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.

What is the Triangle Calculator?

Free triangle calculator — enter the three side lengths and get the area, perimeter, all three interior angles and the triangle type. It runs entirely in your browser and nothing is uploaded. It runs free in your browser on Gera Tools, with nothing uploaded.

Triangle Calculator — Gera Tools

Name: Triangle Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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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.

Common triangle types and when they appear

Understanding what the type label means saves time when applying the result:

Equilateral — all three sides equal, all angles exactly 60°. The area formula simplifies to (√3/4) × side².
Isosceles — two sides equal, two base angles equal. Common in architecture and bridge designs.
Scalene — all sides different, all angles different. The most general case; most real-world triangles are scalene.
Right triangle — largest angle exactly 90°. The Pythagorean relationship a² + b² = c² holds. If you enter a near-right triangle the tool may show 89.99° due to floating-point rounding.
Obtuse — largest angle above 90°, but below 180°. The altitude from the obtuse vertex falls outside the triangle.
Acute — all angles below 90°. All altitudes fall inside the triangle.

Practical tips

Units: enter all three sides in the same unit. The area result is in that unit squared and the perimeter in the same linear unit. Mixing centimetres and metres will produce a nonsense answer.

The triangle inequality check: if the two shorter sides sum to less than or equal to the longest side, no triangle can close. A common mistake is entering sides like 1, 2, 10 — the tool will flag this as impossible before computing.

From a real measurement: if you measure the three sides of a physical object (a fence corner, a room diagonal, a roof pitch), enter them here to find whether the corner is truly square (angle near 90°) or to calculate the area of the footprint.

Second worked example: for an isosceles triangle with sides a = 5, b = 5, c = 6, the semi-perimeter s = 8, area = √(8 × 3 × 3 × 2) = √144 = 12, perimeter = 16, and the equal angles at the base are each arccos((25 + 36 − 25) / (2 × 5 × 6)) = arccos(0.6) ≈ 53.13°, with the apex angle at ≈ 73.74°.