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Triangle Calculator (Three Sides)

Enter the lengths of all three sides in any unit. The calculator checks the triangle is possible, then finds its area, angles and type.

Area

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Angles A, B, C
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Type
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Perimeter
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Tips for using the triangle calculator

  • Use the same unit for all three sides; the area comes out in that unit squared.
  • To check a corner is square, measure 3 ft along one side, 4 ft along the other and confirm the diagonal is 5 ft.
  • Very thin triangles are sensitive to rounding; enter measurements as precisely as you can.

How the triangle calculator works

Three side lengths fix a triangle completely, provided they satisfy the triangle inequality: each side must be shorter than the sum of the other two.

Semi-perimeter s = (a + b + c) ÷ 2
Area = √(s(s − a)(s − b)(s − c)) (Heron's formula)
Angle A = arccos((b² + c² − a²) ÷ 2bc) (law of cosines)

Heron's formula, known since about 60 AD, gives the area without needing a height. The law of cosines gives each angle opposite its side, and the three always add to 180°. The triangle is right if the largest angle is exactly 90°, obtuse if it is larger and acute if all angles are smaller.

Worked example

For sides 3, 4 and 5, s = 6 and the area is √(6 × 3 × 2 × 1) = 6 square units. The angles are 36.87°, 53.13° and 90°, so it is a right scalene triangle, the classic 3-4-5 right triangle used by builders to square corners. The perimeter is 12.

Frequently asked questions

Can any three lengths make a triangle?

No. Each side must be shorter than the other two added together. 2, 3 and 6 cannot form a triangle.

What is Heron's formula?

Area = √(s(s−a)(s−b)(s−c)), where s is half the perimeter.

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

If a² + b² = c² for the longest side c, the triangle has a 90° angle.

What is the difference between isosceles and scalene?

An isosceles triangle has at least two equal sides; a scalene triangle has three different sides.

Updated October 2026. Results are estimates for education, not financial or medical advice. All math runs in your browser; nothing you type is sent anywhere.

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