Triangle Calculator

What this calculator does

This tool solves a triangle: given enough information about its sides and angles, it works out everything else. You choose which values you know — three sides (SSS), two sides and the included angle (SAS), two angles and the included side (ASA), or two sides and a non-included angle (SSA) — and the calculator returns all three sides, all three angles in degrees, the area, the perimeter, and the triangle’s type. It also validates your input so impossible triangles are rejected rather than producing nonsense. Every result updates live, and all the trigonometry runs locally in your browser.

Why you might need it

Triangles are the workhorses of geometry, and “solving” one comes up far beyond the classroom. Surveyors and navigators use triangulation to fix positions from known distances and bearings. Builders and carpenters check whether a corner is truly square. Designers and 3D artists need angles and side lengths to lay out shapes precisely. Students working through trigonometry need a reliable way to check homework. Because the four input modes cover the standard cases taught in every geometry course, this calculator handles almost any “find the missing side or angle” problem you are likely to meet.

How to use it

1. Pick the Known values mode that matches what you have: SSS, SAS, ASA, or SSA.
2. Enter the three values into the labelled fields — the labels change with the mode, and angles are always in degrees.
3. Read the triangle type, area, and perimeter in the result card.
4. Check the table for every side and angle, use the copy button to grab the full solution, and Reset to return to the example triangle.

How it’s calculated

The two core tools are the law of cosines and the law of sines. In SSS mode each angle is recovered from the law of cosines, for example cos A = (b² + c² − a²) / 2bc. In SAS mode the unknown third side comes from the law of cosines, c² = a² + b² − 2ab·cos C, after which the triangle is treated like SSS. In ASA mode the third angle is 180° minus the two known angles, and the law of sines, a/sin A = b/sin B = c/sin C, gives the remaining sides. In SSA mode the law of sines finds the second angle, which is where the ambiguous case arises.

The area always uses Heron’s formula: with semi-perimeter s = (a + b + c) / 2, the area is √(s(s − a)(s − b)(s − c)). Validation enforces the triangle inequality — each side must be shorter than the sum of the other two — and checks that angle sets stay below 180°.

Common pitfalls

The classic trap is the SSA “ambiguous case”: the same data can describe two different triangles, and this calculator returns the primary (acute) solution. Mixing up degrees and radians is another frequent error — every angle field here expects degrees. People also forget the triangle inequality and try side lengths like 1, 2, 5 that simply cannot close. Finally, in SAS mode the angle must be the one between the two sides you entered; an angle opposite a side belongs in SSA mode instead.

Tips and related calculations

A quick sanity check after solving: the three angles must always add to exactly 180°, and the longest side must sit opposite the largest angle. If you only need the area and already know the base and height, the simpler formula ½ × base × height applies — Heron’s formula is for when you have the sides instead. Because every calculation runs on your device, you can adjust a value and immediately see how the rest of the triangle responds, which makes this a good way to build intuition for how sides and angles depend on one another.