Math

Triangle Calculator (Three Sides)

Enter three sides and get everything else.

Your numbers

Your results

Area
Area
—
Perimeter
—
Angle A (°)
—
Angle B (°)
—
Angle C (°)
—
Type
—

Triangle Calculator (Three Sides) by TheCalcTools

How the Triangle Calculator (Three Sides) works

Enter the three side lengths in any unit.

Heron’s formula gives the area from the semi-perimeter s.

The law of cosines gives each angle.

The formula

s = (a + b + c) ÷ 2Area = √(s(s − a)(s − b)(s − c))

Worked example

Using the default values shown in the calculator:

Side a5
Side b6
Side c7
  1. s = (5 + 6 + 7) ÷ 2 = 9; area = √(9 × 4 × 3 × 2) = 14.697.
  2. Angles: A = 44.42°, B = 57.12°, C = 78.46°. The triangle is Scalene.

Result:

Area14.697
Perimeter18.000
Angle A (°)44.42
Angle B (°)57.12
Angle C (°)78.46
TypeScalene

Frequently asked questions

What is the triangle inequality?

Each side must be shorter than the sum of the other two; otherwise the sides cannot close into a triangle.

Is the triangle right-angled?

If a² + b² = c² for the longest side, one angle is exactly 90°. Check the angle results.

Sources and further reading

More in Math · All calculators

This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.