Equilateral Triangle Calculator

An equilateral triangle is the most symmetrical triangle possible: all three sides are the same length, all three interior angles are exactly 60 degrees, and every line of symmetry maps one vertex onto another. Because of this perfect regularity, a single number, the side length, determines every other measurement. This calculator takes the side length and returns the area, height, perimeter, circumradius, and inradius, all updating as you type. The area formula, square root of three over four times the side squared, is a classic result in geometry worth knowing by heart. The height is the perpendicular distance from any side to the opposite vertex, equal to the side times root three over two. This height splits the equilateral triangle into two 30-60-90 right triangles, which is the geometric origin of all those root-three terms. The perimeter is simply three times the side. The circumradius is the radius of the circle that passes through all three vertices, and the inradius is the radius of the largest circle that fits inside touching all three sides. For an equilateral triangle the circumradius is exactly twice the inradius, a clean relationship not shared by other triangles. The tool is useful for students learning plane geometry and checking homework, for engineers and designers working with triangular bracing, trusses, or floor tiles, and for anyone who needs to quickly scale a triangular shape. Enter any positive side length and all five results appear instantly.

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