Equilateral Triangle Area Calculator

Enter an equilateral triangle's side length to get its area (A = (√3/4)s²), perimeter (P = 3s), and height (h = (√3/2)s), plus an optional material cost estimate.

Quick Facts

Area formula
A = (√3/4)s² ≈ 0.4330 × s²
All three sides and all three interior angles (60° each) are equal.
Height formula
h = (√3/2)s ≈ 0.8660 × s
Follows from the Pythagorean theorem: the altitude splits the triangle into two 30-60-90 right triangles.
Perimeter formula
P = 3s
Sum of all three equal sides.

Your Results

Calculated
Area
-
A = (√3/4) × side², in square units
Perimeter
-
P = 3 × side
Height
-
h = (√3/2) × side
Estimated Material Cost
-
Area × cost per square unit

Ready

Enter a side length and unit, then press Calculate.

Formula and Method for the Area of an Equilateral Triangle

Area of an Equilateral Triangle:

A = (√3/4) × s²

where s is the length of one side; all three sides and all three 60° angles are equal

An equilateral triangle is a triangle with all three sides the same length and all three interior angles equal to 60°. Because of that symmetry, its area, perimeter, and height can all be derived from a single measurement — the side length. This calculator uses the side length to compute the area, perimeter, and height, plus an optional material cost estimate from the area.

How the calculation works

Enter the side length and choose the unit it is measured in. The calculator squares that value and multiplies by √3/4 (≈ 0.4330) to get the area: A = (√3/4)s². This comes from the general triangle formula A = ½ × base × height, where the base is s and the height is (√3/2)s — a result of the Pythagorean theorem, since the altitude splits the equilateral triangle into two congruent 30-60-90 right triangles with hypotenuse s and one leg s/2, so the height leg equals √(s² − (s/2)²) = (√3/2)s. The perimeter is simply three times the side length: P = 3s. If you enter a cost per square unit, the tool multiplies it by the area to estimate total material cost.

Common mistakes

  • Confusing side length with area: a triangle with 6 ft sides has an area of (√3/4) × 36 ≈ 15.59 ft², not 6 ft² and not 18 ft² (that's the perimeter).
  • Mixing units: keep the side length in one consistent unit — convert inches to feet, or centimeters to meters, before entering the value.
  • Height vs. side: the height ((√3/2)s ≈ 0.866s) is always shorter than the side itself; do not substitute it for the side length when computing area or perimeter.

Real-world applications

  • Flooring, tiling, and roofing estimates use the area directly to calculate how much material to buy (add 5–10% extra for cuts and waste on triangular patterns).
  • Fencing, framing, and trim work use the perimeter to determine how much linear material is needed for triangular sections, gables, or trusses.
  • Structural engineering and architecture use the height (altitude) to check truss geometry, roof pitch, and load paths in triangular bracing.
  • Signage, landscaping, and construction budgets combine area with a cost per square unit to estimate material costs before purchasing.

Frequently Asked Questions

What is the formula for the area of an equilateral triangle?
The area of an equilateral triangle equals (√3/4) times the side length squared: A = (√3/4)s² ≈ 0.4330 × s². For example, a triangle with a 6 ft side has an area of (√3/4) × 6² ≈ 15.59 ft².
How do I find the height of an equilateral triangle?
The height (altitude) is the side length times the square root of 3 divided by 2: h = (√3/2)s ≈ 0.8660 × s. This comes from the Pythagorean theorem applied to the right triangle formed by the altitude, half the base, and a full side. A 6 ft side gives a height of about 5.196 ft.
How do I find the perimeter of an equilateral triangle?
Multiply the side length by 3, since all three sides are equal: P = 3s. A triangle with a 6 ft side has a perimeter of 3 × 6 = 18 ft.
How is the area formula A = (√3/4)s² derived?
Start from the general triangle area formula A = ½ × base × height. The base is s and the height is (√3/2)s, so A = ½ × s × (√3/2)s = (√3/4)s². The same result follows from the general formula A = ½ab·sin(C) with a = b = s and C = 60°, since sin(60°) = √3/2.

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