HomeCalculatorsMathTriangle Solver
Math calculator

Triangle Solver

Solve a Euclidean triangle from SSS, SAS, ASA, AAS, or SSA (ambiguous case). Not the Pythagorean-only calculator. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Specification checked · 10/10 tests · Production surface contract 4/4 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Sides, angles, and area of a Euclidean triangle.
Scope
Euclidean plane
Verification
Engine tested · 10/10 tests · Production surface contract 4/4 · Specification checked · v1.0.0
Named expert review
Optional · Not performed
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence
3 golden · 2 boundary · 5 property · Production surface contract 4/4 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-16T06:44:24.909Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

Law of sinesa / sin A = b / sin B = c / sin C
Law of cosinesc² = a² + b² − 2ab cos C
Areaarea = (1/2) ab sin C
iAngles in degrees. Side a is opposite angle A. This is not the right-triangle Pythagorean page.

How to use

1

Choose the case

SSS needs three sides. SAS is sides a,b and included C. SSA is side a, opposite A, and side b.

2

Enter positive sides and angles in (0°, 180°)

A + B + C = 180°.

3

Read sides, angles, and area

SSA may list two solutions.

Example calculations

Common configurations with formula and result.

ϟ

3-4-5

SSS right triangle

c² = 3² + 4²
C=90°, area=6
ϟ

SSA ambiguous

a=7, A=30°, b=10

two triangles
2 solutions

Triangle Solver specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
A Euclidean triangle is determined by SSS, SAS, ASA, or AAS. SSA may yield zero, one, or two triangles (ambiguous case).
What it calculates
Sides, angles, and area of a Euclidean triangle.
Inputs
  • mode
  • a?
  • b?
  • c?
  • A_deg?
  • B_deg?
  • C_deg?
Outputs
  • a
  • b
  • c
  • A_deg
  • B_deg
  • C_deg
  • area
  • solutions
Formula
law of sines / law of cosines
Assumptions
  • Euclidean plane
  • Not spherical trigonometry
  • Not Pythagorean-only
Units
  • length (consistent units)
  • degrees
Boundary conditions
  • triangle inequality fail → INVALID_INPUT
  • unknown mode (including hl) → INVALID_MODE
Example
mode=sss a=3 b=4 c=5 → C=90°
Validation cases

2 published on this page · 10/10 tests · Production surface contract 4/4 · View evidence

  • mode=sss a=3 b=4 c=5 → C_deg=90
  • mode=ssa a=7 A_deg=30 b=10 → solution_count=2
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Calculation version
1.0.0

Other calculators in this family: Pythagorean, Sine, Linear equation .

a²+b² Pythagorean › sin Sine › ax+b Linear equation ›
}

Frequently asked questions

Key distinctions behind the calculation.

Is this the Pythagorean calculator?

No. Right-triangle a²+b²=c² is /calc/math/pythagorean. This page solves general Euclidean triangles, including 3-4-5 as SSS.

What is the SSA ambiguous case?

Given a, A, and b, there can be two triangles when height < a < b and A is acute.

Where does this run?

Locally in the browser by default. REST and MCP call the same triangle-solver engine.