Equilateral Triangle Area Calculator
Enter the side length or height of an equilateral triangle to get its exact area, with the perimeter and the remaining dimension.
Find area by
(√3/4) × a²
- 1
Side squared
8² = 64 - 2
Area
(√3 ÷ 4) × 64 = 27.7128
How does this calculator work?
Area of an equilateral triangle: (√3/4)×a² from side a, or h²/√3 from height h. Enter the side or height; the calculator returns the area, the other dimension, and the perimeter. All formulas derive from the 30-60-90 geometry of the altitude.
Formula
How this is calculated
An equilateral triangle has three equal sides (length a) and three 60° angles. Its area is derived from the standard triangle formula — half base times height. The height can be found from the Pythagorean theorem on the 30-60-90 triangle formed by the altitude: h = (√3/2)·a. Substituting gives Area = (1/2)·a·(√3/2)·a = (√3/4)·a².
If the height h is known instead of the side, the relationship h = (√3/2)·a is inverted to give a = 2h/√3. Substituting this back into the area formula yields Area = (√3/4)·(2h/√3)² = h²/√3. Both paths give the same result for consistent inputs.
The calculator accepts any positive side or height and returns the area, the missing dimension, and the perimeter (3a). Results are exact real-number arithmetic; extremely large or small inputs may encounter floating-point precision limits but typical geometric values are accurate to many decimal places.
Frequently asked questions
Area = (√3/4) × a², where a is the side length. This comes from the standard area = ½ × base × height, using height h = (√3/2)a derived from the Pythagorean theorem on the 30-60-90 right triangle formed by the altitude.
Rearrange the height formula h = (√3/2)a to get a = 2h/√3, then substitute into the area formula: Area = (√3/4) × (2h/√3)² = h²/√3. Equivalently, Area = (h² × √3)/3.
By the isoperimetric inequality for polygons, among all triangles with the same perimeter the equilateral triangle has the greatest area. This makes it the most 'efficient' triangle shape in terms of enclosing area for a given boundary length.
Also known as
TG we-Calculate Editorial Team. (2026). Equilateral Triangle Area Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/equilateral-triangle-area-calculator
TG we-Calculate Editorial Team. "Equilateral Triangle Area Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/equilateral-triangle-area-calculator.
TG we-Calculate Editorial Team, "Equilateral Triangle Area Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/equilateral-triangle-area-calculator
@misc{wecalculate_equilateral_triangle_area_calculator, title = {Equilateral Triangle Area Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/equilateral-triangle-area-calculator}}, year = {2026}, note = {TG we-Calculate} }
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