Triangle Area Calculator

Created by Luis Hoyos
Last updated: Jul 03, 2022

Welcome to our triangle area calculator, with which you'll find the area of any triangle. The basic triangle area formula requires knowing its base and height, but if you don't know them, this calculator can even find the area of a triangle with 3 sides.

Triangle area calculation is crucial in physics problems, such as calculating the hydraulic radius of triangular channels, which is needed consequently to calculate the friction factor of the Darcy Weisbach equation.

In the next section, we talk about how to find the area of a triangle using the formulas and using this triangle area calculator.

Triangle area formula

First of all, what is the area of a triangle? Area triangle is the total space occupied by its three sides in a 2-dimensional plane.

The best-known formula to calculate the triangle area (A) is A = 0.5 × b × h, where b is the length of the base, and h is the height/altitude.

Unfortunately, most of the time, we don't know the base and height, and we must use other equations depending on what we know about the triangle:

Triangle area: triangle with two sides and angle between them (SAS)
  • Three sides (SSS)

    To get the area of a triangle with 3 sides, use the Heron's formula:

       A=0.25(a+b+c)(a+b+c)(ab+c)(a+bc)\ \ \ \ \ \ \ \scriptsize A = 0.25 \sqrt{ (a + b + c) (-a + b + c) (a - b + c) (a + b - c)}
Triangle area: triangle with two angles and side between them (ASA)
  • Two angles and a side between them (ASA)

    Use the following formula, which relies on the law of sines:

       A=a2sinβsinγ2sin(β+γ)\ \ \ \ \ \ \ \scriptsize A = \frac{a^2 \sin{\beta} \sin{\gamma}}{2 sin(\beta + \gamma)}

A simplification of the previous equations arises when dealing with a right triangle. In that case, the formula to calculate the triangle area is more straightforward, as we explain in our Pythagorean theorem calculator.

Example: How to find the area of a triangle

Suppose you know two sides and the angle between them:

  1. In the triangle area calculator, type the first side length. It can be 10 in in our example
  2. Enter the second triangle side. Let's choose 6 in in this case.
  3. Input the angle between two known sides. For example, 45 degrees.
  4. That's it. Now you know what is the area of that triangle. It should be 136.86 in².
Luis Hoyos
base and height
Triangle area: triangle with base and height

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