How is the area calculated?

It uses Heron's formula from the three side lengths, and the interior angles are found with the law of cosines.

What does the triangle type mean?

It classifies the triangle by sides (equilateral, isosceles or scalene) and by its largest angle (acute, right or obtuse).

Is anything uploaded?

No — all calculations run entirely in your browser and nothing is sent to a server.

What is the triangle inequality?

For three lengths to form a triangle, each pair must sum to more than the third side. If a + b is not greater than c (and so on), no triangle exists and the tool flags the input.

Can I solve a triangle from angles or two sides and an angle?

This is an SSS solver — it needs all three side lengths. For other known combinations (such as two sides and the included angle), a different solver is required.

How does it know if a triangle is right-angled?

After finding the angles with the law of cosines, it checks whether the largest angle is 90°. If so it labels the triangle right; above 90° is obtuse and below is acute.

What units does it use?

Any consistent unit. Enter all three sides in the same unit; the area comes out in that unit squared and the perimeter in the same linear unit.

Triangle Calculator — Gera Tools

Triangle calculator (SSS)

This calculator solves a triangle from its three side lengths (the SSS case), returning the area, perimeter, all three interior angles, and the triangle’s type. It suits geometry homework, trigonometry practice, and practical layout or surveying checks.

How it works

First it checks the triangle inequality — every pair of sides must sum to more than the third — and flags impossible inputs. Then, with the semi-perimeter s = (a + b + c) / 2, it applies Heron’s formula for the area and the law of cosines for each angle:

Area    = √(s(s − a)(s − b)(s − c))
angle A = arccos((b² + c² − a²) / (2bc))     (degrees)

It classifies the triangle by sides (equilateral, isosceles, scalene) and by its largest angle (acute, right, obtuse).

Example

For sides a = 3, b = 4, c = 5: s = 6, so area = √(6·3·2·1) = √36 = 6, and the perimeter is 12. The angle opposite the longest side is arccos((9 + 16 − 25)/(2·3·4)) = arccos(0) = 90°, so it is a right scalene triangle.

Property	Value
Area	6
Perimeter	12
Angles	36.87°, 53.13°, 90°
Type	Scalene · right

Everything runs in your browser — nothing is uploaded.