Triangle Calculator
Enter what you know about a triangle (SSS, SAS, ASA or AAS) and get every side and angle, plus the area, perimeter and type. Show the work lists the law of cosines or sines used.
Last updated November 4, 2026
Above 0.
Above 0.
Above 0.
Result
Sides 3, 4, 5; angles 36.8699°, 53.1301°, 90°
| Measure | Value |
|---|---|
| Side a | 3 |
| Side b | 4 |
| Side c | 5 |
| Angle A | 36.8699° |
| Angle B | 53.1301° |
| Angle C | 90° |
| Area | 6 |
| Perimeter | 12 |
| Type | scalene, right |
Side a is opposite angle A, b opposite B and c opposite C. Two sides and a non-included angle (SSA) can give two triangles and is not supported.
Show the work
Formula: cos A = (b² + c² − a²) ÷ 2bc, and the same for B and C
- Triangle check: each side is shorter than the other two combined.
- A = 36.8699°, B = 53.1301° from the law of cosines; C = 180° − A − B = 90°.
- Area = ½ × a × b × sin C = ½ × 3 × 4 × sin(90°) = 6.
- Perimeter = 3 + 4 + 5 = 12.
Result: Sides 3, 4, 5; angles 36.8699°, 53.1301°, 90°
How the triangle is solved
c² = a² + b² − 2ab·cos C
a ÷ sin A = b ÷ sin B = c ÷ sin C
area = ½·a·b·sin C
With three sides (SSS) or two sides and the angle between them (SAS), the law of cosines gives the missing parts. With two angles and one side (ASA or AAS), the third angle is 180° minus the other two, and the law of sines scales the sides.
Side a is opposite angle A, side b opposite B and side c opposite C. The area is half the product of two sides and the sine of the angle between them.
The type comes from the results: equilateral (three equal sides), isosceles (two equal) or scalene (none); and acute, right or obtuse by the largest angle.
See how we calculate for the formulas, sources and review schedule behind every calculator.
What is not supported
Two sides and an angle that is not between them (SSA) can describe two different triangles, one or none, so this calculator does not solve it. Impossible input is rejected: sides must satisfy the triangle inequality, and two angles must add up to less than 180°.
How to use the Triangle Calculator
- Choose what you know: three sides, two sides and the angle between them, or two angles and a side.
- Enter the values. Angles are in degrees.
- For two angles, say whether the known side faces angle A or lies between A and B.
- Read the sides, angles, area, perimeter and type, then open Show the work.
Worked example
Sides 3, 4 and 5 give angles of 36.8699°, 53.1301° and 90°, so the triangle is right and scalene with area 6.
| Sides | Angles | Area | Type |
|---|---|---|---|
| 3, 4, 5 | 36.8699°, 53.1301°, 90° | 6 | Scalene, right |
| 5, 5, 8 | 36.8699°, 36.8699°, 106.2602° | 12 | Isosceles, obtuse |
| 2, 2, 2 | 60°, 60°, 60° | 1.7321 | Equilateral, acute |
Frequently asked questions
Which inputs can I use to solve a triangle?
Three sides (SSS), two sides with the angle between them (SAS), or two angles with any one side (ASA or AAS). Each fixes exactly one triangle.
Why is SSA not supported?
Two sides and a non-included angle can fit two triangles, one, or none. Because the answer is not unique, this tool leaves that case out.
What makes a triangle impossible?
Either one side is as long as or longer than the other two combined, or the angles add up to 180° or more. The calculator tells you which.
How is the area calculated?
Area is half of side a times side b times the sine of the angle C between them. For 3, 4 and 5 that is ½ × 3 × 4 × sin 90°, which is 6.