⬟ Pentagon Calculator

Welcome to the Pentagon Calculator – a fast, intuitive tool for anyone working with regular pentagons. Whether you're an architect, student, or math enthusiast, you can compute key dimensions instantly: side length, area, perimeter, diagonal, inradius (apothem), and circumradius. The regular pentagon, with its five equal sides and angles, is rich with golden ratio relationships and appears in everything from sacred geometry to modern design.

How to use: simply enter any known value – side, area, or perimeter – and the remaining fields update in real time. The calculator applies standard geometric formulas for a regular pentagon with side a: area A = (1/4)√(5(5+2√5)) a², perimeter P = 5a, diagonal d = ( (1+√5)/2 ) a ≈ 1.618a (the golden ratio φ), inradius r = (1/2) a √( (5+2√5)/5 ) , and circumradius R = (1/2) a √( (5+√5)/2 ) . If you input area or perimeter, the tool computes the side first using inverse formulas, then derives all other values.

All calculations run locally in your browser – no data is sent to any server, guaranteeing privacy and speed. The visual diagram updates dynamically to illustrate the pentagon’s proportions, and the results show up to six decimal places (with a clean rounded value). The layout is fully responsive, working seamlessly on phones, tablets, and desktops. We built this tool as part of the MultiCalculators family to simplify geometry for everyone. The pentagon’s connection to the golden ratio (φ ≈ 1.618) makes it especially fascinating: the diagonal to side ratio is exactly φ, a number revered in art and architecture.

We hope this calculator aids in homework, DIY projects, or professional work. If you encounter any issues or have suggestions, please use the contact link in the header. More polygon tools are on the way – bookmark this page and explore the symmetry of five. Thank you for choosing MultiCalculators.org, where math meets clarity.