Equilateral Triangle Area Calculator

Created by Steven Wooding
Reviewed by Krishna Nelaturu
Last updated: Oct 14, 2022

With this equilateral triangle area calculator, you are able to compute the area of an equilateral triangle simply by entering either its side length or its height. Perfect if you want to know the area of your tortilla chip snack 😋 or a road sign 🚸

Read on to learn about:

  • What is an equilateral triangle, and how is it defined?
  • How to calculate the area of an equilateral triangle from its formula.
  • How to find the area of an equilateral triangle with its height.

What is an equilateral triangle?

An equilateral triangle is a particular triangle where all three sides are the same length. Given this restriction, it also means that all three angles of an equilateral triangle are the same – 60°.

Equilateral triangles are a special case of the isosceles triangle, with all three sides equal. We met the generic isosceles triangle at the isosceles triangle calculator.

How to calculate the area of an equilateral triangle

There are two main ways to calculate the area of an equilateral triangle. Either by using the length of its side or the equilateral triangle's height. The formula for area AA using the equilateral triangle's side is:

A=34a2A = \frac{\sqrt{3}}{4}a^2

...where aa is the side length of the equilateral triangle.

If the height of the equilateral triangle is what you know, we can use it alone to calculate the area. Given the relationship between side length and height hh:

h=32ah = \frac{\sqrt{3}}{2}a

...we can rearrange this and substitute for aa in the area equation to get:

A=4312h2A = \frac{4\sqrt{3}}{12}h^2

Wait: are your sides all different from each other? You are in the wrong place: the scalene triangle area calculator is what you need!

How to use this equilateral triangle area calculator

It really couldn't be simpler. Just enter the length of the side of the equilateral triangle, and you will be instantly shown its area. No wasted time clicking a calculate button.

Alternatively, enter the height to get the area of your equilateral triangle. As a bonus, it also gives you the side length as well.

Depending on the size of your equilateral triangle, you can change the units of the lengths and area to best match your application.

If you want a more general equilateral triangle calculator, then the equilateral triangle calculator is what you need. It also calculates an equilateral triangle's perimeter, circumcircle radius, and incircle radius. Or even more general is the triangle area calculator. Does your triangle has a right angle? Our area of a right triangle calculator is here to help!

FAQ

How many degrees in each angle of an equilateral triangle?

60°. Recall from elementary geometry that the inside angles of any triangle add up to 180°. Since for an equilateral triangle, the inside angles are all the same, one inside angle is 180° divided by 3, which equals 60°.

What's the area of an equilateral triangle with a side length of 5 inches?

10.83 square inches. To get this answer, you perform the following steps:

  1. Square the side length of the equilateral triangle.
  2. Multiply the result by the square root of three.
  3. Divide by four.

Mathematically, that is:

Area = √3 × a² / 4 = 1.734 × 25 / 4 = 10.83 in²

Steven Wooding
Image of equilateral triangle, with sides, angles, and height marked.
Side (a)
in
Height (h)
in
Area (A)
in²
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