Diameter of cone
Turn a cone's volume and height into the diameter of its base, which is twice √(3V ÷ (π·h)), without rearranging the formula by hand. Give both in the same unit system and the answer comes back in the matching length unit. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Volume
- 94.2477796077
- Height
- 9
- Diameter
- 6.324555
- Radius
- 3.162278
- Pi
- 3.1415926536
- Decimal places
- 6
The diameter of cone calculator reverses the standard volume formula: given the volume of a right circular cone and its perpendicular height, it returns the diameter of its circular base. Instead of rearranging V = (1/3)·π·r²·h by hand, squaring and taking a root on a calculator, you send two numbers and get the diameter, rounded to the precision you choose. It is useful whenever the space a conical object occupies is known but its footprint is not — a hopper, a funnel, a conical tank, a pile of grain.
From volume and height back to a diameter
The volume of a right circular cone is one third of the volume of the cylinder that would contain it: V = (1/3)·π·r²·h, where r is the base radius and h is the perpendicular height from the apex to the center of the base. Solving that equation for the radius gives r = √(3V / (π·h)), and the diameter is simply twice the radius.
You provide the volume and the height in any consistent unit system — cubic meters and meters, cubic inches and inches, liters and centimeters — and the result comes back in the matching linear unit. If you feed it cubic feet and feet, the diameter is in feet. There is nothing to configure except how many decimal places you want in the answer.
Units, precision and edge cases
The calculator does not convert units, and that is deliberate: mixing systems silently is the most common source of wrong geometry results in automated pipelines, so the input contract keeps you in control. Whatever unit cubed you send as volume must correspond to the unit you send as height. The optional decimals parameter controls half-up rounding of the result, from 0 to 12 places, with a default of 6.
Internally the computation uses double-precision arithmetic and the full value of Math.PI, so the only rounding that happens is the one you explicitly asked for. Extremely large or small magnitudes that overflow double precision are also rejected rather than returned as Infinity.
Where it fits in real work
Engineers sizing silos, hoppers and conical tanks often know the capacity they need and the vertical space available, and must derive the floor footprint from those two constraints — that is exactly this computation. The same applies in reverse logistics for funnels and nozzles, in agriculture for estimating the base of a stored pile from its volume and repose height, and in education for checking homework against a trusted source.
What you can do with it
Size a conical hopper
Given the required storage capacity and the vertical clearance, derive the base diameter the hopper will occupy on the plant floor.
Estimate a grain pile footprint
From the measured volume and the height of a conical pile, compute how much ground area it covers before choosing a storage site.
Check geometry homework
Verify the diameter step of a cone-volume exercise against a deterministic reference instead of redoing the algebra by hand.
FAQ
Which formula does it use?
It solves V = (1/3)·π·r²·h for the radius, r = √(3V / (π·h)), and returns twice that value as the diameter.
What units does the result have?
The linear unit consistent with your inputs: if the volume is in cubic meters and the height in meters, the diameter is in meters.
What happens with a zero or negative input?
Volume and height must both be positive finite numbers, and rejected requests are not billed.
How precise is the result?
The computation uses double-precision arithmetic and full Math.PI; the only rounding is the half-up rounding at the decimals you request, from 0 to 12 places (default 6).
Does it work for oblique cones?
No. It assumes a right circular cone, where the apex sits directly above the center of the circular base.
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/math/diameter-of-cone \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"volume":94.24777960769379,"height":9}'const res = await fetch("https://api.kit.forhosting.com/math/diameter-of-cone", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"volume": 94.24777960769379,
"height": 9
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/diameter-of-cone",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"volume": 94.24777960769379,
"height": 9
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/diameter-of-cone", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"volume":94.24777960769379,"height":9}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"volume":94.24777960769379,"height":9}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/diameter-of-cone", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"volume": 94.24777960769379,
"height": 9
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.diameter_of_cone",
"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 same code runs free in your browser and behind the paid API, so the number you see on this page is exactly the number your integration receives.
From volume and height back to a diameter
This endpoint performs that rearrangement for you, in a single deterministic step with no iteration and no approximation beyond the value of π itself.
Units, precision and edge cases
Both values must be positive finite numbers; a zero or negative volume or height has no physical meaning for a cone and is rejected with an invalid_input error, which is never billed.
Where it fits in real work
Because the endpoint is a pure function with no state and no network calls, it is safe to call inside loops, batch jobs and CI checks. It runs on our global edge with the same code that runs free in your browser on this page, so you can validate a case by hand here and then automate it via the API for $0.002 per request, with the guarantee that both paths produce identical output.
Technical questions
What does it cost?
$0.002 per request via the API. It is also free to run in your browser on this page.