Equilateral Triangle Calculator
Enter any one main measurement of an equilateral triangle — side, height, area, or perimeter — and calculate the rest with formulas and steps explained below.
Equilateral triangle basics
An equilateral triangle has three equal sides and three equal angles. Since every triangle has 180° total, each angle in an equilateral triangle is 60°. OpenStax includes equilateral triangles among the standard triangle types in its overview of triangle properties and classifications.
This calculator can start from side length, height, area, or perimeter. That is useful because homework questions do not always give the side directly. Sometimes they give the height or area and ask you to work backward.
Equilateral triangle formulas
The height formula comes from splitting the equilateral triangle into two 30-60-90 right triangles. The side length becomes the hypotenuse of each smaller right triangle, and half the side becomes the short leg.
Worked example
Why equilateral triangle problems are good calculator targets
Equilateral triangle problems look simple, but students often mix up the height and side length. They also confuse the area formula with the ordinary triangle formula. This page gives both: the shortcut formula and the reason behind it, so it can rank for calculator searches and informational searches such as “how to find the height of an equilateral triangle.”
Common questions
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Use area = (√3/4)s², where s is the side length. This formula comes from using area = base × height ÷ 2 and replacing the height with (√3/2)s. If you only know the height or perimeter, first convert that value to side length, then calculate the area.
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Use height = (√3/2)s. The height splits the equilateral triangle into two 30-60-90 right triangles. The original side is the hypotenuse, and the height is the longer leg of the right triangle.
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Yes. Since all three sides are equal, all three angles are equal. A triangle has 180° total, so each angle is 180° ÷ 3 = 60°. This is true for every equilateral triangle no matter how large or small it is.
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Yes. Rearrange the area formula. Since A = (√3/4)s², the side length is s = √(4A/√3). The calculator does this when you choose area as the known value. This is useful when a problem gives area and asks for perimeter or height.
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Yes. All three angles are 60°, and each angle is less than 90°, so every equilateral triangle is acute. It is also often considered a special isosceles triangle because it has at least two equal sides.
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An equilateral triangle has all three sides equal. An isosceles triangle has at least two equal sides. Every equilateral triangle can fit the isosceles definition, but not every isosceles triangle is equilateral because the base may be different from the two equal sides.