Triangle Calculator
Triangle Solver works out Side a and Side b from Side a (opposite angle A), Side b (opposite angle B) and Side c (opposite angle C). The default figures on this page give area of 6; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
4 steps
- Three sides known (SSS): each angle comes from the law of cosines.
- cos A = (b^2 + c^2 - a^2)/(2bc) = (4^2 + 5^2 - 3^2)/(2*4*5) -> A = 36.869898 deg
- Area by Heron: s = 6, A = sqrt(s(s-a)(s-b)(s-c)) = 6
- Sides a=3, b=4, c=5; angles A=36.869898, B=53.130102, C=90 degrees.
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the Triangle Solver calculates
Solves any triangle from three known measurements (SSS, SAS, ASA, AAS or SSA), returning every side, angle, altitude, median, area, inradius and circumradius.
How to use this Triangle Solver
Enter Side a (opposite angle A), Side b (opposite angle B), Side c (opposite angle C) and Angle A. Side a updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Side a, Side b and Side c.
The method follows NIST Digital Library of Mathematical Functions, 4.15 Trigonometric identities and the solution of triangles, Abramowitz & Stegun, Handbook of Mathematical Functions, Section 4.3.148-4.3.152 (plane triangle formulas) and Weisstein, Eric W. "Triangle" and "SSA Theorem", MathWorld.
SSS 3-4-5 right triangle example
With Side a (opposite angle A): 3, Side b (opposite angle B): 4, Side c (opposite angle C): 5, the calculator returns Area: 6, Perimeter: 12, Angle C: 90. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Side a, Side b and Side c. The inputs you can vary are Side a (opposite angle A), Side b (opposite angle B), Side c (opposite angle C), Angle A, Angle B and Angle C.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How do I calculate a triangle?
Solves any triangle from three known measurements (SSS, SAS, ASA, AAS or SSA), returning every side, angle, altitude, median, area, inradius and circumradius. Open “How this is worked out” beside the result to see each step for your own figures.
How do I calculate the missing side of a triangle?
It needs Side a (opposite angle A), Side b (opposite angle B), Side c (opposite angle C), Angle A, Angle B and Angle C. Nothing else is required, and the figures stay in your browser.
How do I calculate the 3rd side of a triangle?
The result gives Side a, Side b, Side c, Angle A, Angle B and Angle C, each labelled with its unit so the figure can be read on its own.
How do I calculate the long side of a triangle?
The page opens with worked default figures: area of 6. Replace them with your own and every figure updates as you type.
What information do I need for the Triangle Solver?
You need Side a (opposite angle A), Side b (opposite angle B), Side c (opposite angle C), Angle A, Angle B, Angle C, Angle unit and Side-side-angle solution. The page opens with default figures that give area of 6, so you can see the scale before entering your own.
What does this Triangle Solver show?
It shows Side a, Side b, Side c, Angle A, Angle B, Angle C, Area and Perimeter, with the working and any warnings for your entries.