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
- Enter side length (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Side length | A 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.
| Result | Value |
|---|---|
| Area | 1.732051 |
| Height | 1.732051 |
| Perimeter | 6 |
Example 2
Inputs: Side length = 10.
| Result | Value |
|---|---|
| Area | 43.30127 |
| Height | 8.660254 |
| Perimeter | 30 |
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.
| Side length | Area | Height | Perimeter |
|---|---|---|---|
| 1 | 0.433013 | 0.866025 | 3 |
| 2 | 1.732051 | 1.732051 | 6 |
| 4 | 6.928203 | 3.464102 | 12 |
| 8 | 27.712813 | 6.928203 | 24 |
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.
| Calculator | You enter | It returns |
|---|---|---|
| [Triangle Calculator](/math/triangle-calculator/) | side a, side b and side c | Area |
| [45-45-90 Triangle Calculator](/math/45-45-90-triangle-calculator/) | leg length | Leg |
| [30-60-90 Triangle Calculator](/math/30-60-90-triangle-calculator/) | short leg length | Short leg |
| [Right Triangle Calculator](/math/right-triangle-calculator/) | leg a and leg b | Hypotenuse c |
| [Triangle Area Calculator](/math/triangle-area-calculator/) | base and height | Area |
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.
Related calculators
- 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.
- Right Triangle Calculator — Solve a right triangle from its two legs: hypotenuse, angles, area and perimeter.
- Triangle Area Calculator — Area of a triangle from base and height.
- SAS Triangle Calculator — Solve a triangle from two sides and the included angle.
- SSS Triangle Calculator — Angles and area of a triangle from its three sides.
- Forty-Five Ninety Triangle Calculator — Sides of a 45-45-90 triangle from one leg.
- Isosceles Triangle Calculator — Height, area and angles of an isosceles triangle from its base and equal sides.
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.