HomeCalculatorsMathGeometryCylinder Calculator
Math calculator

Cylinder Calculator

Right circular cylinder V = πr²h and A = 2πr(r+h). Same engine as Solid Geometry. Not CAS. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Specification checked · 16/16 tests · Production surface contract 3/3 · v1.1.0
Input interpretation
Enter values to calculate.
Result
—
Model
Right circular cylinder volume and surface.
Scope
Right circular cylinder
Verification
Engine tested · 16/16 tests · Production surface contract 3/3 · Specification checked · v1.1.0
Named expert review
Optional · Not performed
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence
5 golden · 3 boundary · 8 property · Production surface contract 3/3 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.1.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain CURRENT) @ 2026-09-20T09:01:12.147Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

VolumeV = πr²h
Total surfaceA = 2πr(r+h)
iSame engine as /solid-geometry. The sphere and cone of this family share that hub. Not a second engine.

How to use

1

Enter r and h

Both must be positive. r = 1, h = 1 is the unit cylinder.

2

Read V and A

Unit cylinder V = π, A = 4π.

Example calculations

Common configurations with formula and result.

ϟ

Unit cylinder

r = 1, h = 1

V = π
π
ϟ

r = 2, h = 3

r = 2, h = 3

V = 12π
12π

Cylinder calculator specification

Version 1.1.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
A right circular cylinder of radius r>0 and height h>0 has volume πr²h, lateral area 2πrh, and total surface 2πr(r+h). This page is mode=cylinder on math.geometry.solid. Not oblique. Not CAS.
What it calculates
Right circular cylinder volume and surface.
Inputs
  • r
  • h
Outputs
  • volume
  • surface
  • lateral
Formula
V = πr²h, A = 2πr(r+h)
Assumptions
  • Right circular cylinder
  • Not oblique
  • Not CAS
Units
  • length (consistent units)
  • volume (length³)
  • area (length²)
Boundary conditions
  • r ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE
  • unknown mode → INVALID_MODE
Example
r=1 h=1 → V=π
Validation cases

2 published on this page · 16/16 tests · Production surface contract 3/3 · View evidence

  • r=1 h=1 → V=π A=4π
  • r=2 h=3 → V=12π
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Calculation version
1.1.0

Other calculators in this family: Angle Between Lines Calculator, Circle Calculator, Cone Calculator, Conic Section Calculator, Coordinate Geometry Calculator, Cross Product Calculator, Dot Product Calculator, Ellipse Calculator . Explore all Geometry.

→ Angle Between Lines Calculator Acute angle between two plane lines, each given by two points. Parallel is 0°. Perpendicular is 90°. Degenerate points are invalid. Same engine as Coordinate Geometry. Not a second engine. Not CAS. Runs locally. › → Circle Calculator Compute diameter, circumference, and area from r, or arc and sector from a central angle. Not the Pythagorean page. Runs locally. › → Cone Calculator Right circular cone V = (1/3)πr²h and slant l = √(r²+h²). Same engine as Solid Geometry. Not ISO 5167-5. Not CAS. Runs locally. › → Conic Section Calculator Axis-aligned ellipse, parabola, and hyperbola in standard form. Discovery /ellipse, /parabola, /hyperbola. Not the circle-only page. Not coordinate geometry. Not CAS. Runs locally. › → Coordinate Geometry Calculator Distance, midpoint, and slope of two points in the plane. Line through two points is /line-equation. Point-to-line distance is /point-line-distance. Intersection is /line-intersection. Angle is /angle-between-lines. Not the Pythagorean-only page. Runs locally. › → Cross Product Calculator Vector product u × v in R³. 2-D uses uz = vz = 0. Same engine as Vector. Not a matrix. Not CAS. Runs locally. › → Dot Product Calculator Scalar product u · v = ux vx + uy vy + uz vz. Same engine as Vector. Not a matrix. Not CAS. Runs locally. › → Ellipse Calculator Standard ellipse x²/a² + y²/b² = 1. Same engine as Conic Section. a = b is a valid ellipse with e = 0; the circle-only page is /circle. Not CAS. Runs locally. ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this a second solid engine?

No. It is mode=cylinder on math.geometry.solid, the same engine as /calc/math/solid-geometry.

Does this include an oblique cylinder?

No. Only the right circular case. Oblique solids are out of scope.

Where does this run?

Locally in the browser by default. REST and MCP call the same solid-geometry engine.