Triangle Calculator
Solve a triangle's remaining sides, angles, and area from three known values.
Try an example
36.9°
53.1°
90°
6
12
About this calculator
What Is a Triangle?
A triangle is a polygon with three sides, three vertices and three interior angles that always add up to 180°. Triangles are the simplest rigid shape, which is why they hold up bridges, roofs and trusses and sit at the heart of trigonometry. This triangle calculator solves for the missing sides, angles, area, perimeter, height and more when you provide three values — including at least one side.
Types of Triangles
By side length:
- Equilateral: all three sides and all three angles (60°) are equal.
- Isosceles: two sides, and the two angles opposite them, are equal.
- Scalene: all sides and angles differ.
By angle:
- Acute: every angle is below 90°.
- Right: one angle is exactly 90° — see the Pythagorean Theorem Calculator.
- Obtuse: one angle is above 90°.
Worked Example
For a 3-4-5 triangle: the angles are 36.87°, 53.13°, and 90° (a right triangle), and the area is 6 square units.
Which Inputs Can You Solve From?
You can fully determine a triangle from several combinations of three values: three sides (SSS), two sides and the angle between them (SAS), two angles and a side (ASA or AAS), or two sides and a non-included angle (SSA, which is sometimes ambiguous and can have two solutions). Three angles alone fix only the shape, not the size, so at least one side length is required.
Essential Formulas
- Angle sum: A + B + C = 180°.
- Law of sines: a ÷ sin A = b ÷ sin B = c ÷ sin C.
- Law of cosines: c² = a² + b² − 2ab·cos C.
- Area: ½ × base × height, or ½ab·sin C, or Heron's formula √[s(s − a)(s − b)(s − c)] where s is half the perimeter.
- Perimeter: a + b + c.
- Triangle inequality: any two sides must add up to more than the third.
Where Triangles Are Used
Surveyors measure land by triangulation, engineers analyze truss forces, and graphics programs build 3D models from meshes of triangles. For distances along a slope, see the Slope Calculator, and for circular shapes, the Circle Calculator.
Worked example
A 3-4-5 triangle (a classic right triangle) has angles of 90°, 53.13°, and 36.87°, an area of 6, and a perimeter of 12.
Frequently asked questions
What if the three lengths I enter can't form a triangle?
The calculator checks the triangle inequality — each side must be shorter than the sum of the other two. If it fails, no valid triangle exists with those lengths, and no result is shown.
Can this solve a triangle from angles instead of sides?
Not currently — this calculator specifically solves for angles and area given three side lengths (the SSS case).
What's Heron's formula?
A way to find a triangle's area purely from its three side lengths, without needing to know any angle or height directly: Area = √(s(s−a)(s−b)(s−c)), where s is half the perimeter.
