Triangle Calculator

Calculate area, perimeter, angles, and sides of any triangle given known values.

Triangle Properties
Calculated from sides
Area14.6969
Perimeter18
Triangle TypeScalene Acute
Angle A44.4153°
Angle B57.1217°
Angle C78.463°
Semiperimeter9
Inradius1.633
Circumradius3.5722

What is a Triangle Calculator?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. The sum of the internal angles of a triangle in Euclidean space is always 180 degrees.

How it Works

Here are the key formulas used for triangles, given side lengths a, b, and c:

  • Perimeter: P = a + b + c
  • Semi-perimeter (s): s = P / 2
  • Area (Heron's Formula): Area = √(s(s-a)(s-b)(s-c))
  • Law of Cosines (for angles): c² = a² + b² - 2ab cos(C)

Example Calculation

Calculate the area of a triangle with sides 3, 4, and 5.

  1. Calculate the semi-perimeter (s): (3 + 4 + 5) / 2 = 6.
  2. Apply Heron's Formula: √(6(6-3)(6-4)(6-5))
  3. Simplify: √(6 × 3 × 2 × 1) = √36
  4. The Area is 6.

Frequently Asked Questions

How do I find the area of a triangle with 3 sides?

Use Heron's Formula. First calculate the semi-perimeter (s), then the area is √(s(s-a)(s-b)(s-c)).

What is the Triangle Inequality Theorem?

It states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

How to calculate the perimeter?

Simply add the lengths of all three sides together: P = a + b + c.

What is a right triangle?

A right triangle is a triangle in which one angle is a right angle (90 degrees). The sides satisfy the Pythagorean theorem: a² + b² = c².

Can a triangle have two right angles?

No, because the sum of angles in a triangle must be 180 degrees. If two angles were 90 degrees, the third would have to be 0.