voltage Calculator
This calculator allows you to easily convert between RMS voltage, peak voltage, and peak-to-peak
voltage. These conversions are commonly used in AC circuit analysis and signal processing where voltage waveforms are sinusoidal. Simply select the type of conversion, input the known value, and click "Calculate" to obtain the result.
Understanding the Relationships
Voltage conversions between RMS (Root Mean Square), peak, and peak-to-peak values are based on the
properties of a sinusoidal waveform:
-
RMS Voltage: Represents the effective value of an AC voltage, equivalent to the DC
voltage that would produce the same power in a resistive load.
-
Peak Voltage: The maximum voltage reached by the waveform above or below the zero
point.
-
Peak-to-Peak Voltage: The total voltage difference between the positive and
negative peaks of the waveform.
Formulas
The following formulas define the relationships between these voltages:
-
RMS Voltage to Peak Voltage:
\[
\text{Peak Voltage} = \text{RMS Voltage} \times \sqrt{2}
\]
-
Peak Voltage to RMS Voltage:
\[
\text{RMS Voltage} = \frac{\text{Peak Voltage}}{\sqrt{2}}
\]
-
Peak Voltage to Peak-to-Peak Voltage:
\[
\text{Peak-to-Peak Voltage} = 2 \times \text{Peak Voltage}
\]
Example Calculations
Here are example scenarios demonstrating these conversions:
1. Converting Peak Voltage to RMS Voltage
If the peak voltage is \( 10 \, \text{V} \):
\[
\text{RMS Voltage} = \frac{\text{Peak Voltage}}{\sqrt{2}} = \frac{10 \, \text{V}}{\sqrt{2}} \approx 7.07
\, \text{V}
\]
2. Converting RMS Voltage to Peak Voltage
If the RMS voltage is \( 7.07 \, \text{V} \):
\[
\text{Peak Voltage} = \text{RMS Voltage} \times \sqrt{2} = 7.07 \, \text{V} \times \sqrt{2} \approx 10
\, \text{V}
\]
3. Converting Peak Voltage to Peak-to-Peak Voltage
If the peak voltage is \( 10 \, \text{V} \):
\[
\text{Peak-to-Peak Voltage} = 2 \times \text{Peak Voltage} = 2 \times 10 \, \text{V} = 20 \, \text{V}
\]
Tips for Accurate Results
- Ensure the waveform is purely sinusoidal when using these formulas. For other waveform types,
different coefficients may apply.
- Use high-precision instruments to measure peak or RMS voltages when performing real-world
calculations.