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Triangle Calculator

Enter the lengths of the three sides. This calculator gives the area, perimeter, all three angles, the type of triangle and whether it has a right angle.

All three sides must use the same unit.

This result is an estimate only. Check with your bank or the relevant authority before making decisions.

How it is calculated

  1. Check that each side is shorter than the sum of the other two. If not, there is no triangle.
  2. Perimeter = a + b + c
  3. Semi-perimeter, s = (a + b + c) ÷ 2
  4. Heron’s formula: area = √(s × (s − a) × (s − b) × (s − c))
  5. Law of cosines: cos A = (b² + c² − a²) ÷ (2bc), and likewise for angles B and C. Angles are shown in degrees.

Type: equilateral if all three sides are equal, isosceles if two sides are equal, and scalene if no sides are equal. A triangle has a right angle if any angle is 90°.

Worked example

Sides 3, 4 and 5:

  • Area = 6.00
  • Perimeter = 12.00
  • Angles = 36.87°, 53.13° and 90.00°
  • Type: scalene, and it has a right angle

Sides 5, 5 and 5 give an area of 10.83 and three 60° angles, which is an equilateral triangle.

Why your number may differ

Angles and area are rounded to two decimal places, so the three angles shown may add up to slightly more or less than 180°. Make sure all three sides use the same unit.

Frequently asked questions

How do I know three sides can form a triangle?

Each side must be shorter than the sum of the other two. Sides 1, 2 and 3 cannot form a triangle because 3 equals 1 + 2.

What is Heron's formula?

Heron's formula finds the area from the three sides alone, without needing the height. It uses the semi-perimeter, s.

How are the angles calculated?

The angles are worked out from the three sides using the law of cosines and are shown in degrees.

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