Triangle Calculator
Solve any triangle from sides and angles — area, perimeter and the missing values.
Enter any 3 values (at least one side). Sides a, b, c are opposite angles A, B, C.
Fill in three values to solve.
About this calculator
A triangle calculator solves a triangle from the values you know (three sides, two sides and an angle, or two angles and a side) using the law of sines and law of cosines. It returns every missing side and angle plus the area and perimeter. Enter the values you have and leave the rest blank.
You need any three values that include at least one side. From that it picks the right theorem: the law of cosines recovers an angle from three sides or a third side from two sides and their included angle, while the law of sines pairs a known side with its opposite angle to find the rest. Because a triangle’s angles always sum to 180°, once two angles are known the third follows immediately. It then reports the perimeter and the area.
For a worked example, entering the three sides 3, 4 and 5 identifies a right triangle: the angle opposite the longest side is exactly 90°, the other two are about 36.87° and 53.13°, the perimeter is 12 and the area is ½·3·4 = 6. Give it two sides and the included angle instead — say 5, 7 and 40° — and it uses the law of cosines to find the third side. It is used in geometry and trigonometry homework, surveying, construction layout and any job that needs the missing measurements of a triangle.
Frequently asked questions
What do I need to know to solve a triangle?
Any three values that include at least one side: three sides (SSS), two sides and the included angle (SAS), two angles and a side (ASA/AAS), or two sides and a non-included angle (SSA).
How is the area calculated?
From three sides it uses Heron’s formula; with two sides and the included angle it uses ½·a·b·sin(C). Both give the same result for a valid triangle.
How do I solve a 3-4-5 triangle?
Enter the three sides as 3, 4 and 5 and leave the angles blank. The calculator confirms it is a right triangle with a 90° angle opposite the side of length 5, angles of about 36.87° and 53.13°, area 6 and perimeter 12.
What is the difference between the law of sines and the law of cosines?
The law of cosines links all three sides to one angle, so it is used when you know three sides or two sides and the included angle. The law of sines links a side to its opposite angle and is used once you have a matching side–angle pair.
Why does SSA sometimes give two possible triangles?
With two sides and a non-included angle (the ambiguous case), the given side can reach the base at two different points, so two valid triangles may fit the same data. The calculator flags this when it happens.
Can it tell me if my values do not form a valid triangle?
Yes. If the sides break the triangle inequality (one side longer than the other two combined) or the angles cannot sum to 180°, the calculator reports that no such triangle exists instead of returning a result.
Results are estimates for general guidance only, not financial, medical or tax advice.