# Cylinder Calculator

> Computes the volume, base area, lateral (curved) surface area and total surface area of a right circular cylinder from its radius and height.

- Calculator id: `cylinder` · Category: Geometry (`geometry`) · Tool name: `calculate_cylinder_properties`
- Canonical page: https://tttkmbb.com/geometry/cylinder · This document: https://tttkmbb.com/geometry/cylinder.md · JSON definition: https://tttkmbb.com/geometry/cylinder.json

## Purpose

Computes the volume, base area, lateral (curved) surface area and total surface area of a right circular cylinder from its radius and height.

**Use when:** You need the capacity or surface of a can, tank, pipe, pillar or any straight circular cylinder.

**Do not use when:** The cylinder is hollow (compute outer minus inner), tilted (oblique), or tapers to a point (use cone).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `radius` | number | units | required | Radius of the circular base. (> 0) |
| `height` | number | units | required | Distance between the two bases, measured perpendicular to them. (> 0) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `volume` | number | units³ | π × r² × h. |
| `base_area` | number | units² | π × r², area of one circular end. |
| `lateral_area` | number | units² | 2 × π × r × h, the curved side only. |
| `total_surface_area` | number | units² | 2 × π × r × (r + h), both ends plus the side. |

## Formula

`volume = π · radius² · height; base_area = π · radius²; lateral_area = 2 · π · radius · height; total_surface_area = 2 · π · radius · (radius + height)`

## Data Sources

- Wikipedia – Cylinder — https://en.wikipedia.org/wiki/Cylinder (reference, retrieved 2026-09-23)
- Wolfram MathWorld – Cylinder — https://mathworld.wolfram.com/Cylinder.html (reference, retrieved 2026-09-23)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/cylinder?radius=…&height=…`
- `POST https://tttkmbb.com/api/v1/calculate/cylinder` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/cylinder · OpenAPI operationId `calculate_cylinder_properties` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "cylinder", "inputs": {…}}`

## Example

- Radius 3, height 5: inputs `{"radius":3,"height":5}` → `{"volume":141.3717,"base_area":28.2743,"lateral_area":94.2478,"total_surface_area":150.7964}`
- Radius 1, height 1: inputs `{"radius":1,"height":1}` → `{"volume":3.1416,"lateral_area":6.2832,"total_surface_area":12.5664}`

```
GET https://tttkmbb.com/api/v1/calculate/cylinder?radius=3&height=5
```

## Limitations

The cylinder is hollow (compute outer minus inner), tilted (oblique), or tapers to a point (use cone). All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**How do I get litres from the volume?**

Use the cube of the input unit: 1 dm³ = 1 litre, 1 cm³ = 1 ml, 1 m³ = 1000 litres. Enter dimensions in dm to read the volume directly in litres.

**Is the top included in the surface area?**

total_surface_area includes both circular ends; lateral_area is the curved side only (e.g. a label wrapped around a can).

## Related

- [Cone Calculator](https://tttkmbb.com/geometry/cone.md) — Same base but tapering to a point (one third of the volume).
- [Circle Calculator](https://tttkmbb.com/geometry/circle.md) — Properties of the circular base.
- [Volume Converter](https://tttkmbb.com/conversion/volume.md) — Convert the volume to litres or gallons.