At One Place

Triangle solver

Leave any field blank. Give three values — three sides, two sides and an angle, or two angles and a side.

Solve any triangle from three known values, with area, perimeter and all angles.

How it works

Give three values — three sides, two sides and an angle, or two angles and a side — and this finds the rest, plus area, perimeter and the triangle type.

Three sides always determine a triangle uniquely, which is why triangulation works and why a triangular frame is rigid while a rectangular one racks.

Two sides and a non-included angle is the case that can be ambiguous. Depending on the numbers there may be two valid triangles, one, or none — the so-called SSA case. Where two exist the tool reports both rather than silently picking one.

The triangle inequality is checked first: any side must be shorter than the sum of the other two, or no triangle exists at all.

This tool runs entirely in your browser. Nothing you enter is sent to a server, logged or stored, and the page keeps working with the network disconnected.

Common questions

Can any three lengths form a triangle?
No. Each side must be shorter than the sum of the other two. Three lengths failing that describe no triangle.
Why is SSA ambiguous?
Two sides and a non-included angle can sometimes be satisfied by two different triangles. Both are valid, which is why the case needs care.

Related pages

Sources

  1. Calculated on this page — At One Place

How these figures are compiled and checked