Triangle Calculator

Enter the lengths of all three sides to find the triangle's area, perimeter, and all three interior angles.

Triangle Calculator

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Side a

Side b

Side c

Area

14.7

Perimeter

Angles

44.4 deg, 57.1 deg, 78.5 deg

The three sides must be able to form a valid triangle (any two sides must add up to more than the third).

The formulas

Area (Heron's formula): s = (a+b+c)/2, Area = sqrt( s(s-a)(s-b)(s-c) ) Angles (law of cosines): A = acos( (b^2+c^2-a^2) / 2bc ), and similarly for B and C

Example

Sides 5, 6, 7: s = 9, area = sqrt(9x4x3x2) ≈ 14.7. Angles come out to approximately 44.4°, 57.1°, and 78.5°, which sum to 180° as expected.

Step-by-step guide

Enter the lengths of all three sides.
Check the triangle is valid - any two sides must add up to more than the third, or the calculator will flag it.
Read the area, perimeter, and all three angles.

Common mistakes

Entering three side lengths that can't actually form a triangle - for example, 2, 3, and 10 can never meet to close a triangle.

Using base-times-height for area when you only know the three sides - that formula needs a height measurement instead, which Heron's formula avoids needing.

Frequently asked questions

Do the three angles always add up to 180°?

Yes, always, for any triangle on a flat plane - this is a fundamental geometric rule and a good way to double-check the calculator's output.

What if I only know two sides and an angle?

This calculator specifically needs all three sides (SSS). If you have two sides and the included angle instead, the law of cosines can find the third side first, which you can then enter here.

What's a right triangle shortcut?

If one angle is exactly 90°, the Pythagorean theorem (a² + b² = c²) applies - see our dedicated Pythagorean Theorem Calculator for that specific case.

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