WorldCalcs

Triangle Calculator

Enter any 3 of the 6 values (at least one side) to solve all sides, angles, area and perimeter.

Reviewed by the WorldCalcs team · Methodology · Last reviewed: July 2026

Enter any 3 values, including at least one side. Angle A is opposite side a, B opposite b, C opposite c.

Enter three values above to solve the triangle.

What is a triangle calculator?

A triangle calculator solves a triangle when you already know some of its measurements. A triangle has six parts — three sides (a, b, c) and three angles (A, B, C), where each angle sits opposite the side with the matching letter. If you know any three of these parts, and at least one of them is a side, there is enough information to work out all the rest: the missing sides, the missing angles, the area and the perimeter. The one combination that does not work is three angles on their own, because that fixes the shape of the triangle but not its size — many triangles of different sizes can share the same three angles.

How the triangle is solved

The calculator looks at which three values you entered and picks the right method. When you give all three sides (SSS), it finds each angle with the law of cosines, for example A = arccos((b² + c² − a²) / (2bc)). When you give two sides and the angle between them (SAS), it finds the third side with the law of cosines and then the remaining angles. When you give two angles and a side (ASA or AAS), it finds the third angle by subtracting from 180°, then uses the law of sines — a / sin A = b / sin B = c / sin C — to find the sides. The trickiest case is two sides and an angle that is not between them (SSA), known as the ambiguous case: depending on the numbers it can produce no triangle, exactly one, or two valid triangles, and the calculator shows every solution it finds.

Worked example

Take the classic right triangle with sides a = 3, b = 4 and c = 5. Because all three sides are known, the law of cosines gives angle A = arccos((4² + 5² − 3²) / (2·4·5)) = arccos(0.8) = 36.869898°, and angle B = arccos((3² + 5² − 4²) / (2·3·5)) = arccos(0.6) = 53.130102°. The third angle is C = 180° − 36.869898° − 53.130102° = 90°, confirming the right angle. The area is ½ · 3 · 4 = 6 and the perimeter is 3 + 4 + 5 = 12. Enter a = 3, b = 4, c = 5 above and you will see exactly these results. For the law of cosines the tool often needs a square root; if your triangle has a right angle you can also check it with the Pythagorean theorem calculator. For area alone from base and height, see the triangle area calculator, or browse all geometry calculators.

All calculations happen in your browser. Nothing is sent, stored, or tracked.

Results are estimates and may contain errors — for general information only, not professional advice. Always verify before relying on them. Disclaimer

How to use

Fill in any three of the six fields — three sides, three angles, or a mix — as long as at least one is a side. Angle A is opposite side a, B opposite b, C opposite c. Angles are in degrees.

The tool auto-detects the case (SSS, SAS, ASA, AAS or SSA) and applies the law of sines or cosines. The ambiguous SSA case can produce two triangles — both are shown when they exist.

Frequently asked questions

What do I need to solve a triangle?+

Any three of the six parts, as long as at least one is a side. Common combinations are three sides (SSS), two sides and the included angle (SAS), two angles and a side (ASA or AAS), and two sides and a non-included angle (SSA).

Why can't I solve a triangle from three angles?+

Three angles set the shape but not the size. Infinitely many triangles — small and large — share the same three angles, so the sides can't be pinned down without at least one length. This calculator asks for at least one side.

What is the ambiguous case (SSA)?+

When you know two sides and an angle that isn't between them, the numbers can match zero, one, or two different triangles. The tool tests both possible angles and shows every triangle that is geometrically valid.

What is the law of sines?+

It states that a / sin A = b / sin B = c / sin C for any triangle. It's used when you know an angle and its opposite side, plus one more part, to find the remaining sides or angles.

What is the law of cosines?+

It generalises the Pythagorean theorem: c² = a² + b² − 2ab·cos C. It's used to find a side from two sides and the angle between them, or to find an angle from all three sides.

How is the area calculated?+

With two sides and the included angle the area is ½·a·b·sin C. With three sides the tool uses Heron's formula, area = √(s(s−a)(s−b)(s−c)) where s is half the perimeter. Both give the same result.

Does it handle right, isosceles and equilateral triangles?+

Yes. A right triangle simply comes out with one 90° angle, an isosceles triangle with two equal sides and angles, and an equilateral triangle with three 60° angles and three equal sides.

What units does it use?+

The sides are unit-neutral — use centimetres, inches, metres or anything else, as long as you're consistent — and the angles are in degrees. For area work in square units, see the triangle area calculator.

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