Pick's Theorem

The Pick's Theorem calculator provides the approximate area of a polygon based on the number of lattice points inside the polygon, the number of points on the boundary and the size of a lattice square.

INSTRUCTIONS: Choose units and enter the following:

• (i) Interior Lattice Points
• (b) Boundary Lattice Points
• (LSA) Area of Lattice Square

Pick's Theorem Area (A): The calculator returns the area in square meters.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

i=7, b=8
A=i+b/2-1=10

Pick's Theorem provides a simple formula for calculating the area A of a simple polygon constructed on a grid of equal-distanced points such that all the polygon's vertices are grid points. The following formula is used: `A=i+b/2-1`, where:

• `i` = lattice points in the interior
• `b` = lattice points on the boundary

References

Wikipedia (https://en.wikipedia.org/wiki/Pick%27s_theorem)