Triangle Calculator
Fill in any two sides — the third calculates automatically.
Enter all three side lengths.
Invalid triangle
Area
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Perimeter
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Angle A
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Angle B
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Angle C
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Triangle Type
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Missing Side
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Enter values above to calculate
Right Triangles
A right triangle has one 90° angle. The side opposite the right angle is the hypotenuse (c) — the longest side. The other two sides are called legs (a and b). The Pythagorean theorem relates them: a² + b² = c². Knowing any two sides lets you solve for the third.
Heron's Formula (SSS)
When you know all three side lengths, Heron's formula finds the area without needing a height or angle:
Law of Cosines (Finding Angles)
Given three sides, the law of cosines finds each angle:
Triangle Types
- Equilateral — all three sides equal; all angles are 60°.
- Isosceles — exactly two sides equal; the angles opposite the equal sides are equal.
- Scalene — all three sides different; all angles different.
- Right — one 90° angle; identified by a² + b² = c².
Frequently Asked Questions
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the 90° angle) equals the sum of the squares of the other two sides: a² + b² = c². It only applies to right triangles.
How do you find the area of a triangle?
For a right triangle: Area = (1/2) × base × height. For any triangle when all three sides are known, use Heron's formula: Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2 is the semi-perimeter.
What makes a valid triangle?
The triangle inequality theorem states that the sum of any two sides must be greater than the third side. If a + b > c, b + c > a, and a + c > b, the sides form a valid triangle. If any of these fail, no triangle can be constructed.
What is Heron's formula?
Heron's formula calculates the area of a triangle using only its three side lengths, without needing to know an angle or height. Given sides a, b, c: first compute the semi-perimeter s = (a+b+c)/2, then Area = √(s(s−a)(s−b)(s−c)).