Pentagon Calculator

A regular pentagon is a five-sided shape with all sides and all angles equal, one of the most recognisable figures in geometry and design, seen in everything from sports balls and building plans to logos, paving and the famous building it shares its name with. This calculator gives you all the key measurements of a regular pentagon from a single input, the side length. Enter the side and it instantly returns the area enclosed, the perimeter around the outside, the apothem, and the circumradius. The apothem is the perpendicular distance from the centre to the middle of a side, which is handy because the area can also be found as half the perimeter times the apothem, and the circumradius is the distance from the centre out to a corner, the radius of the circle that would pass through all five vertices. Pentagons crop up in real tasks more often than you might expect: laying out a five-sided garden bed, deck or gazebo, cutting a five-pointed template, designing a badge or tile, or simply working through a geometry assignment. Doing the maths by hand means wrestling with an awkward formula involving nested square roots, which is easy to get wrong, so having it calculated accurately and instantly saves time and removes the risk of slips. Because the tool recalculates as you type, you can size a pentagon to fit a space by trying different side lengths and watching the area and radius respond. Below the calculator you will find the exact formulas, the fact that the interior angles total 540 degrees, and a clear worked example so you can understand and reuse the method yourself.