Telescope resolution calculator
See the diffraction limit of any telescope from its size and the colour of light: a 10 cm aperture at 550 nm resolves 1.3840368499 arcseconds, and larger mirrors or shorter wavelengths go finer. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Aperture
- 0.1
- Wavelength
- 0.00000055
- Angular resolution
- 0.00000671 rad
- Angular resolution rad
- 0.00000671
- Angular resolution arcsec
- 1.3840368499
- Rayleigh factor
- 1.22
This telescope resolution calculator returns the diffraction-limited angular resolution of a circular aperture from the classical Rayleigh criterion. The closed form is fully deterministic: theta equals one point two two times wavelength lambda over aperture diameter D, so larger apertures and shorter wavelengths resolve finer angular separations. With D and lambda in the same length units—metres preferred in SI—the primary result is in radians, and the response also reports arcseconds for common astronomical comparison. Well-known checks include a ten-centimetre amateur aperture at five hundred fifty nanometres yielding about six point seven micro-radians, and a two-point-four-metre space telescope at the same wavelength yielding a few tenths of a micro-radian. The engine uses only finite arithmetic with no network calls, no sampling, and no date-dependent shortcuts.
Where telescope resolution fits in study, observing, and software
Students meet the Rayleigh criterion when a textbook moves from geometric optics to diffraction, when a contest problem asks for the resolving power of a given objective, or when they compare amateur, professional, and space telescopes without full wave-optics machinery. Teachers can pre-generate answer keys for modest aperture and wavelength pairs without trusting opaque calculator apps that silently switch between arcseconds and milliarcseconds.
Developers call the same contract from scripts to seed deterministic test vectors for instrument simulators, to normalize user-entered diameters before mission or observatory demos, or to satisfy programming-challenge statements that demand theta rather than a hand-waved seeing value. Contest practice often needs a fast, offline source of diffraction limits so solutions can be checked without graphing calculators under time pressure.
Product and education tools use the formula when a learner types an aperture in metres and a wavelength in metres and the UI must show the Rayleigh angle in radians and arcseconds next to comparisons with famous telescopes.
What you can do with it
Homework and diffraction-limit checks
Compute θ from textbook aperture and wavelength pairs and verify Rayleigh resolution before optics or astronomy problems.
Observatory and education software
Normalize user-entered D and λ into radians and arcseconds for planners, demos, and interactive lessons.
FAQ
What does the telescope resolution calculator cost?
It is free in your browser on this page.
How is angular resolution defined?
For a circular aperture the Rayleigh criterion is θ = 1.22 · λ / D, with θ in radians when λ and D share the same length units (SI metres preferred).
What happens if the aperture is zero?
Zero or negative aperture makes θ = 1.22·λ/D undefined.
Does this include atmospheric seeing?
No. It returns only the diffraction-limited Rayleigh angle. Seeing, figure error, and detector sampling are out of scope.
Why are results rounded to a precision?
Default precision is 10 decimal places; you can set precision from 0 to 15.
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/telescope-resolution \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"aperture":0.1,"wavelength":5.5e-7}'const res = await fetch("https://api.kit.forhosting.com/astro/telescope-resolution", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"aperture": 0.1,
"wavelength": 5.5e-7
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/astro/telescope-resolution",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"aperture": 0.1,
"wavelength": 5.5e-7
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/astro/telescope-resolution", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"aperture":0.1,"wavelength":5.5e-7}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"aperture":0.1,"wavelength":5.5e-7}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/astro/telescope-resolution", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"aperture": 0.1,
"wavelength": 5.5e-7
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "astro.telescope_resolution",
"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.
Limits
max_abs_aperture | 1000000 |
max_abs_wavelength | 1000 |
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
What Rayleigh resolution means and what the response contains
The Rayleigh criterion states that two equal point sources imaged through a circular aperture are just resolved when the central peak of one Airy pattern falls on the first dark ring of the other. For monochromatic light of wavelength lambda the corresponding minimum angular separation is theta equals one point two two times lambda over D, where D is the clear aperture diameter. That limit is a diffraction floor, not a guarantee of scientific performance: atmosphere, figure error, and detector sampling can all degrade the real beam, but the Rayleigh angle remains the standard textbook figure of merit for comparing telescopes and for sizing apertures against a science goal. This calculator returns the normalized aperture and wavelength you supplied, the computed angular_resolution and angular_resolution_rad fields in radians, angular_resolution_arcsec for sky units, the fixed rayleigh_factor of one point two two, a unit string rad, the method tag rayleigh_criterion, the precision used, and a short formula reminder. There is no approximate wave-optics integrator and no random sampling of pupil modes: the engine either builds exact floating-point theta inside the supported magnitude range or rejects the input with invalid_input. Rejected cases include missing aperture or wavelength, non-finite values, magnitudes above the documented ceilings, zero or negative aperture—because division by D is undefined—and non-positive wavelength.
How aperture and wavelength are read and how theta stays reproducible
Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong resolution. Wavelength must likewise be positive so the product has a physical meaning. The preferred fields are aperture for the diameter D in metres and wavelength for lambda in metres, but aliases diameter, D, and aperture_m for the first, and lambda, wavelength_m, and wl for the second, are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Aperture must be strictly positive and non-zero: if D is zero, negative, or negative zero, the request fails with invalid_input because Rayleigh resolution theta equals one point two two lambda over D is undefined for a zero or negative aperture. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for aperture, wavelength, and the resolution fields, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the Rayleigh formula yourself.
Where telescope resolution fits in study, observing, and software
On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with surface-gravity or light-travel-time tools when you need related astronomy steps, and with other physics endpoints when you are building a small lab of free, deterministic science helpers.
Integration use cases
Deterministic test fixtures
Generate reproducible angular resolutions for unit tests, property checks, and CI assertions on instrument modules.