Equilateral Triangle Calculator

Calculate the area, perimeter, height, inradius, and circumradius of an equilateral triangle from its side length.

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Enter the side length of an equilateral triangle to calculate its area, perimeter, height, inradius, and circumradius.

Enter side length Provide the side length of an equilateral triangle to see all its geometric properties.

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Geometry

Equilateral triangle area, height, and radii from side length

The equilateral triangle calculator finds the area, perimeter, height, inradius, and circumradius of an equilateral triangle from its side length. All three sides are equal, so a single measurement determines every property.

Equilateral triangle formulas

An equilateral triangle has three equal sides and three 60-degree angles. The height splits it into two 30-60-90 right triangles, giving h = s * sqrt(3) / 2.

Area = (sqrt(3) / 4) * s^2. Perimeter = 3s. The inradius (inscribed circle) is s * sqrt(3) / 6 and the circumradius (circumscribed circle) is s * sqrt(3) / 3. The circumradius is always exactly twice the inradius.

A = (sqrt(3) / 4) * s^2

Area from side length s.

h = s * sqrt(3) / 2

Height (altitude) from side length.

Practical applications

Equilateral triangles appear in truss structures, tiling patterns, and road signs. Their symmetry makes them the strongest triangular shape for distributing loads evenly.

In tessellations, equilateral triangles tile the plane perfectly alongside squares and hexagons, making them fundamental to geometric design and architecture.

Frequently asked questions

What are the angles of an equilateral triangle?

All three interior angles are exactly 60 degrees. The angles of any triangle sum to 180 degrees, and equal sides guarantee equal angles.

 How is the height related to the side?

Height = side times sqrt(3) / 2, approximately 0.866 times the side length. This comes from the 30-60-90 triangle formed by the altitude.

 What is the relationship between inradius and circumradius?

The circumradius is always exactly twice the inradius in an equilateral triangle: R = 2r.

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