Cylinder volume calculator
Enter the radius and height of a right cylinder and get three answers at once: with radius 3 and height 5, the volume is 45π, the curved wall 30π and the full surface 48π. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Radius
- 3
- Height
- 5
- Volume
- 141.3716694115
- Lateral surface area
- 94.2477796077
- Total surface area
- 150.7964473723
- Base area
- 28.2743338823
A right circular cylinder is one of the most common solids in school geometry, packaging, civil takeoff, and manufacturing: a circular base extruded straight up by a constant height. Given a positive base radius r and a positive height h, three closed-form measures answer most practical questions at once. Volume is π r squared times h—the amount of space inside a tank, drum, or pipe segment of uniform cross-section. Lateral surface area is two π r h—the curved wall only, which matters for labels, insulation wrap, and side coating. Total surface area is two π r times (r plus h), adding both circular bases to the wall for full paint, material skin, or heat-transfer surface.
What volume and surface area mean for a right cylinder
A right circular cylinder has two congruent circular bases whose centres are joined by a line segment perpendicular to both base planes; that segment length is the height h, and each base has radius r. Lateral surface area unwraps the curved wall into a rectangle of width equal to the circumference two π r and height h, giving L equals two π r h.
Total surface area adds the two bases: T equals two π r squared plus two π r h, which factors as two π r times (r plus h). Units stay consistent with whatever length unit you pass for r and h—metres yield cubic metres of volume and square metres of area; inches yield cubic and square inches. A classic classroom check is r equals three and h equals five: volume is forty-five π, lateral area is thirty π, and total surface is forty-eight π.
The arithmetic is elementary multiplications after coercion, so there is no iteration, no Monte Carlo sampling, no dependence on wall-clock time, and no need for slant height of a cone or coordinates of generators in the input. Related solids such as hollow tubes (inner and outer radius) or oblique cylinders need different formulas and are out of scope here.
Practical tips, limits, and related searches
When teaching, prefer paired examples: radius three and height five against forty-five π volume and thirty π lateral area; radius one and height one for a unit cylinder with volume π and total surface four π; and a zero or negative dimension to demonstrate the hard rejection path. Prefer this tool when you already know the right-cylinder radius and height and need volume plus both surface measures in one shot.
Round-trip checks are easy: after solving, confirm that lateral surface equals circumference times height, that total surface equals two times base area plus lateral surface, and that volume equals base area times height within floating tolerance. If you need only planar circle measures without height, use the dedicated circle equation capability; if you need arc length of a circular sector on the base, use the arc length calculator instead of forcing a degenerate cylinder height.
What you can do with it
Tank, drum, and packaging takeoff
Turn a cylinder radius and fill height into volume for capacity estimates, or wall and total skin area for paint, wrap, and material orders.
CAD and manufacturing pre-checks
Validate stock cylinder dimensions in scripts before nesting or quoting: volume for mass estimates, lateral and total area for coating and heat treatment.
FAQ
What is the formula for the volume of a right cylinder?
With base radius r and height h, volume is π·r²·h (base area times height). Radius and height must use the same length unit.
What is lateral surface area versus total surface area?
Lateral surface area is the curved wall only: 2·π·r·h. Total surface area adds both circular bases: 2·π·r·(r+h).
Why are zero or negative radius and height rejected?
A solid right cylinder needs strictly positive radius and height.
Does this handle hollow pipes or oblique cylinders?
No. This tool models a solid right circular cylinder from outer radius and height only. Hollow walls and slanted axes need different formulas.
Is the cylinder volume calculator free?
The browser tool is free and runs locally.
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/geom/cylinder \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"radius":3,"height":5}'const res = await fetch("https://api.kit.forhosting.com/geom/cylinder", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"radius": 3,
"height": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geom/cylinder",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"radius": 3,
"height": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geom/cylinder", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"radius":3,"height":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"radius":3,"height":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geom/cylinder", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"radius": 3,
"height": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geom.cylinder",
"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.
Limits
max_radius | 1000000000000 |
min_radius | 1e-15 |
max_height | 1000000000000 |
min_height | 1e-15 |
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
This capability packages those identities as deterministic JSON with no computer-algebra system, no random seeds, and the same pure solve function in the free browser tool and the prepaid API path. Non-positive radius or height is rejected with invalid_input so scripts and grading pipelines see an honest error instead of a silent absolute value or a zero-volume solid.
What volume and surface area mean for a right cylinder
The volume formula V equals π r squared h follows from the base area times height: every cross-section parallel to the bases is the same disk of area π r squared, so the solid is a straight prism with a circular footprint. Zero or negative dimensions are not accepted under this contract because they do not describe a solid right cylinder of positive extent; the API returns invalid_input rather than inventing a magnitude.
How to call the API and what comes back
Both must be finite numbers strictly greater than zero and inside the published limits. Use it from geometry homework pipelines, packaging and tank takeoff scripts, interview-prep sandboxes, CAD pre-checks, or any workflow that needs reproducible cylinder numbers without installing a computer-algebra package on every machine. Send a JSON body with radius and height. Field radius is the positive base radius; aliases r and R are accepted. Field height is the positive height; aliases h and H map to the same meaning. On success the response echoes radius and height; returns volume, lateral_surface_area, and total_surface_area as the primary results; and includes base_area for one circular base, circumference of the base circle, method set to right_cylinder, and a short formula block documenting the closed forms. Failed validation—missing a required field, a non-finite number, a non-positive radius or height, or a value outside published limits—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price. Pair the call with unit conversion only when your source data mixes millimetres and metres; this capability does not convert linear units for you, so keep r and h in the same unit before you send the request.
Practical tips, limits, and related searches
Keep radius and height inside the published positive range up to one trillion so intermediate products stay finite in IEEE double precision on the Worker and in the browser. Because the formulas only need r and h, students can recompute by hand for nice fractions of π and match the API line by line after dividing reported floats by π if desired. This landing targets people searching for a cylinder volume calculator or lateral and total surface area from radius and height; it is not a cone, sphere, or pipe-wall thickness tool. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when users type impossible measures while learning the contract.
Integration use cases
Homework checks for cylinder volume and surface area
Give students a radius and height; compare their hand-computed volume, lateral area, and total surface against a deterministic API or free browser result.