VRMS from peak voltage calculator
A 170 V peak sine wave equals about 120.2 V RMS: enter the peak voltage and get the RMS value by dividing by the square root of two, plus the crest factor and the peak-to-peak swing. For pure sine waves. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- V peak
- 170
- V rms
- 120.208152802 V
- Voltage rms
- 120.208152802
- Factor
- 0.7071067812
- Crest factor
- 1.4142135624
AC power, true-RMS meters, and amplifier datasheets constantly move between peak voltage and the root-mean-square value that drives heating and wattage formulas. For a pure sine wave the relationship is fixed: divide the peak by the square root of two, about zero point seven zero seven one. Students, electricians, and automation scripts need that conversion without a calculator app that forgets the crest factor or silently assumes a triangle wave. This VRMS from peak voltage calculator accepts a non-negative peak voltage in volts, applies Vrms equals Vpeak over square root of two, and returns the RMS result together with crest factor, peak-to-peak, and a printable expression.
Why sine-wave peak to RMS uses division by √2
Root-mean-square voltage is the equivalent DC value that would produce the same average power in a resistive load. For any periodic waveform you square the instantaneous voltage, average over one period, then take the square root. A pure sinusoid v of t equals Vpeak times sine of omega t has a mean-square value of Vpeak squared over two, so the RMS magnitude collapses to Vpeak divided by the square root of two.
That ratio is also written as the reciprocal of the crest factor: crest factor for a sine is Vpeak over Vrms equals square root of two, approximately one point four one four. Other shapes differ: a triangle wave uses a different factor, a square wave has crest factor one, and distorted mains may need a true-RMS instrument rather than a pure geometric conversion.
This capability deliberately targets the pure-sine case only, which is the default assumption in introductory circuit courses, nominal wall-outlet math, and many audio and RF peak-to-RMS estimates when distortion is neglected. Dividing by square root of two is therefore not a vague rule of thumb; it is the closed-form result of the period integral for a sinusoid. Multiplying Vrms by square root of two recovers Vpeak; multiplying Vrms by two square root of two recovers peak-to-peak.
Keeping the waveform label sine in the response makes the contract honest for clients that might later chain a different crest-factor model.
Where peak-to-RMS conversion earns its keep in the field
Electrical technology courses assign peak and RMS drills so learners can move from oscilloscope peak readings to the RMS numbers printed on wall outlets and nameplates. Audio and RF technicians convert amplifier peak swing into equivalent RMS for power calculations and to compare against true-RMS multimeter displays. Panel designers and energy auditors often start from a peak estimate on a scope capture and need a deterministic Vrms before they compute apparent power or load heating.
Failed validation does not consume balance. Keep square-wave crest factor, triangle-wave RMS, and full true-RMS of arbitrary samples as separate landings so each search intent has one clear page rather than an overloaded multi-waveform tool that confuses both students and search engines.
What you can do with it
Mains and nameplate RMS from scope peak
Convert an oscilloscope peak reading on a wall outlet or transformer secondary into the RMS value used on labels and power formulas.
Audio and RF peak-to-RMS power estimates
Turn amplifier peak voltage swing into sine-equivalent RMS before computing load power as Vrms squared over resistance.
Classroom peak vs RMS homework keys
Generate deterministic Vrms answers from assigned Vpeak values for pure-sine drills without hand calculator drift.
FAQ
Does this work for triangle or square waves?
No. This capability applies only the pure-sine crest factor √2. Other waveforms need different factors or a true-RMS sample computation.
What happens if I enter a negative peak voltage?
It is rejected instead of being quietly turned into a positive number. Peak voltage is treated as a magnitude, so enter the size of the swing; zero is accepted and gives zero volts RMS.
How many volts RMS is 325 V peak?
Roughly 230 V, the European nominal mains voltage. Dividing 325 by the square root of two gives that figure, which is why a 230 V outlet swings to about 325 V at each peak.
What is crest factor?
It is the peak voltage divided by the RMS voltage. For a pure sine wave it is the square root of two, about 1.414, and the calculator shows it next to the result. Multiplying the RMS value by it gives the peak back.
What does RMS voltage actually mean?
It is the steady DC voltage that would deliver the same average power to a resistive load. That is why heating and wattage formulas use RMS, and why outlets and nameplates are labelled with it.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/elec/vrms-from-vpeak \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"v_peak":170}'const res = await fetch("https://api.kit.forhosting.com/elec/vrms-from-vpeak", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"v_peak": 170
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/vrms-from-vpeak",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"v_peak": 170
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/vrms-from-vpeak", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"v_peak":170}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"v_peak":170}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/vrms-from-vpeak", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"v_peak": 170
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.vrms_from_vpeak",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Zero peak yields zero RMS; negative peak is rejected as invalid_input rather than a silent absolute value.
Input contract, response fields, and validation errors
Classic checks include one hundred seventy volts peak giving about one hundred twenty point two volts RMS, three hundred twenty-five volts peak for roughly two hundred thirty volts RMS European nominal, and one volt peak giving about zero point seven zero seven one volts RMS. POST a JSON object with a single required non-negative finite number under v_peak, the AC peak voltage in volts. The same quantity is accepted under the aliases vpeak, V_peak, Vpeak, peak, or peak_voltage, but only one of those keys may appear in a request so the chosen value is unambiguous. Numeric JSON numbers and numeric strings are both accepted so form widgets and spreadsheet paste stay convenient; bare unit strings such as one hundred seventy V written as text are not parsed, so pass one hundred seventy for a typical one-hundred-twenty-volt RMS mains peak estimate. Missing fields, empty strings, NaN, and Infinity fail with invalid_input naming the problem and are not billed. On success the body includes cleaned v_peak, v_rms and voltage_rms as the same RMS result, factor equal to one over square root of two, crest_factor equal to square root of two, v_peak_to_peak equal to two times Vpeak, waveform set to sine, unit set to V, formula Vrms equals Vpeak over square root of two, and an expression string that substitutes the numeric peak and RMS for display. Pair the response with your own power formula P equals Vrms squared over R when you need watts; this endpoint converts voltage only and does not require resistance or frequency. Successful API calls use the published base price of $0.002 per item; validation failures do not consume prepaid balance.
Where peak-to-RMS conversion earns its keep in the field
If you only measured peak-to-peak on a scope, divide by two first to obtain Vpeak, then send that value here; the response already returns v_peak_to_peak for the reverse check so you can confirm your scope scale without a second formula lookup.
Technical questions
How do I convert peak voltage to RMS for a sine wave?
Send a non-negative finite v_peak in volts. The API returns Vrms = Vpeak / √2 (about 0.7071 × Vpeak), plus crest factor √2 and peak-to-peak 2·Vpeak.
What peak voltage corresponds to 120 V RMS mains?
For a pure sine, Vpeak = 120 × √2 ≈ 169.7 V. Sending v_peak ≈ 170 returns about 120.2 V RMS, a common classroom check.
What if I enter a negative peak voltage?
The task fails with invalid_input. Peak magnitude must be ≥ 0; the handler does not silently take an absolute value.
What does the VRMS from peak voltage calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.