Quick answer
For a sine wave, V_rms = V_peak ÷ √2 and V_pp = 2 V_peak. A 120 V RMS supply has a peak of 169.71 V and a peak-to-peak value of 339.41 V.
Choose which voltage you know and enter it. The calculator returns RMS, peak and peak-to-peak voltages.
Related tools: Voltage Divider Calculator: Output voltage of a two-resistor divider. RLC Impedance Calculator: Impedance and phase angle of a series RLC circuit. Parallel Plate Capacitor Calculator: Capacitance of two parallel plates.
How to use the RMS Voltage Calculator
- Choose i know the: RMS, Peak and Peak-to-peak.
- Enter voltage (V) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| I know the | Choose one: RMS; Peak; Peak-to-peak | Starts at RMS |
| Voltage | A number, in V | > 0 |
Formula and method
Formula
V_rms = V_peak ÷ √2; V_pp = 2 V_peak
IEEE-754 double precision; shown to the decimals indicated.
Valid for sinusoidal waveforms only.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: I know the = RMS; Voltage = 120.
| Result | Value |
|---|---|
| RMS voltage | 120 V |
| Peak voltage | 169.7056 V |
| Peak-to-peak voltage | 339.4113 V |
Example 2
Inputs: I know the = Peak; Voltage = 170.
| Result | Value |
|---|---|
| RMS voltage | 120.2082 V |
| Peak voltage | 170 V |
| Peak-to-peak voltage | 340 V |
The first line is the headline result (rMS voltage). Below it the rMS Voltage Calculator lists peak voltage and peak-to-peak voltage, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Why RMS
RMS is the equivalent DC voltage that would deliver the same heating power. Mains voltage is quoted as RMS, so a '120 V' outlet actually swings between about +170 V and −170 V.
Waveforms
The √2 ratio applies only to sine waves. A square wave has V_rms equal to its peak, and a triangle wave a ratio of √3. Multimeters that are not 'true RMS' give errors on non-sinusoidal signals.
How the result changes with voltage
Holding every other input at the first worked example, this table changes only voltage. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Voltage | RMS voltage | Peak voltage | Peak-to-peak voltage |
|---|---|---|---|
| 60 | 60 V | 84.8528 V | 169.7056 V |
| 120 | 120 V | 169.7056 V | 339.4113 V |
| 240 | 240 V | 339.4113 V | 678.8225 V |
| 480 | 480 V | 678.8225 V | 1,357.645 V |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Voltage: entering "0" shows "Voltage must be greater than 0." beside that field and no result.
Choosing between the RMS Voltage Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Voltage Divider Calculator](/engineering/voltage-divider-calculator/) | input voltage, r1 and r2 | Output voltage |
| [RLC Impedance Calculator](/engineering/rlc-impedance-calculator/) | resistance, inductance and capacitance | Impedance |
| [Parallel Plate Capacitor Calculator](/engineering/parallel-plate-capacitance-calculator/) | plate area, plate separation and relative permittivity εr | Capacitance |
| [Current Divider Calculator](/engineering/current-divider-calculator/) | total current, r1 and r2 | Current through R1 |
| [Inductive Reactance Calculator](/engineering/inductor-reactance-calculator/) | inductance and frequency | Inductive reactance |
Background: electrical circuits
Ohm's law links voltage, current and resistance: V = I × R, so I = V ÷ R and R = V ÷ I. Power is P = V × I, which also equals I² × R and V² ÷ R.
These relations hold for ohmic components, where resistance is constant. Diodes and transistors are non-linear, and in AC circuits with reactive parts impedance (Z) takes the place of resistance. Check component ratings and local electrical code before relying on any calculation.
Assumptions and limitations
- Other waveforms have different ratios
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for voltage to confirm this.
Frequently asked questions
What is the peak of 230 V mains?
A 230 V RMS supply peaks at 230 × √2 ≈ 325 V.
Is RMS the average?
No, the average of a sine wave over a cycle is zero.
What is peak-to-peak?
The difference between the maximum and minimum.
What does the RMS Voltage Calculator calculate?
Convert between RMS, peak and peak-to-peak voltage of a sine wave. It returns RMS voltage, Peak voltage and Peak-to-peak voltage.
What formula does the RMS Voltage Calculator use?
V_rms = V_peak ÷ √2; V_pp = 2 V_peak. Valid for sinusoidal waveforms only.
What do I need to enter in the rMS Voltage Calculator?
You enter I know the and Voltage (V).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Other waveforms have different ratios.
What does the “I know the” option change?
It sets how the rMS Voltage is worked out. The choices are RMS, Peak and Peak-to-peak.
What is an example of a rMS Voltage result?
With i know the RMS and voltage 120, the rMS voltage is 120 V.
Can I rely on this calculator for a decision?
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them. For this calculator in particular: Other waveforms have different ratios.
Related calculators
- Voltage Divider Calculator — Output voltage of a two-resistor divider.
- RLC Impedance Calculator — Impedance and phase angle of a series RLC circuit.
- Parallel Plate Capacitor Calculator — Capacitance of two parallel plates.
- Current Divider Calculator — Current through each of two parallel resistors.
- Inductive Reactance Calculator — Reactance of an inductor at a frequency.
- RC Circuit Calculator — Time constant, cutoff frequency and charge level of an RC circuit.
Sources
- OpenStax, University Physics Volume 2 (Rice University): electricity, circuits and thermodynamics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.