Area of an Equilateral Triangle Calculator

Enter side length, height, or area — instantly get all equilateral triangle properties with step-by-step working.

Unit:
Side length (s)
cm
Height (h)
cm
Area (A)
cm²

Enter any one value — the others update instantly.

Triangle Diagram

Equilateral Triangle Formulas

From Side

A = (√3 ÷ 4) × s²

Multiply s² by (√3/4) ≈ 0.4330 to get the area.

Height

h = (√3 ÷ 2) × s

The altitude from any vertex to the opposite side bisects the base.

Perimeter

P = 3 × s

All three sides are equal, so perimeter = 3 times one side.

From Height

s = (2 ÷ √3) × h

Rearrange h = (√3/2)s to find side from height.

Worked Example — Side 10 cm

Equilateral triangle with side 10 cm:

Given: s = 10 cm
Step 1: h = (√3 ÷ 2) × 10 = 5√3 ≈ 8.66 cm
Step 2: A = (√3 ÷ 4) × 100 = 25√3 ≈ 43.30 cm²
Step 3: P = 3 × 10 = 30 cm
Answer: Area ≈ 43.30 cm², Perimeter = 30 cm

Common Equilateral Triangle Measurements

Side Height Area Perimeter
5 cm 4.33 cm 10.83 cm² 15 cm
10 cm 8.66 cm 43.30 cm² 30 cm
12 cm 10.39 cm 62.35 cm² 36 cm
15 m 12.99 m 97.43 m² 45 m
20 m 17.32 m 173.21 m² 60 m

Real-World Applications

⚠️

Signs & Safety

Yield signs, warning triangles, and hazard markers worldwide are equilateral triangles.

🔺

Architecture

Triangular facades, glass pyramid skylights, and geodesic dome panels use equilateral triangles.

⚙️

Engineering

Triangular frames offer maximum rigidity — used in trusses, bridges, and space frames.

🎲

Games

Triangular game boards, tetrahedral dice faces, and playing card suits use equilateral geometry.

🔬

Science

Crystal structures, molecular geometry (trigonal planar), and snowflake patterns exhibit equilateral triangle symmetry.

Frequently Asked Questions

What is the formula for area of an equilateral triangle?
A = (√3/4) × s² where s is the side length. The constant (√3/4) ≈ 0.4330. For example, side 10 cm: A = 0.4330 × 100 = 43.30 cm². This formula comes directly from the height formula h = (√3/2)s and the general triangle formula A = ½ × base × height.
How is the height of an equilateral triangle derived?
The altitude from any vertex bisects the opposite side, creating two 30-60-90 right triangles. Using trigonometry: h = s × sin(60°) = s × (√3/2). For s = 10 cm: h = 10 × 0.8660 ≈ 8.66 cm.
How do you find area from height alone?
From h = (√3/2)s, rearrange: s = 2h/√3. Then apply A = (√3/4)s². This calculator does this automatically when you enter the height field.
Why does an equilateral triangle have all angles equal to 60°?
The sum of interior angles in any triangle is always 180°. Since an equilateral triangle has all three sides equal, all three angles must also be equal. Therefore each angle = 180° ÷ 3 = 60°.
What is special about the centroid of an equilateral triangle?
In an equilateral triangle, the centroid, circumcenter, incenter, and orthocenter all coincide at the same point — the perfect center of symmetry. This is unique among triangle types and reflects the triangle's 3-fold rotational symmetry.
Is an equilateral triangle also isosceles?
Yes — an equilateral triangle is a special case of isosceles. Isosceles requires at least 2 equal sides, and an equilateral triangle satisfies this for all 3 possible pairs of sides. However, an isosceles triangle is not necessarily equilateral.

Related Area Calculators

Circle Semicircle Square Rectangle Parallelogram Rhombus Trapezium Scalene Triangle Right Angle Triangle Equilateral Triangle Isosceles Triangle Regular Hexagon Sector & Segment