ForHosting KIT · Math

Cylinder height from volume calculator

Get the missing height of a right cylinder from its volume and the radius of its base: with radius 3, a volume equal to ten times the base area means a height of exactly 10. Handy for tanks, cans and silos. Free in your browser.

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Worked example

If you enter

Volume: 282.7433388231
Radius: 3

You get

Volume: 282.7433388231
Height: 10
Base area: 28.2743338823

When you already know how much space a right circular cylinder holds and the radius of its circular base, the missing dimension is height. This cylinder height from volume calculator inverts the classic formula volume equals pi times radius squared times height, returning a single positive height so you can size tanks, pipes, columns, packaging, and classroom exercises without rearranging algebra by hand. A zero or negative radius is rejected because division by zero base area is undefined and a physical cylinder cannot have a collapsed base.

What the inverse cylinder formula means and when it applies

A right circular cylinder is the solid swept by a rectangle rotated around one side: every cross-section parallel to the base is a disk of the same radius, and the distance between the bases is the height. The volume formula used in every school textbook and engineering handbook is V equals pi times r squared times h. Solving for height is a one-step rearrangement: h equals V divided by pi r squared.

That quotient is exactly volume divided by base area, which is the average height of a solid whose base is a disk of radius r. The formula assumes a right circular cylinder—constant radius along the axis, bases perpendicular to the generators—not an oblique cylinder, a frustum, a barrel, or a pipe wall thickness problem. Units must be consistent: if radius is in centimetres, volume must be in cubic centimetres so that height comes out in centimetres; the calculator does not convert units for you.

Positive volume with positive radius always yields a unique positive height, which is why this inverse is so useful in reverse engineering: given a known fill volume and a mould or tank radius, height is determined. When radius approaches zero the base area collapses and height would need to grow without bound to hold a fixed volume; the capability therefore treats radius zero as invalid input rather than returning Infinity. Negative volume or negative radius have no geometric meaning for a solid cylinder and are rejected the same way.

Use this tool when your known quantities are volume and radius; if you instead know radius and height and want volume or surface areas, use a forward cylinder volume calculator instead.

When you need the height of a cylinder

Manufacturing and packaging teams size cans, bottles, and drums when the target fill volume and the die or mould radius are fixed and the free variable is height. Civil and mechanical notebooks recover the height of cylindrical tanks, silos, or columns from known capacity and base radius without pulling a full CAD stack for a two-scalar problem. Science classrooms and exam generators need a deterministic oracle that marks zero radius as invalid instead of silently returning Infinity that a buggy grader might accept.

Process engineers who know batch volume and vessel radius use the inverse height to check whether a vessel fits under a ceiling or on a rack.

What you can do with it

Tank and silo sizing from capacity

Given required storage volume and available base radius, compute the cylinder height needed so the vessel fits under a roof or on a skid.

Packaging and can design

Fix fill volume and can radius from tooling constraints, then solve for body height before ordering dies or labels.

FAQ

What happens if the radius is zero?

Height = V/(πr²) is undefined when the base area is zero, so a zero radius is rejected and not billed.

Which units should I use?

Use any consistent length unit: if radius is in metres, volume must be in cubic metres so height is in metres. The calculator does not convert units.

Is this a right circular cylinder only?

Yes. The formula assumes constant radius and bases perpendicular to the axis. Oblique cylinders, frustums, and barrels need different capabilities.

How do I find the height of a cylinder from its volume?

Divide the volume by the area of the circular base, pi times the radius squared. The result is the height in the same length unit as the radius, as long as the volume uses the matching cubic unit.

What if I know the radius and height and want the volume?

Then you need the forward calculation: volume equals pi times radius squared times height. This tool works the other way round, starting from a known volume and radius and returning only the height.

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

POSThttps://api.kit.forhosting.com/geom/cylinder-height-volume

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/geom/cylinder-height-volume \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"volume":282.7433388230814,"radius":3}'

const res = await fetch("https://api.kit.forhosting.com/geom/cylinder-height-volume", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "volume": 282.7433388230814,
    "radius": 3
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/geom/cylinder-height-volume",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "volume": 282.7433388230814,
    "radius": 3
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/geom/cylinder-height-volume", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"volume":282.7433388230814,"radius":3}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"volume":282.7433388230814,"radius":3}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geom/cylinder-height-volume", 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": 282.7433388230814,
  "radius": 3
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "geom.cylinder_height_volume",
  "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.

Technical notes

Enter a positive volume and a positive base radius in matching units; the endpoint divides volume by the base area pi r squared and returns height together with the echoed inputs, the base area used in the division, and a short formula string for display.

Input contract, response shape, and error behaviour

In particular, radius equal to zero raises an explicit error because height equals volume over pi r squared is undefined when the base area is zero—this matches the product requirement that a zero radius must not produce a numeric height. Example: volume approximately two hundred eighty-two point seven four and radius three yields height approximately ten, because pi times nine times ten recovers that volume. Failed validation is not billed. POST a JSON body with two required finite positive numbers: volume (aliases V or v) and radius (aliases r or R). Each field may arrive as a JSON number or as a numeric string; missing fields, empty strings, non-finite values, values at or below zero, and values outside the documented min and max limits fail with invalid_input naming the field. On success the body includes the echoed volume and radius rounded for stable display, height as the principal result, base_area equal to pi r squared used in the division, method set to right_cylinder_height_from_volume, and formula set to the string h = V / (π r²). Pair the response with your own unit labels; this endpoint does not emit plots, mesh geometry, or multi-step textbook prose beyond the formula field. Successful calls use prepaid KIT balance at the published $0.002 base price because the path is pure parse with no model tokens and no outbound network.

Integration use cases

Classroom and exam auto-grading

Check student answers for h = V/(πr²) with a deterministic API that rejects zero radius as invalid_input instead of Infinity.

Technical questions

How do I find the height of a cylinder from volume and radius?

Send positive finite numbers volume and radius. The API returns height = volume / (π · radius²), plus base_area and the formula string h = V / (π r²).

What does the cylinder height from volume calculator cost?

The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.

Read the full KIT documentation →

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