Triangle Area Calculator

Created by Hanna Pamuła, PhD candidate
Reviewed by Bogna Szyk and Adena Benn
Last updated: Sep 15, 2022

This triangle area calculator can help in determining the triangle area. The basic triangle area formula needs to have a base and height given, but what if we don't have it? How can we calculate the area of a triangle with 3 sides only? The triangle area calculator is here for you. Give it a go! If you are still unsure how to find the area of a triangle, check the description below.

Triangle area formula

Triangle area: triangle with base and height

A triangle is one of the most basic shapes in geometry. The best known and the most straightforward formula, which almost everybody remembers from school, is:

  • area = 0.5 * b * h, where b is the length of the base of the triangle, and h is the height/altitude of the triangle.

However, sometimes it's hard to find the height of the triangle. In that cases, many other equations may be used, depending on what you know about the triangle:

Triangle area: triangle with three sides
  • Three sides (SSS)

    If you know the lengths of all sides, use the Heron's formula:

    area = 0.25 * √( (a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c) )

Triangle area: triangle with two sides and angle between them (SAS)
  • Two sides and the angle between them (SAS)

    You can calculate the area of a triangle easily from trigonometry:

    area = 0.5 * a * b * sin(γ)

Triangle area: triangle with two angles and side between them (ASA)
  • Two angles and a side between them (ASA)

    There are different triangle area formulas versions - you can use, for example, trigonometry or law of sines to derive it:

    area = a² * sin(β) * sin(γ) / (2 * sin(β + γ))

If you are looking for other formulas or calculators connected with triangles, check out this right triangle calculator, pythagorean theorem calculator, and law of cosines calculator.

How to find the area of a triangle?

Assume that we know two sides and the angle between them:

  1. Type the first side length. It can be equal to 9 inches in our example
  2. Enter the second triangle side. Let's choose 5 in.
  3. Determine the angle between two known sides. For example, 30 degrees.
  4. Watch our triangle area calculator performing all calculations for you! The area for our case is equal to 11.25 in².

Area of an equilateral triangle

To calculate the area of an equilateral triangle, you only need to have the side given:

area = a² * √3 / 4

Although we didn't make a separate calculator for the equilateral triangle area, you can quickly calculate it in this triangle area calculator. Simply use the subpart for the area of a triangle with 3 sides - as you know, every side has the same length in an equilateral triangle. It's possible to calculate that area also in the angle-side-angle or side-angle-side version - you probably remember that every angle in the equilateral triangle is equal to 60 degrees (π/3 rad).

Want more?

For areas of different shapes, check the other awesome calculators:

Hanna Pamuła, PhD candidate
Given
base and height
Triangle area: triangle with base and height





Base
in
Height
in
Area
in²
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