Line to phase voltage calculator
A 400 V three-phase supply gives loads about 230 V from line to neutral: enter either the line or the phase voltage of a balanced wye system and get the other, linked by the square root of three. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Line to line
- 400
- Line to neutral
- 230.9401076759
- Factor
- 1.7320508076
- Ratio
- 1.7320508076
- Solved
- line_to_neutral
In a balanced three-phase wye (star) system the line-to-line RMS voltage and the line-to-neutral RMS voltage are locked by a single constant: the square root of three. Electricians, panel designers, and students constantly need to go from a 400 V line rating to the 230 V phase value that loads actually see, or from a known phase voltage back to the line-to-line figure used on nameplates and utility feeders.
Why line and phase voltages differ by √3 in a wye
A balanced three-phase wye source has three phase legs joined at a common neutral. Each line-to-neutral voltage is a phase-to-neutral phasor; the three phasors are equal in magnitude and spaced one hundred twenty degrees apart. The line-to-line voltage between any two phases is the vector difference of two phase-to-neutral phasors.
For equal magnitudes V_LN that geometry produces a magnitude of exactly √3 times V_LN, independent of the absolute size of the system as long as balance holds. That is why European 400 V three-phase distribution presents roughly 230 V to single-phase loads connected phase to neutral, and why North American 480 V industrial services present about 277 V phase to neutral. The identity is magnitude-only: this calculator works with positive RMS values and does not model phase angles, sequence, or unbalance.
Delta systems do not expose a system neutral the same way; the √3 relation still links line voltage to phase-winding voltage inside a delta machine, but the parameter names here follow the common wye field language of line-to-line versus line-to-neutral. Always confirm whether your equipment datasheet quotes V_LL or V_LN before converting, because treating a line figure as a phase figure understates insulation and overvoltage stress by about seventy-three percent.
Where this conversion prevents costly mix-ups
Panel schedules and load calculations often list breaker ratings and bus voltages as line-to-line while branch circuits and control transformers are specified line-to-neutral; a tiny deterministic converter avoids spreadsheet mistakes when filling BOM and one-line drawings. Training platforms and licensing-exam prep tools need an oracle that always applies √3 the same way so graders never argue about intermediate rounding. IoT gateways and energy dashboards that ingest mixed SCADA tags—some tagged Vab, some Van—can normalize to a single base before computing power or imbalance metrics.
Content sites targeting line to phase voltage calculator and three phase wye line to neutral queries benefit from a live tool whose free browser path matches the paid automation path on the same pure module. Failed validation does not consume balance. Keep requests small, pin the rounded voltages in tests, and you get reproducible line and phase figures without standing up a full power-flow engine for a single identity.
What you can do with it
Panel and one-line schedules
Convert nameplate line-to-line bus voltage to the line-to-neutral value that single-phase loads and control transformers actually see in a wye service.
Exam and training checks
Verify student answers for balanced three-phase V_LL ↔ V_LN conversions with a deterministic √3 oracle that rejects zero or negative magnitudes.
SCADA and energy dashboards
Normalize mixed Vab and Van telemetry tags to one voltage base before computing power, utilization, or simple imbalance indicators.
FAQ
Why must I provide exactly one of the two voltages?
The √3 identity determines the unknown from the known. Providing both would either be redundant or inconsistent; providing neither leaves nothing to convert. Exactly one field keeps the contract unambiguous.
Does this work for delta systems or unbalanced feeds?
The calculator models balanced wye magnitude conversion only. Unbalance, sequence components, and delta terminal wiring are out of scope; use a full three-phase analysis tool for those cases.
What is the phase voltage of a 400 V three-phase supply?
About 230 V from each line to neutral. Divide the line-to-line voltage by the square root of three; that is the voltage a single-phase load connected between one phase and neutral actually receives.
How do I get the line voltage from the phase voltage?
Multiply the line-to-neutral voltage by the square root of three. A North American service with about 277 V from phase to neutral therefore has 480 V between any two lines.
Should I enter the line or the phase voltage from a datasheet?
Enter whichever the datasheet actually quotes, and check which one it is first. Treating a line figure as a phase figure seriously understates the insulation and overvoltage stress the equipment will see.
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/line-phase-voltage \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"line_to_line":400,"v_ll":1}'const res = await fetch("https://api.kit.forhosting.com/elec/line-phase-voltage", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"line_to_line": 400,
"v_ll": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/line-phase-voltage",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"line_to_line": 400,
"v_ll": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/line-phase-voltage", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"line_to_line":400,"v_ll":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"line_to_line":400,"v_ll":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/line-phase-voltage", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"line_to_line": 400,
"v_ll": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.line_phase_voltage",
"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
This line to phase voltage calculator accepts exactly one known magnitude—either line_to_line or line_to_neutral—applies V_LL equals root three times V_LN (or the inverse division), and returns both voltages plus the factor and ratio for display. Zero, negative, or missing inputs fail with invalid_input so automation never bills a nonsensical conversion. The same pure module powers the free browser path and the API, so notebook checks and field apps never disagree on a classic power-systems identity.
Input contract, formulas, and response fields
POST a JSON body with exactly one of two optional numeric fields: line_to_line (aliases v_ll, vll, line_voltage) or line_to_neutral (aliases v_ln, vln, phase_voltage, line_to_phase). Each value may be a JSON number or a numeric string and must be a finite positive voltage in volts RMS. Providing both fields, neither field, zero, or a negative magnitude fails with invalid_input and is not billed. When line_to_line is supplied the solver sets line_to_neutral to line_to_line divided by √3 and marks solved as line_to_neutral. When line_to_neutral is supplied it sets line_to_line to line_to_neutral times √3 and marks solved as line_to_line. Success responses always include both voltages rounded for stable cross-runtime goldens, factor equal to √3, ratio equal to line_to_line over line_to_neutral (also √3 under ideal math), system set to balanced_wye, a short formula string, and units for each voltage field. Example: line_to_line four hundred yields line_to_neutral near two hundred thirty point nine four volts. Example: line_to_neutral two hundred thirty yields line_to_line near three hundred ninety-eight point three seven volts. Pair the numbers with your own single-line diagram; this endpoint only converts magnitudes.
Technical questions
How do I convert line-to-line voltage to line-to-neutral?
Send a positive finite line_to_line in volts. The API returns line_to_neutral = V_LL / √3 for a balanced three-phase wye, plus factor √3 and the solved field set to line_to_neutral.
How do I convert phase (line-to-neutral) voltage to line voltage?
Send a positive finite line_to_neutral in volts. The API returns line_to_line = V_LN · √3 and marks solved as line_to_line.
What does the line to phase 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.