ForHosting KIT · Developer Utilities

Telescope objective focal length calculator

This telescope objective focal length calculator works backward from the view you want.

● BetaFree · in your browser

Use it from WebAPIEmailTelegramApp soon

Enter the focal length of an eyepiece and the desired magnification, and it returns the objective focal length needed by a simple astronomical telescope. The calculation is useful when comparing optical tubes, planning a telescope build, or checking whether an eyepiece and objective combination can reach a particular power. Both focal lengths use the same unit, while magnification is a dimensionless ratio.

Turn a target power into an objective specification

Telescope specifications are often presented in the forward direction: divide the objective focal length by the eyepiece focal length to obtain magnification. Design and purchasing questions frequently begin at the other end. You may already own a 25 mm eyepiece, know that you want a 40x view, and need to identify an optical tube that makes that combination possible. This calculator rearranges the standard telescope magnification relationship and multiplies the desired power by the eyepiece focal length. In that example, 40 multiplied by 25 mm gives a required objective focal length of 1,000 mm. The result is a focal length, not an aperture diameter and not the physical tube length. Those measurements influence brightness, resolution, portability, and construction, but they are not interchangeable with the optical focal length calculated here. Treat the answer as a clean design target that can be compared with the stated focal length of a telescope objective or optical tube assembly.

Use consistent units and realistic magnification

The equation is unit-neutral as long as both focal lengths use the same unit. If the eyepiece value is entered in millimetres, the objective result is in millimetres; if it is entered in inches, the result is in inches. Magnification itself has no length unit and is commonly written with an x, such as 80x. Enter only the numeric power. A mathematically valid focal-length combination does not guarantee a useful image. Practical maximum magnification also depends on objective aperture, optical quality, atmospheric steadiness, target brightness, observer eyesight, and mechanical stability. Very high power can enlarge blur without revealing additional detail. Likewise, a requested objective focal length may not correspond to a readily available telescope. Use the computed value to shortlist equipment, then check the telescope aperture, focal ratio, mounting requirements, and manufacturer guidance. The calculator intentionally does not claim that every positive target magnification is advisable; it provides the exact focal-length relationship so that optical feasibility can be assessed separately.

Compare eyepieces, objectives, and observing plans

A useful planning method is to repeat the calculation for several eyepieces while holding the target magnification constant. A shorter-focal-length eyepiece requires a proportionally shorter objective focal length for the same power, while a longer eyepiece requires a longer objective. You can also hold the eyepiece constant and compare several target powers to see how quickly the required objective focal length changes. This is especially helpful when assembling an educational telescope, evaluating a replacement optical tube, or documenting the assumptions behind an observing setup. The output repeats both inputs, states the rearranged formula, and explains the unit relationship, making it suitable for a worksheet or an automated equipment-selection step. For an existing telescope whose objective focal length is already known, use a telescope magnification calculator instead; that solves the forward problem. This capability is deliberately focused on the inverse question, where objective focal length is the unknown and desired magnification is the design requirement.

What you can do with it

Plan a telescope build

Convert an available eyepiece and a target power into the objective focal length required by the design.

Compare optical tubes

Calculate a focal-length target before checking which commercial telescope tubes best match an observing plan.

Prepare an astronomy lesson

Demonstrate the rearranged magnification equation with reproducible values and clearly stated units.

FAQ

What formula does the calculator use?

It uses objective focal length = desired magnification × eyepiece focal length.

What unit is the answer in?

The answer uses the same length unit as the eyepiece focal length. Enter millimetres to receive millimetres.

Is magnification entered as 40 or 40x?

Enter the numeric value 40. Magnification is a positive dimensionless ratio.

Does the result tell me the objective aperture?

No. Objective focal length and aperture are different specifications; aperture must be selected separately.

Does a calculated combination guarantee a sharp image?

No. Image quality and useful power also depend on aperture, optical quality, atmospheric conditions, the target, and mount stability.

What does an API calculation cost?

Each API request costs $0.002; the same deterministic calculation can run free in the browser.

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/optics/telescope-objective-focal

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/optics/telescope-objective-focal \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"eyepiece_focal_length":25,"desired_magnification":40}'

const res = await fetch("https://api.kit.forhosting.com/optics/telescope-objective-focal", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "eyepiece_focal_length": 25,
    "desired_magnification": 40
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/optics/telescope-objective-focal",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "eyepiece_focal_length": 25,
    "desired_magnification": 40
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/optics/telescope-objective-focal", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"eyepiece_focal_length":25,"desired_magnification":40}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"eyepiece_focal_length":25,"desired_magnification":40}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/optics/telescope-objective-focal", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "eyepiece_focal_length": 25,
  "desired_magnification": 40
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "optics.telescope_objective_focal",
  "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.

Read the full KIT documentation →