Triangle Calculator
Enter three known values and solve the rest of the triangle — every side and angle, the area, the perimeter, and whether it's acute, right or obtuse.
Enter all three sides a, b and c.
Solved with the law of cosines (c² = a² + b² − 2ab·cos C) and the law of sines (a/sin A = b/sin B = c/sin C); area = ½·a·b·sin C. Sides can be in any unit — results use the same unit. Two sides and a non-included angle (SSA) isn't offered because it can describe zero, one or two different triangles.
3
Side a
4
Side b
5
Side c
36.8699°
Angle A
53.1301°
Angle B
90°
Angle C
6
Area
12
Perimeter
Scalene, right
Type
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How to use triangle calculator
- 1Choose what you know: three sides, two sides and the angle between them, or two angles and a side.
- 2Enter the values using the labelled diagram — side a is opposite angle A, and so on.
- 3Read the missing sides and angles, area, perimeter and triangle type.
About this tool
Three sides (SSS) are solved with the law of cosines, which gives each angle from the sides. Two sides and the included angle (SAS) use the law of cosines to find the third side first. Two angles and a side (ASA or AAS) find the third angle from the 180° angle sum, then the remaining sides from the law of sines, a/sin A = b/sin B = c/sin C. Area is ½ × a × b × sin C.
A 3-4-5 triangle is the classic check: the angles come out as about 36.87°, 53.13° and exactly 90°, with an area of 6 and a perimeter of 12. Sides can be in any unit — centimetres, inches, metres — as long as they're all the same; area is in that unit squared.
Impossible inputs are rejected with an explanation: three sides where the two shortest don't add up to more than the longest, or two angles totalling 180° or more. The ambiguous case (two sides and an angle that isn't between them) isn't offered because it can describe zero, one or two different triangles.
Frequently asked questions
The two shorter sides must add up to more than the longest side (the triangle inequality). 3, 4 and 5 work; 1, 2 and 3 don't — they'd lie flat in a straight line.
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