Tool to apply and calculate a surface using the Pick's Theorem. The Pick's theorem allows the calculation of the area of a polygon positioned on a normalized orthogonal grid and whose vertices are points of the grid.

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day! A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Tool to apply and calculate a surface using the Pick's Theorem. The Pick's theorem allows the calculation of the area of a polygon positioned on a normalized orthogonal grid and whose vertices are points of the grid.

Answers to Questions

What is the Pick Theorem?

Pick's theorem easily calculates the area of a polygon with $ b $ vertices built on a 2D grid of points with integer coordinates (points with equal distances). If all $ b $ vertices of the polygon (vertices can be flat) are grid points and the polygon has $ i $ points inside itself then Pick's formula indicates that the polygon area $ A $ is equal to $$ A = i + \frac{b}{2} - 1 $$

How to calculate an area with the Pick Theorem?

The Pick formula requires only two parameters: the number $ i $ of interior points of the polygon and the number $ b $ of vertices of the polygon (which is in the number of grid points on the perimeter of the polygon). Thearea $ A $ of the polygon is$ A = i + \ frac {b} {2} - 1 $

Example: The polygon drawn below has 15 points inside the polygon (light gray), and 10 vertices (dark gray). Its area is therefore $ A = 15 + 10/2 - 1 = 19 $.

Source code

dCode retains ownership of the source code of the script Pick's Theorem online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Pick's Theorem script for offline use on PC, iPhone or Android, ask for price quote on contact page !