Search for a tool
Pick's Theorem

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

Results

Pick's Theorem -

Tag(s) : Geometry

Share
dCode and more

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!

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Feedback and suggestions are welcome so that dCode offers the best 'Pick's Theorem' tool for free! Thank you!

Pick's Theorem

Pick Polygon Area Calculator

What is the Pick Theorem?

Pick's theorem (or rule) easily calculates the area (surface) of a polygon with $b$ vertices built on a lattice, 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 $$A = i + \frac{b}{2} - 1$$

All the points present on the contour are considered as vertices.

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 $A = 15 + 10/2 - 1 = 19$.

Who created Pick's Theorem?

The formula owes its name to Georg Alexander Pick who described it in 1899.

Source code

dCode retains ownership of the "Pick's Theorem" source code. Except explicit open source licence (indicated Creative Commons / free), the "Pick's Theorem" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Pick's Theorem" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Pick's Theorem" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.

Cite dCode

The copy-paste of the page "Pick's Theorem" or any of its results, is allowed as long as you cite dCode!
Cite as source (bibliography):
Pick's Theorem on dCode.fr [online website], retrieved on 2023-02-08, https://www.dcode.fr/pick-theorem

Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!