Peak voltage from RMS calculator for sine waves
A 10 V RMS sine wave peaks at about 14.142 V and spans about 28.284 V peak to peak: enter the RMS voltage and get both, multiplied by the square root of two. Made for ideal sine waves. Free in your browser.
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Worked example
- Vrms
- 120
- V peak
- 169.7056274848
- V peak to peak
- 339.4112549695
- Conversion factor
- 1.4142135624
- Waveform
- sine
This peak voltage from RMS calculator converts the effective voltage reported by an RMS meter into the maximum amplitude expected on an oscilloscope for an ideal sine wave. Enter a non-negative voltage in volts RMS and the calculator multiplies it by the square root of two. The result includes peak voltage, peak-to-peak voltage, the conversion factor, and the formula used. It is useful when a meter, specification, or power calculation uses RMS while a scope display, component rating, or waveform generator uses amplitude.
Why RMS and peak voltage are different
Alternating voltage changes throughout each cycle, so a single label can describe several different properties of the same waveform. Peak voltage is the largest magnitude reached relative to zero. Peak-to-peak voltage spans from the negative extreme to the positive extreme.
RMS voltage describes the equivalent heating effect of the waveform in a resistive load, which is why mains supplies, multimeters, and many electrical specifications use it. For an ideal sine wave, integrating the squared waveform over one complete cycle gives an RMS value equal to the peak amplitude divided by the square root of two. Reversing that relationship gives Vpeak = Vrms × sqrt(2).
The conversion factor is approximately 1.414213562, but the calculator uses the platform's full numeric square-root constant before returning a stable result. A 10 V RMS sine wave therefore reaches about 14.142 V at each positive and negative extreme, and spans about 28.284 V peak to peak. These values are not competing measurements; they are different descriptions of one sinusoidal signal.
Keeping the labels explicit matters because confusing RMS with peak can understate insulation, headroom, clamp, and oscilloscope range requirements. This calculator returns all three voltage descriptions together so the relationship remains visible instead of leaving an unlabeled number that could be reused incorrectly.
How to enter and interpret the result
Provide the sine wave's RMS voltage in the vrms field as a finite, non-negative number measured in volts. Use plain numeric values: enter 230 for 230 volts RMS rather than a string containing a unit symbol. Zero is valid and produces zero for both peak and peak-to-peak voltage.
Negative input is rejected because this tool treats RMS voltage as a non-negative magnitude, not as an instantaneous signed sample. Peak-to-peak voltage is twice the calculated peak amplitude, so it equals two times sqrt(2) times Vrms. Choose display precision appropriate to the accuracy of the original meter or specification, since extra decimal places do not create extra measurement certainty.
When the square-root-of-two rule applies
Use this conversion only when the voltage is sinusoidal and the supplied RMS value represents that sine wave. The ratio between RMS and peak depends on waveform shape, often described through crest factor. An ideal sine has a crest factor of sqrt(2), but a square wave has equal RMS and peak magnitudes, while narrow pulses, clipped audio, inverter outputs, and distorted mains can have very different ratios.
A true-RMS meter may correctly measure a nonsinusoidal waveform, yet multiplying that reading by sqrt(2) still will not reveal its actual peak. In those cases, measure the peak directly with suitable bandwidth or use a calculator based on the known waveform and duty cycle. Also distinguish amplitude from a voltage rating: a capacitor, diode, transistor, probe, or ADC input may need margin above the theoretical peak for tolerance, transients, ringing, DC offset, and measurement uncertainty.
This tool intentionally does not invent that engineering margin. It provides the exact mathematical bridge between RMS and peak for a centered ideal sine wave, plus peak-to-peak as a convenient scope quantity. Common uses include reconciling a multimeter reading with an oscilloscope trace, setting a waveform generator whose interface asks for amplitude, checking whether an input range can accommodate a sinusoid, and teaching why mains voltage reaches a substantially larger instantaneous maximum than its familiar RMS label suggests.
What you can do with it
Compare meter and oscilloscope readings
Turn a sine-wave RMS meter value into the peak and peak-to-peak values expected on a correctly scaled scope trace.
Check voltage headroom
Estimate the ideal sinusoidal peak before selecting a probe range, ADC input range, amplifier supply, or protective component.
Configure signal equipment
Convert an RMS requirement into peak amplitude when a waveform generator or simulation expects a sine-wave amplitude.
FAQ
What formula converts RMS voltage to peak voltage?
For an ideal sine wave, Vpeak = Vrms × sqrt(2).
Does this work for square waves or pulses?
No. Their crest factors differ from a sine wave, so their peak voltage cannot generally be found by multiplying RMS by sqrt(2).
What is peak-to-peak voltage?
For a centered sine wave, peak-to-peak voltage is twice peak voltage, or 2 × sqrt(2) × Vrms.
Can RMS voltage be negative?
RMS is a magnitude and is non-negative. This capability rejects negative input as invalid.
Why does it matter whether a rating is RMS or peak?
Insulation, headroom, clamp circuits and oscilloscope ranges have to cope with the peak, not the RMS figure. Treating an RMS value as if it were the peak understates those requirements, which is why the calculator shows all three values side by side.
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/vpeak-from-vrms \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"vrms":120}'const res = await fetch("https://api.kit.forhosting.com/elec/vpeak-from-vrms", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"vrms": 120
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/vpeak-from-vrms",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"vrms": 120
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/vpeak-from-vrms", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"vrms":120}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"vrms":120}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/vpeak-from-vrms", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"vrms": 120
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.vpeak_from_vrms",
"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
How to enter and interpret the result
The aliases v_rms and rms_voltage are accepted for integration convenience, although a request should supply only one of those names. The response reports vrms, v_peak, and v_peak_to_peak in volts. It also includes the square-root-of-two conversion factor, a readable formula, and a waveform marker that states sine. Values are rounded only to a stable fifteen-significant-digit representation for dependable JSON comparisons; no coarse display rounding is imposed. The browser and API execute the same pure function, and the API price for a successful item is $0.002. Invalid input produces a typed error instead of a misleading numerical result.
Technical questions
What does the API request cost?
A successful API request costs $0.002 per item. The browser calculator runs locally for free.