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Equilateral Triangle Calculator

Find an equilateral triangle’s area, height and perimeter.

Result

27.71
6.93
24.00

How it is calculated

From one side length a the tool computes Area = (√3 / 4) · a², Height = (√3 / 2) · a and Perimeter = 3a. The units follow whatever you enter: if a is in centimetres, height and perimeter are in centimetres and the area is in square centimetres. The side must be greater than zero or there is no result. Values are rounded to two decimals for display only, the calculation uses full precision. The height formula comes from splitting the triangle into two right triangles with hypotenuse a and base a/2, so h² = a² − (a/2)². The square root of 3 is about 1.732.

Worked example

An equilateral triangular panel has a side of 8 cm. Perimeter: 3 × 8 = 24.00 cm. Height: (√3 / 2) × 8 = 0.8660 × 8 = 6.93 cm. Area: (√3 / 4) × 8² = 0.4330 × 64 = 27.71 cm². You can cross-check with the usual triangle rule: half of base times height is 0.5 × 8 × 6.93 = 27.71, which matches.

Try this example →

Common mistakes

  • Reading the area result as a length. The number is in square units, so 27.71 is cm², not cm.
  • Entering the height or the perimeter in the side field. Only one side goes in, and the other two values are computed from it.
  • Mixing units, such as a side in millimetres and expecting square metres. Convert first; area scales with the square of the unit (1 m² is 1,000,000 mm²).
  • Using this tool for a triangle with two equal sides (isosceles). The formulas only hold when all three sides are equal.
  • Rounding the height to 6.9 and then using it for the area. Multiplying rounded values gives a slightly different area than the exact 27.71.

About this calculator

This calculator finds the area, height and perimeter of an equilateral triangle — a triangle where all three sides and all three angles are equal — from a single side length, using formulas derived from the triangle's symmetry: the height splits it into two identical right triangles, which is what makes area and height computable directly from the side using fixed formulas involving the square root of 3.

This shape appears constantly in geometry coursework as the simplest case for practicing area and height formulas, since its symmetry removes the need for a separately measured base and height. It's also used practically in design, construction and fabrication whenever equilateral triangular panels, trusses, tiles or structural elements are being sized, since knowing just one side length is enough to determine every other measurement needed to cut or place the piece.

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Comments (1)

  • Editorial team

    If you are cutting triangles from sheet material, the height matters as much as the side: a triangle with a 10 cm side is 8.66 cm tall, so it fits in a strip about 8.7 cm wide, and its area is 43.30 square cm. A handy check is that height is roughly 0.866 times the side. Which related measure would you like next to these three, for example the inscribed circle?

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