Triangle Calculator

Enter the three side lengths. You'll get the area (Heron's formula), the perimeter, all three interior angles, and the triangle type — right, acute or obtuse, and equilateral, isosceles or scalene.

Enter three sides and press Calculate.

The formula

From three sides a, b and c the perimeter is just their sum, while the area comes from Heron's formula using the semi-perimeter s:

perimeter: P = a + b + c semi-perim: s = (a + b + c) ÷ 2 area: A = √( s(s − a)(s − b)(s − c) ) angle A: A° = arccos( (b² + c² − a²) ÷ (2bc) )

Each interior angle comes from the law of cosines: the angle opposite a given side is the arccosine of the other two sides squared, minus that side squared, over twice their product. Convert the result from radians to degrees by multiplying by 180 ÷ π. The three angles always sum to 180°.

Worked example

For the classic 3-4-5 triangle (a = 3, b = 4, c = 5):

Perimeter: 3 + 4 + 5 = 12.
Semi-perimeter: 12 ÷ 2 = 6.
Area: √(6 × 3 × 2 × 1) = √36 = 6.
Largest angle (opposite c): arccos((9 + 16 − 25) ÷ 24) = arccos(0) = 90° — a right triangle.

Right, acute, obtuse — and side types

Once the angles are known, the triangle is right if its largest angle is exactly 90°, acute if every angle is below 90°, and obtuse if one angle exceeds 90°. Separately, the sides classify it: all three equal is equilateral, exactly two equal is isosceles, and all different is scalene. The 3-4-5 triangle is therefore a right scalene triangle.

Note: the three lengths only form a real triangle if each side is shorter than the sum of the other two — the triangle inequality. The calculator checks this before computing anything.

Frequently asked questions

How do you find the area of a triangle from three sides?

Use Heron's formula. Let s be the semi-perimeter, s = (a + b + c) ÷ 2. Then the area = √(s(s − a)(s − b)(s − c)). It works for any triangle when you know all three side lengths.

How are the angles of a triangle calculated?

By the law of cosines. The angle opposite side a is A = arccos((b² + c² − a²) ÷ (2bc)), and similarly for B and C. The three angles always add up to 180 degrees.

What makes a valid triangle?

The triangle inequality must hold: each side must be shorter than the sum of the other two (a + b > c, a + c > b and b + c > a). If any side equals or exceeds the sum of the other two, the three lengths cannot form a triangle.

How do I know if a triangle is right, acute or obtuse?

Compare the largest angle to 90 degrees. If it equals 90 the triangle is right, if it is less than 90 the triangle is acute, and if it is greater than 90 the triangle is obtuse. A 3-4-5 triangle, for example, is a right triangle.

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Mustafa Bilgic · Editor, Calcool
Heron's formula, the law of cosines and the triangle inequality are standard Euclidean geometry, as described in references such as the Wolfram MathWorld entry on Heron's Formula. All computation runs in your browser. Last updated 20 June 2026.

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