Hollow cylinder volume calculator
Get the volume of material in a tube wall from its outer radius, inner radius and height, so 5, 3 and 10 give 160π, the gap between an outer 250π and an inner 90π. Wall thickness comes too. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Outer radius
- 5
- Inner radius
- 3
- Height
- 10
- Wall thickness
- 2
- Annular area
- 50.2654824574
- Outer volume
- 785.3981633974
- Inner volume
- 282.7433388231
A hollow cylinder — also called a tube or annular cylinder — is a solid right circular cylinder of outer radius R with a concentric cylindrical hole of inner radius r along the full height h. Students, fabricators, and engineers need the material volume of that wall, not only the outer envelope: V equals pi times (R squared minus r squared) times h.
What a hollow cylinder is and why material volume differs from outer volume
A right hollow cylinder is the set of points whose distance from a fixed axis lies between an inner radius r and an outer radius R, extruded straight along a height h. The outer solid cylinder of radius R and height h has volume pi R squared h; the inner void of radius r and the same height has volume pi r squared h; the material that remains is exactly the difference, which factors as pi times (R squared minus r squared) times h.
That identity is the closed form every textbook quotes for the volume of a tube, a pipe wall, a bushing, or a cylindrical shell with concentric circular ends. Wall thickness is the simple difference R minus r, and the annular area in a cross-section perpendicular to the axis is pi times (R squared minus r squared), so material volume is also annular area times height. Units stay consistent with whatever length unit you pass for R, r, and h: millimetres yield cubic millimetres of material; metres yield cubic metres.
A classic classroom check is outer radius five, inner radius three, and height ten: the outer volume is two hundred fifty pi, the inner volume is ninety pi, and the material volume is one hundred sixty pi, with wall thickness two. Related solids such as a filled right cylinder (no bore) or an oblique tube need different formulas and are out of scope here.
Prefer this landing when your search intent is hollow cylinder volume from outer radius, inner radius, and height, especially material volume of the wall rather than fluid capacity alone.
Practical tips, classroom checks, and related searches
When teaching, prefer paired examples: outer five, inner three, height ten against material volume one hundred sixty pi; outer four, inner two, height one for a thin short tube with material volume twelve pi; and an inverted pair such as inner five and outer three to demonstrate the hard rejection path that names the radius ordering.
Round-trip checks are easy: after solving, confirm that material volume equals outer volume minus inner volume, that annular area times height equals material volume, and that wall thickness equals outer radius minus inner radius within floating tolerance. This landing targets people searching for a hollow cylinder volume calculator or material volume from outer and inner radius and height; it is not a solid-only cylinder tool, a cone solver, or a unit converter.
Prefer this tool when you already know the outer radius, the inner radius, and the height and need the tube wall volume in one shot. If you need only a solid right cylinder without a bore, use the dedicated cylinder volume calculator; if you need plumbing-oriented pipe wording for the same annular geometry under a different search phrase, use the pipe volume calculator instead of forcing this hollow-cylinder contract into the wrong landing.
What you can do with it
Homework and exam preparation
Compute hollow-cylinder material volume, outer and inner volumes, and wall thickness from textbook outer radius, inner radius, and height, and verify that ri ≥ ro is rejected.
Tube and bushing material estimates
Size steel, aluminium, or plastic wall volume for straight hollow stock from known outer radius, inner radius, and cut height before ordering or nesting.
FAQ
What is the formula for the volume of a hollow cylinder?
With outer radius R, inner radius r, and height h, the material volume is V = π(R² − r²)h. That is the outer solid volume πR²h minus the void volume πr²h.
Do I enter diameter or radius?
If you have diameters, divide each by two before calling, or convert in your client.
What does the hollow cylinder volume calculator cost?
It is free in your browser on this page.
Is material volume the same as capacity?
No. Material volume is the solid wall π(R² − r²)h. The bore capacity (inner volume) is πr²h. Outer volume is the solid envelope πR²h. This tool reports all three.
What if the inner radius equals or exceeds the outer one?
The tool refuses it, because there would be no wall of positive thickness left. The inner radius must be strictly smaller than the outer radius, and all three lengths must be positive.
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/hollow-cylinder \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"outer_radius":5,"inner_radius":3,"height":10}'const res = await fetch("https://api.kit.forhosting.com/geom/hollow-cylinder", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"outer_radius": 5,
"inner_radius": 3,
"height": 10
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geom/hollow-cylinder",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"outer_radius": 5,
"inner_radius": 3,
"height": 10
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geom/hollow-cylinder", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"outer_radius":5,"inner_radius":3,"height":10}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"outer_radius":5,"inner_radius":3,"height":10}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geom/hollow-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
{
"outer_radius": 5,
"inner_radius": 3,
"height": 10
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geom.hollow_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.
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 hollow cylinder volume calculator accepts three positive finite lengths with the inner radius strictly below the outer radius and returns material volume, outer and inner volumes, wall thickness, and annular cross-sectional area in one deterministic JSON payload. When the inner radius equals or exceeds the outer radius, or any dimension is missing, zero, negative, or non-finite, the tool returns invalid_input instead of a silent NaN or a zero-thickness shell. Through the API a successful request costs $0.002; validation failures are not charged.
What a hollow cylinder is and why material volume differs from outer volume
Zero or negative dimensions do not describe a solid of positive extent under this contract, and an inner radius that is not strictly below the outer radius does not describe a hollow wall with positive thickness; both classes of input return invalid_input rather than inventing an absolute value or printing a zero wall.
How to call the API and what the response contains
Use it from geometry homework pipelines, metal and plastic tube takeoff scripts, interview-prep sandboxes, CAD pre-checks, or any workflow that needs reproducible hollow-cylinder numbers without installing a computer-algebra package on every machine. Send a JSON body with outer_radius, inner_radius, and height. Field outer_radius is the positive outer radius; aliases R, ro, r_outer, and outer_r are accepted. Field inner_radius is the positive inner radius; aliases r, ri, r_inner, and inner_r map to the same meaning. Field height is the positive axial height; aliases h, H, length, and L are accepted for form and spreadsheet callers. All three must be finite numbers strictly greater than zero, and inner_radius must be strictly less than outer_radius. On success the response echoes outer_radius, inner_radius, and height; reports wall_thickness as outer minus inner; annular_area as pi times the difference of the squared radii; outer_volume as pi R squared h; inner_volume as pi r squared h; material_volume as pi times (R squared minus r squared) times h; and short formula strings so a student or a log line can verify the identity without reading the source. Failed validation — missing a required field, a non-finite number, a non-positive dimension, or an inner radius that equals or exceeds the outer radius — returns invalid_input with a message that names the failing constraint, and those failures are never charged. Pricing is a flat $0.002 per successful request with unit item. 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, r, and h in the same unit before you send the request.
Practical tips, classroom checks, and related searches
Because the formulas only need three positive lengths with r less than R, students can recompute by hand for nice multiples of pi and match the API line by line after dividing reported floats by pi if desired. Keep dimensions moderate so intermediate products stay finite in IEEE double precision on the Worker and in the browser. 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
Deterministic geometry fixtures
Generate reproducible annular-cylinder metrics for unit tests, contest validators, and CI assertions without hand-rolled wall-volume logic.
Technical questions
What if the inner radius equals or exceeds the outer radius?
The handler returns invalid_input. A hollow cylinder requires a positive wall: inner_radius must be strictly below outer_radius.