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Equilateral Triangle Calculator

Tested

Area, height and perimeter of an equilateral triangle.

Tested, not yet published. The formula for this calculator is implemented and passes its automated checks. This page stays non-indexable until it is reviewed and published.

Results

Enter your values and press Calculate. Results appear here.

  • • Result

Quick answer

For an equilateral triangle with side s, the area is (√3 ÷ 4)s², the height (√3 ÷ 2)s and the perimeter 3s. With s = 2: area 1.7321, height 1.7321 and perimeter 6.

Enter the side length. The calculator returns area, height and perimeter.

Related tools: Triangle Calculator: Area, perimeter, angles and type of a triangle from its three sides. 45-45-90 Triangle Calculator: Sides of a 45°-45°-90° triangle from one leg. 30-60-90 Triangle Calculator: Sides of a 30°-60°-90° triangle from the short leg.

How to use the Equilateral Triangle Calculator

  1. Enter side length (above 0).
  2. Press Calculate to see the result, and use Reset to start again.
Inputs of the Equilateral Triangle Calculator
InputWhat to enterAllowed values
Side lengthA number> 0

Formula and method

Formula

A = (√3 ÷ 4) s²; h = (√3 ÷ 2) s; P = 3s

IEEE-754 double precision; shown to at most 6 decimal places.

Standard formulas.

Worked examples

These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.

Example 1

Inputs: Side length = 2.

Results of example 1
ResultValue
Area1.732051
Height1.732051
Perimeter6

Example 2

Inputs: Side length = 10.

Results of example 2
ResultValue
Area43.30127
Height8.660254
Perimeter30

The first line is the headline result (area). Below it the equilateral Triangle Calculator lists height and perimeter, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.

Derivation

The height splits the triangle into two 30-60-90 triangles, giving h = s·√3/2. Area = ½ × s × h = (√3/4)s². For s = 2 the height is √3 = 1.7321.

Properties

All angles are 60° and all sides equal. The inradius is s·√3/6 and the circumradius s·√3/3. Doubling the side quadruples the area.

How the result changes with side length

Holding every other input at the first worked example, this table changes only side length. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.

How the result changes with side length
Side lengthAreaHeightPerimeter
10.4330130.8660253
21.7320511.7320516
46.9282033.46410212
827.7128136.92820324

What happens with invalid input

These messages are produced by the calculator itself, so you know what to fix.

  • Side length: entering "-1" shows "Side length must be greater than 0." beside that field and no result.

Choosing between the Equilateral Triangle Calculator and similar calculators

Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.

Choosing between the Equilateral Triangle Calculator and similar calculators
CalculatorYou enterIt returns
[Triangle Calculator](/math/triangle-calculator/)side a, side b and side cArea
[45-45-90 Triangle Calculator](/math/45-45-90-triangle-calculator/)leg lengthLeg
[30-60-90 Triangle Calculator](/math/30-60-90-triangle-calculator/)short leg lengthShort leg
[Right Triangle Calculator](/math/right-triangle-calculator/)leg a and leg bHypotenuse c
[Triangle Area Calculator](/math/triangle-area-calculator/)base and heightArea

Background: geometry measurements

Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.

Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².

Assumptions and limitations

  • Positive side

If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for side length to confirm this.

Frequently asked questions

What is the area for s = 10?

With s = 10 the area is (√3 ÷ 4) × 100 ≈ 43.30.

What are its angles?

All three angles are 60°, so the angles sum to 180°.

Is it also isosceles?

Yes. An equilateral triangle has at least two equal sides, so it counts as isosceles; the reverse isn't true.

What does the Equilateral Triangle Calculator calculate?

Area, height and perimeter of an equilateral triangle. It returns Area, Height and Perimeter.

What formula does the Equilateral Triangle Calculator use?

A = (√3 ÷ 4) s²; h = (√3 ÷ 2) s; P = 3s. Standard formulas.

What do I need to enter in the equilateral Triangle Calculator?

You enter Side length.

How is the result rounded or limited?

IEEE-754 double precision; shown to at most 6 decimal places. Positive side.

What is an example of a equilateral Triangle result?

With side length 2, the area is 1.732051.

Sources

  • OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem

Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.