Hexagon Calculator

A regular hexagon is a six-sided polygon whose sides and interior angles are all equal. Its symmetry makes every important measurement depend on a single value, usually the side length. This calculator accepts a side length, area, perimeter, apothem, long diagonal, or circumradius and converts that measurement to the common side length before deriving all remaining properties. Because the relationships are exact, one valid positive input is enough to describe the entire regular hexagon. The perimeter is six times the side length. The circumradius, measured from the center to any vertex, equals the side length because a regular hexagon can be divided into six equilateral triangles. The long diagonal connects opposite vertices and is twice the side length. The apothem runs from the center perpendicular to a side and equals the side multiplied by the square root of three divided by two. Finally, the area equals three times the square root of three divided by two, multiplied by the square of the side. When a different measurement is supplied, the calculator reverses the appropriate relationship. It divides a perimeter by six, halves a long diagonal, treats the circumradius as the side, or multiplies an apothem by two and divides by the square root of three. For an area, it solves the area equation by multiplying by two, dividing by three times the square root of three, and taking the square root. Results are rounded only for display, while the calculations retain full floating-point precision. Regular hexagons appear in floor tiles, bolt heads, board games, honeycomb structures, architecture, and engineering layouts. The calculator is useful when estimating material, checking a geometric drawing, sizing a hexagonal table, or solving a classroom problem. All linear results use the same unit as the input when the input is a length, while area uses that unit squared. If area is the input, the resulting lengths use the corresponding base unit. Keep units consistent and avoid mixing centimeters with inches in the same design.