ForHosting KIT · Engineering & construction

Sine average voltage calculator

A sine wave of 10 V peak has an average rectified value of about 6.366 V, two over pi times the peak. Enter the peak amplitude to get the full-wave average you would expect from an unfiltered bridge rectifier. Free in your browser.

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Worked example

If you enter

Peak: 10

You get

V peak: 10 volt
V avg: 6.3661977237
Average rectified: 6.3661977237
Factor: 0.6366197724

The average rectified value of a pure sine wave is the mean of its absolute value over one full period, not the algebraic mean that cancels positive and negative half-cycles to zero. Electrical engineering textbooks, rectifier design notes, and instrument-calibration sheets all quote that number as two over pi times the peak amplitude, written V_avg equals (2/π) times V_peak or V_m. Students checking homework need a deterministic answer for ten volts peak, bench technicians converting a scope reading into an expected DC average after full-wave rectification, and automation scripts that grade lab reports all share the same closed-form product. This sine average voltage calculator accepts a non-negative finite peak amplitude in volts, multiplies by two over pi, and returns the average rectified voltage with cleaned inputs, the constant factor, a printable expression, and the formula string. Negative peak is rejected because amplitude is a magnitude for this identity.

What average rectified sine voltage means

A pure sinusoid v(t) equals V_peak times sin of omega t swings symmetrically around zero, so the ordinary arithmetic average over a full period is exactly zero. That zero is useless for sizing rectifier filters, estimating meter readings on older average-responding instruments, or comparing AC magnitude to a DC equivalent that a full-wave bridge would deliver into a resistive load without smoothing. Instead, engineers take the average of the absolute value, which folds the negative half-cycle up and integrates over one period T.

The integral of |V_peak sin(omega t)| from zero to T divided by T evaluates to two times V_peak over pi, so V_avg equals (2/π) V_peak. Numerically, two over pi is about zero point six three six six, so ten volts peak yields roughly six point three six six volts average rectified. Half-wave rectification without the negative half-cycle would halve that figure to V_peak over pi; this calculator implements the full-period absolute average that matches the two-over-pi textbook line.

Root-mean-square voltage is a different quantity, V_peak over square root of two, and form factor is the ratio of RMS to average, about one point one one for a pure sine. Those related identities belong on their own landings so search intent stays clear.

Where sine average voltage calculators earn their keep

Electronics labs convert a measured or assigned peak amplitude into the expected average after full-wave rectification so students can compare multimeter readings on an unfiltered bridge against the closed-form (2/π) V_peak prediction. Power-electronics notes and charger design primers use the same product when estimating mean load voltage before adding capacitor smoothing or control loops.

Content sites ranking for sine average voltage calculator or average rectified value of a sine wave need a focused page that states the two-over-pi identity without mixing in RMS, form factor, or half-wave-only variants that would dilute the query. Keep RMS, crest factor, and half-wave average landings separate so each search intent has one clear tool rather than an overloaded multi-formula calculator that confuses both learners and search engines.

What you can do with it

Lab and homework average-rectified checks

Convert a known peak amplitude into V_avg = (2/π)·V_peak so students can match meter readings on full-wave rectifier benches without hand arithmetic errors.

Rectifier design estimates

Estimate mean DC-side voltage from AC peak before filter capacitors for chargers, bridges, and power-electronics notes that quote the two-over-pi identity.

FAQ

Is this full-wave or half-wave average?

Full-period average rectified value: V_avg = (2/π)·V_peak. Half-wave average without the folded negative half-cycle would be V_peak/π and is not what this tool computes.

How is average different from RMS?

RMS for a pure sine is V_peak/√2 ≈ 0.707 V_peak. Average rectified value is (2/π)·V_peak ≈ 0.637 V_peak. Form factor is RMS divided by average ≈ 1.11.

Why is negative peak rejected?

Peak amplitude for this formula is a magnitude. Zero peak is allowed and returns zero average.

What is the average voltage of 230 V mains?

Its peak is about 325 V, so the average rectified value is about 207 V. Enter the peak rather than the RMS figure of the supply, because the formula starts from the peak amplitude.

Why is the plain average of a sine wave zero?

Because the positive and negative half-cycles cancel over a full period. The useful figure is the average of the absolute value, which folds the negative half up and gives two over pi times the peak.

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

POSThttps://api.kit.forhosting.com/elec/vavg-sine

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/vavg-sine \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"peak":10}'

const res = await fetch("https://api.kit.forhosting.com/elec/vavg-sine", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "peak": 10
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/elec/vavg-sine",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "peak": 10
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/vavg-sine", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"peak":10}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"peak":10}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/vavg-sine", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "peak": 10
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "elec.vavg_sine",
  "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

Per request$0.002

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

Input contract, response shape, and errors

Classic classroom checks include peak ten yielding about six point three six six volts average, and peak three hundred twenty five (approximate European mains peak from two hundred thirty volts RMS) yielding about two hundred seven volts average rectified. Wire the free browser form for homework and quick bench checks, then call the identical contract from scripts when you need bulk answer keys. POST a JSON body with a single required finite number under the field peak, expressed in volts as the peak amplitude V_peak or V_m of the sine wave. The same value is accepted under the aliases v_peak, vpeak, amplitude, vm, vp, Vpeak, or V_m, but only one of those keys may appear in a request. Numeric JSON values and numeric strings are both accepted so browser forms and spreadsheet paste stay convenient; unit suffixes and SI prefix strings are not expanded, so pass ten for a ten-volt peak rather than the text ten V or ten k. Peak must be greater than or equal to zero; a negative peak fails with invalid_input because the amplitude in V_avg equals (2/π) V_peak is a magnitude, not a signed sample from an oscilloscope channel. Missing fields, empty strings, NaN, and Infinity also fail with invalid_input and are not billed. On success the response includes cleaned peak and v_peak, v_avg and average_rectified as the product (2/π) times peak, factor as the cleaned constant two over pi, unit volt, a short expression string showing the product, method vavg_sine, and the formula string restating the average of absolute sine over one period. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.

Integration use cases

Auto-graders and golden fixtures

Script the same (2/π)·V_peak product used in the browser so LMS answer keys and CI fixtures share one deterministic ground truth.

Technical questions

How do I compute the average voltage of a sine wave from peak?

Send a non-negative finite peak amplitude in volts as peak (or v_peak, amplitude, vm, …). The API returns V_avg = (2/π)·V_peak, the average of |Vm sin(ωt)| over one period.

What does the sine average 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.

Read the full KIT documentation →

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