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RMS Calculator

Convert peak AC voltage or current to RMS in one step. This calculator uses the sine-wave formula and explains why RMS matters for AC power measurement.

Result

120.21

A sine wave with a 170 peak has an RMS value of 120.21

Quick Answer

An RMS calculator divides the peak value of a sine-wave AC signal by the square root of 2 (approximately 1.4142) to give the root mean square value. For a 170 V peak AC signal, RMS = 170 ÷ √2 = 120.2 V, which matches the rated 120 V supply. RMS is the value that does equivalent work to the same DC voltage or current.

Why RMS Exists and What This Tool Calculates For You

A simple arithmetic average of a sine-wave AC signal equals zero over a full cycle because the positive and negative halves cancel. This makes the average useless for measuring the heating or working power of an AC signal. Root mean square solves this by squaring the instantaneous values first, taking the average of the squares over one full cycle, and then taking the square root of that average. For a pure sine wave, this process yields a value equal to the peak divided by √2. That value is what your electricity meter, multimeter, and appliance nameplate all use. This calculator computes the sine-wave RMS only.

The RMS Formula for a Pure Sine-Wave AC Signal Used

RMS = peak value ÷ √2 In decimal form: RMS ≈ peak value × 0.7071

  • RMS = peak value ÷ √2
  • In decimal form: RMS ≈ peak value × 0.7071
  • Peak value = RMS × √2 ≈ RMS × 1.4142

How To Apply the RMS Calculator: A Step-By-Step Guide

Inputs

  • Peak value: the amplitude at the positive (or negative) crest of the sine wave, in volts or amperes

Steps

  1. Identify the peak value of the AC signal from an oscilloscope trace or manufacturer data sheet.
  2. Enter the peak value into the calculator.
  3. Read the RMS result, in the same unit as the input (volts or amps).

RMS Calculator Results Shown With Full Step Working

A US household AC voltage signal with a peak amplitude of 169.7 V.

  1. Divide peak value by √2 (1.4142): 169.7 ÷ 1.4142 = 120.0 V.

The RMS voltage is 120.0 V, which matches the standard US wall outlet rating.

Where This RMS Calculator Is the Right Tool To Reach For

Use this calculator when converting oscilloscope peak readings to the RMS values used on equipment nameplates and power specifications. It is also the correct tool when working from a rated supply voltage and needing the peak for capacitor or switch rating checks. Do not use it for non-sinusoidal signals such as variable-frequency drive outputs, clipped waveforms, or pulse-width modulated signals. Those require a true-RMS meter or an integral-based calculation specific to the waveform shape.

Assumptions

  • The input signal is a pure sine wave; the formula is not valid for any other waveform shape.
  • Input and output are in the same unit (both volts or both amps).
  • Frequency does not affect the RMS-to-peak ratio for a sine wave.

Limitations

  • Does not handle non-sinusoidal waveforms; use a true-RMS meter or waveform-specific formula for distorted signals.
  • Does not compute power; power requires both RMS voltage and RMS current along with power factor for AC circuits.
  • Does not convert between volts and amps; enter the correct quantity for the result you need.

In Practice

A common mistake is reading the peak-to-peak value from an oscilloscope instead of the peak value and entering that directly. Peak-to-peak is twice the peak amplitude for a symmetric sine wave. If your oscilloscope reads 339.4 V peak-to-peak, the peak value is 339.4 ÷ 2 = 169.7 V, and the RMS is 169.7 ÷ √2 = 120.0 V. Entering 339.4 directly gives a false RMS of 240 V, which is incorrect for a US 120 V supply.

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Frequently Asked Questions: RMS Calculator Results

What does RMS stand for in electrical measurements?

RMS stands for root mean square. It is calculated by squaring the instantaneous values of the waveform over one full cycle, averaging those squares, and then taking the square root of the result. For a sine wave, this simplifies to peak ÷ √2. The result represents the equivalent DC value that produces the same power in a resistive load.

Why is RMS used instead of average for AC voltage?

The simple time-average of a symmetrical sine wave is zero because the positive half-cycle exactly cancels the negative half-cycle. A zero average gives no useful information about the signal's energy content. RMS avoids this by squaring the values before averaging, which makes negative values positive, giving a meaningful measure of the signal's effective power-delivery capability.

What is the RMS of a 240 V peak AC signal?

For a 240 V peak sine wave, RMS = 240 ÷ √2 = 169.7 V, rounded to one decimal place. This means the signal delivers the same heating power to a resistor as 169.7 V of direct current.

Is this calculator accurate for variable-frequency drive output?

No. Variable-frequency drives produce pulse-width modulated waveforms that are not pure sine waves. The peak-to-RMS ratio for a PWM output depends on the modulation depth and switching frequency, not the simple 1/√2 constant. Use a true-RMS meter at the drive output terminals for an accurate measurement.

How do I find the peak value if I know the RMS?

Multiply the RMS value by √2 (approximately 1.4142). For a 120 V RMS supply, the peak is 120 × 1.4142 = 169.7 V. This peak value is what you need when checking insulation ratings, capacitor working voltage, or switch-contact peak voltage for components on a 120 V AC circuit.

Sources

Last updated: . Reviewed for accuracy against the formula shown above.