Hohmann transfer orbit semi-major axis calculator
A Hohmann transfer from a radius of 7,000 km to 42,164 km follows an ellipse with a semi-major axis of 24,582 km, the average of the two. Enter the inner and outer orbit radii in the same unit to get the transfer ellipse size. Free in your browser.
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Worked example
- Inner radius
- 7,000
- Outer radius
- 42,164
- Semi major axis
- 24,582
This Hohmann transfer orbit semi-major axis calculator finds the size parameter of the elliptical transfer path between two circular, coplanar orbits. Enter the inner and outer orbital radii, measured from the center of the same central body and expressed in the same length unit. The calculator returns their arithmetic average, which is the transfer ellipse semi-major axis. It provides a focused, deterministic result for mission-design exercises, classroom work, spreadsheet checks, and software pipelines. No central-body mass or gravitational parameter is needed for this geometric step, and non-numeric radii are rejected with a clear invalid input error.
Why the transfer ellipse uses the average radius
A classical Hohmann transfer connects two circular, coplanar orbits around one central body with an ellipse tangent to both circles. At one end of the transfer ellipse, the spacecraft is at the inner orbital radius; at the opposite end, it is at the outer orbital radius. Those two distances are the periapsis and apoapsis radii of the transfer ellipse.
For any ellipse measured from a focus, the sum of periapsis and apoapsis equals twice the semi-major axis. For example, a transfer from a radius of 7,000 kilometers to a radius of 42,164 kilometers has a transfer semi-major axis of 24,582 kilometers. Both inputs must describe center-to-spacecraft radius, not altitude above a surface.
If a source provides altitude, add the central body's reference radius before using this calculator. The labels inner and outer describe their intended orbital roles; the calculation itself returns the arithmetic average of the two finite values supplied. This focused result is commonly the first intermediate value used before applying vis-viva equations or calculating the transfer time.
Where this result fits in Hohmann transfer planning
The semi-major axis is one ingredient in an ideal two-impulse Hohmann transfer analysis, not a complete maneuver plan. Comparing those speeds with the circular speeds at the initial and destination radii gives the two ideal velocity changes. The same semi-major axis can also feed Kepler's third law; half of the transfer ellipse period is the ideal coast time between burns.
Those later steps introduce assumptions and additional inputs that this capability intentionally does not hide. It does not model inclination changes, eccentric starting or destination orbits, plane changes, finite burns, atmospheric drag, third-body forces, launch windows, navigation error, or propellant margins. Operational spacecraft commanding requires current state data, appropriate reference frames, perturbation models, uncertainty analysis, and independent flight-dynamics review.
What you can do with it
Mission concept calculations
Find the transfer ellipse semi-major axis before estimating ideal transfer velocities, delta-v, or coast time.
Astronomy and physics coursework
Check the geometric first step of a Hohmann transfer exercise with a transparent formula and structured output.
FAQ
Should I enter orbital radius or altitude?
Enter radius measured from the central body's center. If you have altitude above a surface, add the body's reference radius first.
What units does the result use?
The result uses the same length unit as the inputs. Both radii must use one consistent unit because no conversion is performed.
Does this calculate Hohmann transfer time or delta-v?
No. It returns only the transfer ellipse semi-major axis. Transfer time and velocity changes require additional formulas and the central body's gravitational parameter.
What happens when a radius is non-numeric?
Missing, blank, non-numeric, and non-finite radius values are rejected.
Do I need the mass of the central body?
No. The semi-major axis is purely geometric: it is the average of the inner and outer radii, so no mass or gravitational strength of Earth, the Sun or another body is needed for this step.
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/hohmann-transfer-sma \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"inner_radius":7000,"outer_radius":42164}'const res = await fetch("https://api.kit.forhosting.com/astro/hohmann-transfer-sma", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"inner_radius": 7000,
"outer_radius": 42164
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/astro/hohmann-transfer-sma",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"inner_radius": 7000,
"outer_radius": 42164
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/astro/hohmann-transfer-sma", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"inner_radius":7000,"outer_radius":42164}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"inner_radius":7000,"outer_radius":42164}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/astro/hohmann-transfer-sma", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"inner_radius": 7000,
"outer_radius": 42164
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "astro.hohmann_transfer_sma",
"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
The browser calculator is free, while API use costs $0.002 per request.
Why the transfer ellipse uses the average radius
The required calculation is therefore a_t = (r_inner + r_outer) / 2. This is a geometric relationship, so it does not require the mass of Earth, the Sun, or another primary.
How to enter radii and read the response
Use one consistent length unit for both inputs. The service does not infer units, attach a conversion factor, or repair mixed-unit inputs. Missing values, blank strings, words, arrays, objects, NaN, and infinity are invalid because either radius would not be a usable finite number. Retain enough precision in the orbital radii for the next calculation and round only when presenting the answer, especially when transfer velocity or timing calculations will consume this semi-major axis later. Send inner_radius and outer_radius as finite JSON numbers or numeric strings. If both radii are in kilometers, semi_major_axis is in kilometers; if both are in meters, it is in meters. On success, the response echoes normalized inner_radius and outer_radius values, returns semi_major_axis, and includes the formula string for auditability. The arithmetic is deterministic and does not use network data, random values, or the current time, so the same valid request always produces the same JSON result.
Where this result fits in Hohmann transfer planning
After calculating a_t, an engineer or student can combine it with the central body's gravitational parameter in the vis-viva equation to find speed at the transfer ellipse's periapsis and apoapsis. The browser tool supports quick interactive checks at no charge, while automated workflows can call the API for $0.002 per request and receive the same deterministic contract used by the page.
Integration use cases
Software test fixtures
Generate deterministic reference values for mission-design forms, spreadsheets, SDKs, and orbital mechanics pipelines.
Technical questions
What formula does the calculator use?
It uses a_t = (r_inner + r_outer) / 2, the arithmetic average of the two orbital radii.