Triangle Calculator

Find the area, perimeter, angles and type of a triangle from its three sides.

How the triangle is calculated

• Valid triangle: each side must be shorter than the sum of the other two.
• Area (Heron's formula): with s = (a + b + c) ÷ 2, area = √(s × (s − a) × (s − b) × (s − c)).
• Angles (law of cosines): A = arccos((b² + c² − a²) ÷ 2bc), and the same for B and C.
• Type: equilateral (three equal sides), isosceles (two) or scalene (none). By angle it is acute, right or obtuse.

Worked examples

• 3, 4, 5: perimeter 12, area 6, angles 36.8699°, 53.1301° and 90°. A scalene right triangle.
• 5, 5, 5: perimeter 15, area 10.8253, all angles 60°. Equilateral.
• 7, 8, 9: perimeter 24, area 26.8328, angles 48.1897°, 58.4119° and 73.3985°. Scalene and acute.

Frequently asked questions

Why does it say my sides cannot form a triangle?

The longest side must be shorter than the sum of the other two. For example, 1, 2 and 5 fail because 1 + 2 is less than 5.

How do I know if a triangle is a right triangle?

If the square of the longest side equals the sum of the squares of the other two, it is a right triangle. For example, 3, 4 and 5 work because 9 + 16 = 25.

Do the angles always add up to 180 degrees?

Yes. The three angles of any flat triangle add up to 180 degrees.

What units does it use?

Any units you like. Use the same unit for all three sides. The area is in that unit squared.