Our free triangle calculator solves any triangle — finding all sides, angles, area, and perimeter — given any combination of known values. With support for SSS (three sides), SAS (two sides and an included angle), ASA (two angles and an included side), and right triangle modes, this is the most comprehensive free triangle solver available.

Triangles are fundamental shapes in geometry, engineering, architecture, and navigation. Whether you are a student solving geometry problems, a carpenter building a roof, or a surveyor calculating distances, this triangle calculator gives you all the information you need instantly.

How to Use the Triangle Calculator

Select your known values and the calculator solves the rest:

1. SSS (Three Sides Known): Enter all three side lengths. The calculator finds all three angles, area, and perimeter.
2. SAS (Two Sides and Included Angle): Enter two sides and the angle between them. The calculator finds the third side and remaining angles.
3. ASA (Two Angles and Included Side): Enter two angles and the side between them. The calculator finds the third angle and remaining sides.
4. Right Triangle: Enter any two known values (sides or angles) and the calculator solves for everything else.

When Should You Use a Triangle Calculator?

Use the triangle calculator for geometry homework, construction planning, land surveying, and navigation. In particular, it is essential for any application where you need to find unknown distances or angles using the law of cosines or law of sines. Furthermore, carpenters and builders use it daily to calculate roof pitches, stair angles, and bracing lengths.

Additionally, the right triangle mode is perfect for Pythagorean theorem calculations — the most common triangle calculation in everyday life. Moreover, students preparing for SAT, ACT, or standardized math tests will find the triangle calculator useful for checking their geometry work.

Key Triangle Theorems and Formulas

Here are the essential triangle formulas every student and professional should know:

• Pythagorean theorem: a² + b² = c² — For right triangles only. c is always the hypotenuse (longest side).
• Law of Cosines: c² = a² + b² − 2ab·cos(C) — Used to find an unknown side or angle in any triangle.
• Law of Sines: a/sin(A) = b/sin(B) = c/sin(C) — Used when you know an angle and its opposite side.
• Area formula: Area = ½ × base × height. Alternatively, Area = ½ × a × b × sin(C).
• Angle sum: A + B + C = 180° — The three interior angles of any triangle always sum to 180 degrees.

Frequently Asked Questions About the Triangle Calculator

What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². For example, a triangle with sides 3, 4, and 5 satisfies this equation: 3² + 4² = 9 + 16 = 25 = 5².

Can I solve a triangle if I only know the three angles?

No. Knowing three angles (AAA) gives you the shape of the triangle but not its size. You need at least one side length to calculate the actual dimensions and area.

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