What is the formula for the area of an equilateral triangle?

Area = (√3 / 4) × a², where a is the side length. This comes from the standard triangle area formula (½ × base × height) combined with the equilateral triangle height formula h = (√3 / 2) × a.

How do I find the height of an equilateral triangle?

Height = (√3 / 2) × a. Because the triangle is symmetric, the altitude bisects the base, forming two 30-60-90 right triangles. The longer leg (height) equals half the hypotenuse (side a) times √3.

What is the circumradius of an equilateral triangle?

The circumradius (radius of the circumscribed circle) = a / √3. Equivalently, R = a√3 / 3. For equilateral triangles it equals exactly twice the inradius.

Does this work for very small or very large side lengths?

Yes. The formulas are purely algebraic with no approximation beyond standard floating-point arithmetic, so results are accurate across a wide range of values from sub-millimeter to kilometer scale.

What units does the calculator support?

You can select mm, cm, m, in, or ft. The unit label is appended to all linear results, and area results use the squared unit (e.g. cm²).

Area of an Equilateral Triangle Calculator

Name: Area of an Equilateral Triangle Calculator
Availability: InStock
Author: Nham Vu

Enter a side length to instantly compute the area, perimeter, height, and circumradius of an equilateral triangle.

Side Length

All three sides equal a

Results

Enter a side length and press Calculate.

Formula Reference

Area

(√3 / 4) × a²

Perimeter

3 × a

Height

(√3 / 2) × a

Circumradius

a / √3

Summary

Enter a side length to instantly compute the area, perimeter, height, and circumradius of an equilateral triangle.

How it works

Enter the side length (a) in the input field.
Choose your preferred unit (millimeters, centimeters, meters, inches, or feet).
The calculator applies the formula Area = (√3 / 4) × a² to find the area.
Height, perimeter, and circumradius are derived using their respective formulas.
Results update instantly as you type, with step-by-step formula breakdowns shown below.

Use cases

Homework and exam prep for geometry and trigonometry.
Architectural or engineering layouts using triangular grids.
Game development — calculating tile areas in hexagonal or triangular maps.
Craft and woodworking projects requiring equilateral triangle cuts.
Checking hand-calculated answers quickly.
Teaching geometry concepts with live formula feedback.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu