RMS (Root Mean Square) voltage is the equivalent DC voltage that would deliver the same power to a resistive load. For a sine wave, Vrms = Vpeak / √2 ≈ 0.7071 × Vpeak.

Why do we use RMS instead of peak voltage?

RMS is used because it represents the effective heating value of an AC voltage. A 230V RMS AC supply delivers the same power as a 230V DC supply to a resistive load.

What is the peak voltage of UK mains?

UK mains is 230V RMS. The peak voltage is 230 × √2 = 325.3V. The peak-to-peak voltage is 650.5V.

Does the RMS formula change for different waveforms?

Yes. For a sine wave Vrms = Vpeak/√2. For a square wave Vrms = Vpeak. For a triangle wave Vrms = Vpeak/√3. The conversion factors depend on the waveform shape.

What is average voltage?

Average voltage is the mean of the absolute value of the waveform over one cycle. For a sine wave, Vavg = Vpeak × 2/π ≈ 0.6366 × Vpeak. It is used in rectifier circuits.

Form factor is the ratio of RMS to average voltage: FF = Vrms/Vavg. For a sine wave FF = π/(2√2) ≈ 1.1107. It indicates the shape of the waveform.

RMS Voltage Calculator

V_rms = V_pk/√2

V_pk = V_rms×√2

V_pp = 2×V_pk

V_avg = V_pk×2/π

Enter Any One Voltage — Get All Others

rms RMS VoltageCalculated

pk Peak VoltageCalculated

pp Peak-to-PeakCalculated

avg Average VoltageCalculated

Optional — Frequency / Period

f Frequency

T Period

Enter any one voltage value

All Voltage Values (Sine Wave)

Vrms
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V

V_peak

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V_pp

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V_avg

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Conversion Factors (Sine)

RMS / Peak

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Avg / Peak

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Form Factor

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Table of Contents

Fundamentals

What Is RMS Voltage?
Conversion Formulas
Waveform Comparison Table

Worked Examples

UK Mains 230V RMS
Oscilloscope Reading to RMS
Multimeter on a Square Wave

Deep Dive

Why RMS Matters
How Multimeters Measure RMS
Crest Factor and Form Factor

Reference

Frequently Asked Questions
Related AC Circuit Calculators

What Is RMS Voltage?

RMS stands for Root Mean Square. It is the equivalent DC voltage that would deliver the same average power to a purely resistive load. When someone says “UK mains is 230 volts” they mean 230 V RMS — the peak voltage is actually 325 V, and the peak-to-peak swing is 651 V.

RMS is not simply the average of the waveform. The calculation squares every instantaneous value, takes the mean of those squares, then takes the square root — hence the name. For a sine wave the result is V_rms = V_peak / √2, but for other waveform shapes the factor is different.

Conversion Formulas

Sine wave: V_rms = V_pk × 0.7071 | V_pk = V_rms × 1.4142
V_pp = 2 × V_pk | V_avg = V_pk × 0.6366
Square wave: V_rms = V_pk (identical)
Triangle / sawtooth: V_rms = V_pk / √3 ≈ V_pk × 0.5774

Waveform Comparison Table

Waveform	RMS / Peak	Avg / Peak	Form Factor	Crest Factor
Sine	0.7071	0.6366	1.1107	1.4142
Square	1.0000	1.0000	1.0000	1.0000
Triangle	0.5774	0.5000	1.1547	1.7321
Sawtooth	0.5774	0.5000	1.1547	1.7321

The form factor (RMS/Average) tells you how much a cheap “average-responding” multimeter will be wrong if you apply it to a non-sine waveform. The crest factor (Peak/RMS) tells you the headroom your amplifier or power supply needs.

Worked Example — UK Mains 230V RMS

Given: V_rms = 230 V (sine wave, 50 Hz)

Step 1 — V_peak = 230 × √2 = 325.3 V

Step 2 — V_pp = 2 × 325.3 = 650.5 V

Step 3 — V_avg = 325.3 × 2/π = 207.1 V

Step 4 — Period T = 1/50 = 20 ms

This is why capacitors in mains power supplies must be rated above 325 V even though the supply is “only 230 V”. The Instantaneous Voltage Calculator shows the voltage at any specific point in the cycle.

Worked Example — Oscilloscope Reading to RMS

Given: Oscilloscope shows V_pp = 10 V (sine wave)

Step 1 — V_peak = 10 / 2 = 5 V

Step 2 — V_rms = 5 / √2 = 3.536 V

Oscilloscopes display peak-to-peak by default. You must divide by 2 then multiply by 0.7071 to get RMS. Many digital scopes have an automatic RMS measurement function that does this for you.

Worked Example — Multimeter on a Square Wave

Given: 5 V peak square wave measured with an average-responding meter calibrated for sine

Step 1 — True RMS = 5 × 1.000 = 5.000 V (square wave factor)

Step 2 — Average-responding meter reads: V_avg × 1.1107 (sine form factor) = 5 × 1.1107 = 5.554 V

Step 3 — Error: +11.1%

Cheap multimeters assume a sine wave and multiply the rectified average by 1.11 to display “RMS”. On a square wave this gives an 11% over-reading. Only a true RMS meter gives correct readings on non-sinusoidal waveforms.

Why RMS Matters

RMS is the only voltage measure that directly relates to power. The power dissipated in a resistor is P = V²_rms / R. Using peak voltage instead would overstate the power by a factor of 2 for a sine wave. This is why all AC power ratings, transformer specifications, and electrical safety standards use RMS values.

The Power Factor Calculator uses RMS voltage and current to determine real and reactive power in AC circuits.

How Multimeters Measure RMS

There are two types of AC multimeter. An average-responding meter rectifies the AC signal, measures its average value, and multiplies by 1.1107 (the sine wave form factor) to display a reading labelled “RMS”. This is accurate only for pure sine waves.

A true RMS meter computes the actual RMS value mathematically (or thermally), giving accurate readings on any waveform shape — sine, square, triangle, distorted, or noisy. For switched-mode power supply outputs, motor drives, or any waveform with harmonics, a true RMS meter is essential.

Crest Factor and Form Factor

Crest factor is the ratio of peak to RMS: CF = V_pk / V_rms. It tells you how “peaky” the waveform is. A sine wave has CF = 1.414, a square wave has CF = 1.0, and a narrow pulse can have CF > 10. Amplifiers and power supplies must handle peak voltages, so a high crest factor demands more headroom.

Form factor is the ratio of RMS to average: FF = V_rms / V_avg. It determines how much error an average-responding meter makes on non-sine waveforms. The Voltage Phasor Calculator shows how phasor arithmetic relates to these amplitude quantities.

Frequently Asked Questions

Is mains voltage RMS or peak?

Mains voltage is always stated as RMS. UK mains is 230 V RMS (325 V peak). US mains is 120 V RMS (170 V peak). All electrical safety ratings use RMS.

Why is RMS called root mean square?

The calculation involves three steps: square all instantaneous values, take the mean (average) of those squares, then take the square root. Doing these operations in reverse order gives the name: Root of the Mean of the Squares.

Can RMS be higher than peak voltage?

No. For any waveform, RMS is always less than or equal to the peak value. They are equal only for a square wave (or DC), where RMS = peak.

What is the RMS of a DC voltage?

The RMS of a constant DC voltage equals the DC voltage itself. A 5 V DC supply has V_rms = 5 V, V_peak = 5 V, V_avg = 5 V. All three measures are identical for DC.

Do I need a true RMS meter?

If you only work with pure mains sine waves, an average-responding meter is fine. If you work with PWM signals, motor drives, switching power supplies, distorted waveforms, or audio signals, a true RMS meter is essential for accurate readings.

How do I convert oscilloscope peak-to-peak to RMS?

Divide V_pp by 2 to get V_peak, then multiply by the RMS/peak factor for the waveform shape (0.7071 for sine). Or simply divide V_pp by 2√2 ≈ 2.828 for a sine wave.

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Last updated: March 2026