Triangle Calculator Guide: Area, Perimeter, Sides and Angles

A triangle calculator helps you work out unknown sides, angles, perimeter, or area when enough measurements are known. Triangles appear in geometry, design, surveying, and many practical measurement tasks. You can check supported calculations with the Triangle Calculator.

Types of triangles

By side lengths, triangles can be equilateral (three equal sides), isosceles (at least two equal sides), or scalene (three unequal sides). By angle, they can be acute, right, or obtuse. Every nondegenerate triangle has interior angles adding to 180°.

How to use a triangle calculator

1. Open the Triangle Calculator.
2. Identify the known sides and angles.
3. Enter the measurements into the supported input fields.
4. Calculate the available missing measurements.
5. Check that the side lengths satisfy the triangle inequality and the angles sum to 180°.

Area using base and height

The simplest area formula is A = (base × perpendicular height) / 2. If the base is 10 cm and the perpendicular height is 6 cm, the area is 30 cm². The height must be perpendicular to the chosen base.

Perimeter of a triangle

Add the three side lengths: P = a + b + c. For sides of 5 cm, 7 cm, and 9 cm, the perimeter is 21 cm.

Heron’s formula when all three sides are known

First calculate the semiperimeter s = (a + b + c)/2. Then use A = √[s(s − a)(s − b)(s − c)]. For a triangle with sides 3, 4, and 5, s = 6 and area = √[6 × 3 × 2 × 1] = 6 square units.

Triangle angle sum rule

If two interior angles are 45° and 65°, the third angle is 180° − 45° − 65° = 70°. This rule applies to ordinary plane triangles.

Triangle inequality

For three positive lengths to form a nondegenerate triangle, the sum of any two must be greater than the third. For example, 2, 3, and 6 cannot form a triangle because 2 + 3 is less than 6.

Useful formulas

Quantity	Formula
Perimeter	a + b + c
Area from base and height	bh/2
Semiperimeter	(a + b + c)/2
Area from three sides	√[s(s−a)(s−b)(s−c)]
Third angle	180° − first angle − second angle

Common mistakes

• Using a slanted side as the height without checking perpendicularity.
• Mixing centimetres and metres in the same calculation.
• Assuming three arbitrary positive side lengths always form a triangle.
• Confusing a right-triangle-only formula with one that works for any triangle.

Frequently asked questions

Can a triangle have two obtuse angles?

No. Two angles greater than 90° would already exceed the 180° total.

What is the area of a triangle with base 12 and height 5?

12 × 5 ÷ 2 = 30 square units.

Can I calculate every side from three angles alone?

No. The angles determine shape but not overall scale; at least one length is needed.

Does Heron’s formula work for scalene triangles?

Yes. It works for any nondegenerate triangle when all three side lengths are known.

Use the Triangle Calculator to check your next geometry problem.