Welcome to the RMS voltage calculator, with which you can quickly calculate the RMS of common waveforms. We'll learn about topics such as what RMS voltage is, the general equation for RMS voltage, and how to calculate RMS voltage for your favorite waveforms. Let's charge ahead!
Get it? "Charge"? As in "electrical charge"…? … I'll see myself out.
What is RMS?
Before we can talk about waveforms and their RMS values, we first have to examine the RMS and what it represents. The root mean square of a series of numbers is the root of the mean of the sum of their squares. RMS is also known as the quadratic mean. So, for a set of values y = [x₁, …, xN], our RMS value YRMS would be:
The RMS isn't just an average of the numbers; it's an entirely separate concept with valuable properties, which we'll learn about in the rest of this article.
RMS values of periodic continuous-time functions
Most real-world waves and signals are continuous-time functions. When we deal with these, the equation for the root mean square changes somewhat. We're also only considering periodic functions for this calculator. A periodic function is a function that repeats its values at regular intervals. We denote such a function's period with the symbol T.
Trigonometric functions are great examples of periodic, continuous-time functions — both sine and cosine waves' period is T = 2π = 360°. A periodic function's RMS over one of its periods is the same as its RMS over its entirety. We can obtain the RMS of a periodic, continuous-time waveform y(t) with:
What is the RMS of a voltage?
The RMS voltage (root-mean-square voltage), VRMS, is the value of a constant (DC) voltage that would deliver the same average power to a resistive load as the given time-varying (AC) waveform. That's why RMS is so useful: it lets us compare the heating/power effect of any waveform to plain DC.
For a few of the most common periodic waveforms, the RMS voltage reduces to a simple relationship with the peak voltage Vp:
| Waveform | RMS voltage | Crest factor | Form factor |
|---|---|---|---|
| Sine | Vp / √2 ≈ 0.7071·Vp | √2 ≈ 1.414 | ≈ 1.111 |
| Square | Vp | 1 | 1 |
| Triangle | Vp / √3 ≈ 0.5774·Vp | √3 ≈ 1.732 | ≈ 1.155 |
| Sawtooth | Vp / √3 ≈ 0.5774·Vp | √3 ≈ 1.732 | ≈ 1.155 |
| Half-wave rectified sine | Vp / 2 | 2 | ≈ 1.571 |
| Full-wave rectified sine | Vp / √2 ≈ 0.7071·Vp | √2 ≈ 1.414 | ≈ 1.111 |
| PWM / rectangular pulse | Vp × √D | 1/√D | 1/√D |
| DC (constant) | Vp | 1 | 1 |
Where Vp is the peak (amplitude) voltage and D is the duty cycle (as a fraction between 0 and 1) for the PWM/pulse waveform.
How to use the RMS voltage calculator
- Select your unit system: choose Metric (SI) or American. Voltage is an SI quantity, so both systems share the volt — the toggle simply matches the prefix conventions you prefer.
- Choose the waveform: sine, square, triangle, sawtooth, half- or full-wave rectified sine, PWM pulse, or DC.
- Pick the amplitude type: enter either the peak voltage (Vp) or the peak-to-peak voltage (Vpp).
- Enter the voltage value and pick a unit — µV, mV, V, or kV.
- For PWM only: enter the duty cycle in percent.
- Click Calculate: you instantly get the RMS voltage, peak, peak-to-peak, average value, crest factor, form factor, and the dBV / dBu levels.
How to calculate RMS voltage?
For a sine wave with peak voltage Vp, plug the waveform into the continuous-time RMS integral and you get the famous result:
For example, household mains with a peak of about 170 V (in 120 V regions) gives VRMS = 170 / √2 ≈ 120 V — which is exactly the "120 V" we quote. The calculator applies the correct closed-form factor automatically for whichever waveform you select, so you never have to evaluate the integral by hand.
FAQs
Why is RMS voltage more useful than peak or average voltage?
Because RMS voltage directly relates to power. The average power dissipated in a resistor is P = VRMS² / R. Peak voltage tells you the maximum instantaneous value, and the simple average of a symmetric AC waveform is zero — neither is convenient for power calculations, but RMS is.
What is the RMS voltage of a sine wave?
For a pure sine wave, VRMS = Vp / √2 ≈ 0.707 × Vp, where Vp is the peak (amplitude) voltage. Equivalently, VRMS = Vpp / (2√2) when using peak-to-peak voltage.
What is the crest factor and form factor?
The crest factor is the ratio of the peak value to the RMS value (Vp / VRMS) — it tells you how "peaky" a waveform is. The form factor is the ratio of the RMS value to the rectified average value (VRMS / Vavg). For a sine wave the crest factor is √2 ≈ 1.414 and the form factor is ≈ 1.111.
What are dBV and dBu?
dBV expresses the RMS voltage relative to a 1 V reference: dBV = 20·log₁₀(VRMS / 1 V). dBu uses a reference of about 0.7746 V (the voltage that dissipates 1 mW into 600 Ω): dBu = 20·log₁₀(VRMS / 0.7746 V). These logarithmic units are widely used in audio engineering.
Does the RMS voltage depend on frequency?
No. For an ideal periodic waveform, the RMS value depends only on the waveform shape and amplitude (and duty cycle for pulses) — not on the frequency or the period T. That's why this calculator only asks for the waveform and its amplitude.
How do I get RMS from a peak-to-peak value?
First convert peak-to-peak to peak. For a symmetric (bipolar) waveform such as a sine, square, triangle, or sawtooth, Vp = Vpp / 2. Then apply the waveform's RMS factor. This calculator does the conversion for you when you select the "Peak-to-peak" amplitude type.