Triangle Calculator

What this calculator solves

This page is for the side-side-side case. If you know angles instead of all three sides, use a trigonometry calculator or draw the triangle first so the missing side lengths are defined.

The triangle inequality

For any valid triangle with sides a, b, c: each side must be less than the sum of the other two:

a + b > c
b + c > a
a + c > b

Inputs that violate this rule do not form a real triangle, so the calculator flags the error instead of returning misleading geometry.

Area from three sides

When all three sides are known, the calculator uses Heron’s formula:

s = (a + b + c) / 2
area = √(s(s-a)(s-b)(s-c))

Here, s is the semiperimeter. If the sides are in centimetres, the area is in square centimetres; if the sides are in inches, the area is in square inches.

Angles from three sides

After the sides are validated, each angle comes from the law of cosines:

cos(A) = (b² + c² − a²) / (2bc)
cos(B) = (a² + c² − b²) / (2ac)
cos(C) = (a² + b² − c²) / (2ab)

The calculator converts the results to degrees and rounds them for display.

Triangle type

The side lengths also identify the triangle type:

• Equilateral: all three sides are equal.
• Isosceles: exactly two sides are equal.
• Scalene: all three sides are different.

A 3, 4, 5 triangle is valid and close to a common right-triangle example. A 2, 3, 6 entry is invalid because 2 + 3 is not greater than 6.