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Equilateral Triangle Calculator

Calculate the area, perimeter, and height of an equilateral triangle from its side length.

Reviewed by Chase FloiedUpdated

This free online equilateral triangle calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

All three sides are equal

Results

Area

43.3013 sq units

Perimeter

30 units

Height

8.6603 units

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Equilateral Triangle Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Equilateral Triangle Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Equilateral Triangle Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • Use the Equilateral Triangle Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
  • Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
  • Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
  • Use it to explore the behavior of mathematical functions across a range of inputs.

About This Calculator

The Equilateral Triangle Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Calculate the area, perimeter, and height of an equilateral triangle from its side length. The underlying algorithms implement well-established mathematical formulas and numerical methods. Results are computed instantly in the browser. This tool is useful for learning, verification of hand calculations, and rapid exploration of mathematical relationships. All computation happens locally — no data is sent to a server.

About Equilateral Triangle Calculator

An equilateral triangle is a triangle in which all three sides are equal and all three angles are 60 degrees. It is the most symmetric triangle and has numerous special properties. The area of an equilateral triangle is A = (√3/4)s², and its height is h = (√3/2)s. Equilateral triangles appear throughout mathematics, science, and design — from traffic signs and truss structures to molecular geometry (such as the arrangement of atoms in BF₃) and the faces of regular polyhedra. The equilateral triangle is one of only three regular polygons that can tile the plane by themselves (along with squares and hexagons). Six equilateral triangles form a regular hexagon. This calculator provides the area, perimeter, and height for any side length.

The Math Behind It

The equilateral triangle's height can be derived from the Pythagorean theorem: drop a perpendicular from the apex to the base, bisecting it into two segments of s/2. Then h² + (s/2)² = s², giving h = s√3/2. The area follows from A = ½ × s × s√3/2 = (√3/4)s². The incircle (inscribed circle) has radius r = h/3 = s√3/6 = s/(2√3), and the circumcircle (circumscribed circle) has radius R = 2h/3 = s√3/3 = s/√3. The ratio R/r = 2 for equilateral triangles. Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, their centers form an equilateral triangle. The equilateral triangle maximizes the area among all triangles with a given perimeter. It is also a regular simplex in 2D, the simplest polygon, and generalizes to the regular tetrahedron in 3D.

Formula Reference

Equilateral Triangle Area

A = (√3/4) × s²

Variables: s = side length

Height

h = (√3/2) × s

Variables: s = side length

Worked Examples

Example 1: Musical triangle

A musical triangle instrument has 20 cm sides.

Step 1:h = (√3/2) × 20 = 10√3 ≈ 17.32 cm
Step 2:A = (√3/4) × 20² = (√3/4) × 400 = 100√3

Area ≈ 173.21 cm², Height ≈ 17.32 cm

Common Mistakes & Tips

  • !Using ½ × base × side instead of ½ × base × height — the side is not the height.
  • !Forgetting that the height of an equilateral triangle is not equal to the side length.
  • !Confusing the area coefficient √3/4 with √3/2 (which is the height coefficient).

Related Concepts

Used in These Calculators

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Frequently Asked Questions

Are all equilateral triangles similar?

Yes. Since all angles are 60°, every equilateral triangle is similar to every other equilateral triangle, differing only in scale.

What is the ratio of height to side?

h/s = √3/2 ≈ 0.866. The height is about 86.6% of the side length.