Stellar parallax calculator
A parallax of 0.1 arcseconds puts a star 10 parsecs away, or 32.61563777 light-years. Enter the angle from a catalogue, a textbook or your own measurement and get both distances at once. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Parallax arcsec
- 0.1
- Distance pc
- 10
- Distance ly
- 32.61563777
- Ly per pc
- 3.261563777
Trigonometric stellar parallax is the geometric foundation of the cosmic distance ladder for nearby stars. As Earth orbits the Sun, a nearby star appears to shift against distant background stars by a tiny angle called the parallax. By definition of the parsec, a star with a parallax of one arcsecond lies one parsec away, so distance in parsecs is simply one divided by the parallax angle measured in arcseconds. That closed form turns Hipparcos and Gaia catalogue values, textbook drills, and lab measurements into human-scale distances in parsecs and light-years without iterative solvers or catalogue downloads.
How stellar parallax measures star distance
Start from the classical small-angle geometry of Earth's orbit. Over half a year the baseline is roughly two astronomical units, and the half-angle shift of a nearby star against the distant background is the annual parallax π. For small angles the distance d and the baseline form a right triangle with tan π approximately equal to one AU over d; defining the parsec so that π equals one arcsecond when d equals one parsec collapses the relation to the textbook formula d in parsecs equals one over π in arcseconds.
Parallax must be a finite strictly positive number because division by zero is undefined and a non-positive angle is non-physical under this geometric formula; zero, negative, and near-zero values fail with invalid input instead of returning Infinity. Distance in light-years is obtained by multiplying the parsec result by three point two six one five six three seven seven seven, the same conversion factor used by sibling astronomy tools in this catalogue so multi-unit reports stay aligned.
This page intentionally covers only trigonometric parallax distance from an already-reduced arcsecond angle; milliarcsecond catalogue values must be divided by one thousand before calling, and photometric parallax, spectroscopic parallax, Lutz–Kelker bias corrections, and full Gaia query pipelines are separate search intents and separate landings. Keep units honest: if your source quotes mas, convert first so the numeric reciprocal matches the parsec scale your report claims.
Where stellar parallax calculators show up in real work
Secondary-school and introductory university astronomy courses assign parallax drills, convert Hipparcos-style arcsecond tables into parsecs, and compare nearest-star distances; a single trusted oracle speeds grading and demo setup. Science communicators turn arcsecond measurements into light-year scales for public displays without re-deriving unit conversions each time. Data pipelines that pre-filter nearby-star samples sometimes need a deterministic geometric distance column before heavier bias-correction or Bayesian distance modules run.
Research notebooks comparing raw reciprocal distances against more sophisticated estimators can hold parallax fixed and inspect the baseline d equals one over π result side by side. If you later need Hubble-law galaxy distances from recession velocity, full ΛCDM luminosity distance from redshift, or catalogue lookup of Gaia parallaxes, treat those as separate search intents and landings rather than overloading this stellar parallax calculator page.
What you can do with it
Planetarium and outreach demos
Turn published arcsecond parallaxes into human-readable parsec and light-year distances for exhibits and classroom widgets.
FAQ
What formula does this stellar parallax calculator use?
The classical geometric relation d (pc) = 1 / π with π in arcseconds, plus d (ly) = d (pc) × 3.261563777. By definition a star with parallax 1 arcsec is 1 parsec away.
Is this the same as a Hubble-law galaxy distance calculator?
No. Stellar parallax measures nearby stars geometrically from an angle; Hubble's law estimates galaxy distances from recession velocity and H0. Different inputs, units, and search intents.
What does it cost?
The browser tool is free and runs locally.
How do I use a parallax given in milliarcseconds?
Divide it by 1000 first, so the value is in true arcseconds. Gaia and many catalogues list milliarcseconds, and skipping that step makes the distance a thousand times too small.
How far away is Proxima Centauri by parallax?
Its parallax of roughly 0.7687 arcseconds gives about 1.3 parsecs. That nearest neighbour is a classic check, together with one arcsecond giving exactly one parsec.
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/astro/parallax-distance \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"parallax_arcsec":0.1}'const res = await fetch("https://api.kit.forhosting.com/astro/parallax-distance", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"parallax_arcsec": 0.1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/astro/parallax-distance",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"parallax_arcsec": 0.1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/astro/parallax-distance", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"parallax_arcsec":0.1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"parallax_arcsec":0.1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/astro/parallax-distance", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"parallax_arcsec": 0.1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "astro.parallax_distance",
"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 stellar parallax measures star distance
The calculator evaluates that closed form in deterministic floating-point arithmetic: no random seeds, no wall-clock timestamps, no network calls, and no model drift, so identical inputs always produce identical JSON.
What you send and what you get back
Classic textbook checks include one arcsecond recovering exactly one parsec, one tenth of an arcsecond recovering ten parsecs, and roughly zero point seven six eight seven arcseconds for Proxima Centauri recovering about one point three parsecs. If your catalogue lists milliarcseconds, divide by one thousand first so the input is true arcseconds. Because the engine is pure parse arithmetic, latency stays sub-millisecond and results never depend on external catalogues or clocks. Send one required finite number under the field parallax_arcsec: the stellar trigonometric parallax angle π in arcseconds. Missing fields, non-numeric strings, NaN, Infinity, zero, and negative parallax fail with invalid_input and are not charged. On success the response echoes cleaned parallax_arcsec, returns distance_pc as the primary result in parsecs, distance_ly as the same distance converted to light-years, exposes ly_per_pc as the fixed conversion factor used, includes a units hint object documenting arcseconds, parsecs, and light-years, sets method to stellar_parallax, and sets formula to the explicit reciprocal and conversion string for audit trails. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where stellar parallax calculators show up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Integration use cases
Homework and exam answer keys
Compute d = 1/π for textbook parallax angles so students and auto-graders share one closed-form ground truth in parsecs and light-years.
Nearby-star pipeline fixtures
Generate deterministic geometric distances from reduced parallax angles before applying bias corrections or Bayesian estimators in research notebooks.
Technical questions
What happens if the parallax angle is zero or negative?
The request fails with invalid_input. Distance d = 1/π requires a strictly positive parallax; zero or negative angles are undefined or non-physical and are never turned into Infinity or negative distances.
My catalogue lists milliarcseconds (mas). What should I do?
Divide by 1000 to convert mas to arcseconds, then send parallax_arcsec. This tool expects arcseconds only so the parsec definition applies directly.