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Math calculator

Prism Calculator

Right rectangular prism V = abh from three edge lengths. Same engine as Solid Geometry. Not a frustum. Not a pyramid. Not CAS. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Specification checked · 66/66 tests · Production surface contract 3/3 · v1.11.0
Input interpretation
Enter values to calculate.
Result
—
Model
Right rectangular prism volume, surface, and space diagonal from three edges.
Scope
Right rectangular prism
Verification
Engine tested · 66/66 tests · Production surface contract 3/3 · Specification checked · v1.11.0
Named expert review
Optional · Not performed
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence
25 golden · 13 boundary · 28 property · Production surface contract 3/3 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.11.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain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 = abh
Total surfaceA = 2(ab + ah + bh)
iSame engine as /solid-geometry. The matching pyramid is /pyramid. Regular n-gon prism is /regular-prism. Not a second engine.

How to use

1

Enter a, b, and h

All three edges must be positive. Default 2, 3, 4. Equal edges a=b=h are a valid cube.

2

Read V, A, and d

2-3-4 has volume 24 and surface 52. The unit cube 1-1-1 has V=1, A=6.

Example calculations

Common configurations with formula and result.

ϟ

2-3-4

a = 2, b = 3, h = 4

V = 2×3×4
24
ϟ

Unit cube

a = 1, b = 1, h = 1

V = 1, A = 6
1

Prism calculator specification

Version 1.11.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
A right rectangular prism of edges a>0, b>0, h>0 has volume abh, lateral area 2(a+b)h, total surface 2(ab+ah+bh), and space diagonal √(a²+b²+h²). a=b=h is a cube. This page is mode=prism on math.geometry.solid. Not a frustum. Not a pyramid. Not CAS.
What it calculates
Right rectangular prism volume, surface, and space diagonal from three edges.
Inputs
  • a
  • b
  • h
Outputs
  • volume
  • lateral
  • surface
  • diagonal
Formula
V = abh, A = 2(ab+ah+bh)
Assumptions
  • Right rectangular prism
  • a=b=h is a valid cube
  • Not a frustum
  • Not a pyramid
  • Not CAS
Units
  • length (consistent units)
  • volume (length³)
  • area (length²)
Boundary conditions
  • a ≤ 0 or b ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE
  • unknown mode → INVALID_MODE
Example
a=2 b=3 h=4 → V=24
Validation cases

3 published on this page · 66/66 tests · Production surface contract 3/3 · View evidence

  • a=2 b=3 h=4 → V=24 A=52
  • a=1 b=1 h=1 → V=1 cube=true
  • a=2 b=3 h=0 → VALUE_MUST_BE_POSITIVE
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Calculation version
1.11.0

Other calculators in this family: Angle Between Lines Calculator, Circle Calculator, Cone Calculator, Conic Section Calculator, Coordinate Geometry Calculator, Cross Product Calculator, Cylinder Calculator, Dodecahedron 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. › → Cylinder Calculator Right circular cylinder V = πr²h and A = 2πr(r+h). Same engine as Solid Geometry. Not CAS. Runs locally. › → Dodecahedron Calculator Regular dodecahedron V = (1/4)(15+7√5)a³ and A = 3√(25+10√5) a² from one edge. Same engine as Solid Geometry. Not an icosahedron. Not an n-gon prism. 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=prism on math.geometry.solid, the same engine as /calc/math/solid-geometry.

Is this a frustum?

No. The right circular frustum stays on /calc/math/frustum. This page is a right rectangular box.

Does this include a triangular or regular n-gon prism?

Yes on /calc/math/regular-prism, the same engine. This page stays the right rectangular box. The right rectangular pyramid is /calc/math/pyramid.

Where does this run?

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