Aperture from focal ratio calculator
A 1200 mm telescope at f/6 has a 200 mm aperture: the focal length divided by the f-ratio. Enter both numbers from the tube or catalogue and get the diameter with its f-stop label. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Focal length
- 1,200
- Focal ratio
- 6
- Aperture mm
- 200 mm
- Aperture diameter
- 200
- F stop label
- f/6
Amateur astronomers, telescope shoppers, and optical lab students constantly need the clear aperture of a tube or lens when they already know the focal length and the f-ratio printed on the tube or catalog card. The classical relation is simple: aperture diameter equals focal length divided by the focal ratio, so a twelve-hundred millimetre f slash six system has a two-hundred millimetre entrance aperture. This aperture from focal ratio calculator accepts those two numbers, returns the diameter in millimetres with a printable f-stop label, and rejects a zero or negative focal ratio with a clear validation error instead of emitting Infinity.
How aperture diameter follows from focal length and focal ratio
Start with two quantities that every telescope or camera lens specification already carries: the focal length f, measured here in millimetres, and the focal ratio N, also called the f-number or relative aperture, which is dimensionless. By definition the f-number is the ratio of focal length to entrance-pupil diameter, written N equals f over D. Rearranging that identity gives the aperture diameter you need when the manufacturer quotes f and N but not the clear aperture: D equals f divided by N.
Because N is dimensionless, D inherits the same length unit as f; this calculator standardises on millimetres so a twelve-hundred millimetre f slash six Newtonian reports two hundred millimetres of aperture, matching common Dobsonian and refractor listings. Photographers write the same ratio as f slash N on lens barrels; astronomers speak of fast f slash four tubes versus slow f slash ten planetary scopes. Either way the continuous quantity is always this division.
Focal length must be strictly positive; a zero or negative f is not a usable thin-lens or telescope focal length for this formula. Negative N would invert the sign of the diameter and is not physical for this classical definition.
Where aperture-from-f-ratio calculators show up in real work
Astronomy clubs and retail staff constantly convert a stated focal length and f-ratio into clear aperture when comparing light grasp, resolving power estimates, or whether a tube will fit a given mount and dew shield. Curriculum authors assign problems that ask for D given f and N so students practice the same identity used on every telescope specification sheet; a single trusted oracle speeds grading and demo setup.
Optical engineering notebooks and product databases need the same closed form when catalog rows list focal length and relative aperture but omit pupil diameter, or when sanity-checking that a proposed f-ratio for a given tube length matches a target aperture. Astrophotography planners who start from a desired plate scale or image scale often know the camera-side focal length and the target f-ratio of a reducer or barlow train and want the effective aperture implied by those two numbers before estimating exposure time.
If you later need the inverse conversion from focal length and diameter into an f-number, Rayleigh resolution from aperture and wavelength, telescope magnification from objective and eyepiece, or depth-of-field tables, treat those as separate search intents and landings rather than overloading this aperture-from-focal-ratio page.
What you can do with it
Telescope shopping and club demos
Convert catalog focal length and f-ratio into clear aperture diameter in millimetres so buyers and educators compare light grasp on equal footing.
Homework and lab answer keys
Generate D = f/N ground truth for textbook pairs so teachers and auto-graders share one deterministic oracle.
Catalog and spreadsheet sanity checks
Fill missing aperture columns when product data lists only focal length and relative aperture, or verify that a proposed f-ratio matches a target pupil size.
FAQ
What formula does this aperture calculator use?
The classical definition rearranged: D = f / N, where f is focal length in millimetres and N is the dimensionless focal ratio (f-number).
What units does the calculator use?
Focal length is millimetres; focal ratio is dimensionless.
How is this different from an f-stop calculator?
An f-stop calculator finds N = f/D from known focal length and aperture diameter. This tool does the inverse: given f and N, it returns D. Different search intent, complementary formulas.
What does it cost?
The browser tool is free and runs locally.
Why can't the focal ratio be zero?
Because the aperture is the focal length divided by the f-ratio, and dividing by zero gives no diameter. A negative value would flip the sign, which has no physical meaning, so enter a positive f-number.
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/aperture-from-focal-ratio \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"focal_length":1200,"focal_ratio":6}'const res = await fetch("https://api.kit.forhosting.com/astro/aperture-from-focal-ratio", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"focal_length": 1200,
"focal_ratio": 6
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/astro/aperture-from-focal-ratio",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"focal_length": 1200,
"focal_ratio": 6
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/astro/aperture-from-focal-ratio", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"focal_length":1200,"focal_ratio":6}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"focal_length":1200,"focal_ratio":6}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/astro/aperture-from-focal-ratio", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"focal_length": 1200,
"focal_ratio": 6
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "astro.aperture_from_focal_ratio",
"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 aperture diameter follows from focal length and focal ratio
Focal ratio must also be strictly positive: when N approaches zero the formal diameter diverges, and an exact zero would divide by zero, so the request fails with invalid input rather than returning Infinity or NaN.
What you send and what you get back
Focal length is in millimetres; focal ratio is the dimensionless f-number N. Both fields are required. Classic checks include twelve hundred millimetres at f slash six yielding two hundred millimetres of aperture, eight hundred millimetres at f slash four again yielding two hundred millimetres, and a fifty millimetre camera lens at f slash two yielding twenty-five millimetres of entrance pupil. Send two finite positive numbers under the fields focal_length and focal_ratio. Aliases accepted by the solver include f, focal, fl, and focal_length_mm for the first value, and N, f_number, f_ratio, fstop, and f_stop for the second. Missing fields, non-numeric strings, NaN, and Infinity fail with invalid_input and are not charged. When focal_ratio is zero, negative, or vanishingly close to zero, the request fails with a message that aperture D equals f over N would divide by zero or invert sign, so clients can prompt for a real f-ratio instead of guessing. On success the response echoes cleaned focal_length and focal_ratio, the aperture diameter as aperture_mm and aperture_diameter in millimetres, a human-readable f_stop_label such as f slash six, the formula string D equals f slash N, and unit set to mm. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where aperture-from-f-ratio 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.
Technical questions
What happens if the focal ratio is zero or negative?
The request fails with invalid_input. Aperture D = f/N is undefined when N = 0 and non-physical when N is negative, so the solver rejects non-positive focal ratio instead of returning Infinity.