Triangle calculator (angles and area from sides)
Enter the three sides to get the angles, area, perimeter and type of the triangle.
How the calculation works
From the three sides you can find everything about a triangle: angles, area and perimeter.
Angles — law of cosines
cos A = (b² + c² − a²) ÷ 2bc. Angle A is the arccosine of that value.
Area — Heron's formula
With the semi-perimeter s = (a+b+c) ÷ 2:
area = √[s(s−a)(s−b)(s−c)]
Step-by-step example (sides 3, 4, 5)
- Semi-perimeter: 6
- Area: √[6·3·2·1] = 6
- Largest angle: cos = 0 → 90° (right triangle)
Examples
- Sides 6, 8, 10: area = 24, and it is right-angled (6²+8²=10²).
- Sides 5, 5, 8: isosceles triangle, area = 12.
Frequently asked questions
Which sides form a triangle?
Each side must be less than the sum of the other two. E.g., 3, 4, 5 works — and is right-angled.
Right, isosceles or equilateral?
Equilateral: 3 equal sides. Isosceles: 2 equal. Right: a 90° angle (when a²+b²=c²).
Can I use base and height instead?
Yes: area = (base × height) ÷ 2. Heron's formula is for when you only have the three sides.
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Updated on June 30, 2026 · by Rafael Rossi · Methodology & sources