Equilateral Triangle Calculator

The equilateral triangle is the most perfectly balanced of all triangles, with all three sides the same length and all three angles exactly 60 degrees, and this calculator works out every measurement that follows from a single number: the side length. Enter it and you instantly get the area, the height, the perimeter, the inradius and the circumradius, all updating as you type. Because the shape is so symmetric, its formulas are short and memorable. The area is the square root of three over four, times the side squared, a result worth knowing because it turns up constantly in geometry, trigonometry and tiling. The height, dropped from any corner to the opposite side, is the side times the square root of three over two, and it splits the triangle into two neat 30-60-90 right triangles, which is exactly where those square-root-of-three terms come from. The inradius is the radius of the largest circle that fits snugly inside, and the circumradius is the radius of the circle that passes through all three corners; for an equilateral triangle the circumradius is exactly twice the inradius, a tidy relationship that does not hold for other triangles. That makes this tool genuinely useful for students learning geometry and checking homework, for engineers, architects and designers who use triangular bracing and trusses for their strength, for crafters and quilters laying out triangular patterns, and for anyone needing the dimensions of a triangular sign, garden bed or panel. Because the results recalculate the moment you change the side, you can quickly scale a design up or down and see every measurement adjust together. The formulas and a worked example are explained clearly below, so you can also work them by hand with confidence.

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