Tessellation Repeat Calculator

Grid size and repeat count from paper size and molecule.

Paper size (cm)

Molecule size (cm)

Pleat depth ratio

Border margin (cm)

Tab to move between fields

Repeats per axis

Total molecules

Effective spacing (cm)4.5

Actual border (cm)1.25

Visible area (cm²)225

Coverage (%)36

Paper in pleats (cm²)112.5

Min paper for this grid (cm)24.5

How to Use This Calculator

Enter the side length of your square paper in centimeters.
Set the size of one tessellation repeat unit (molecule) in centimeters — measure a practice molecule if possible.
Enter the pleat depth ratio: shallow pleats are ~0.3, medium ~0.5, deep or complex molecules ~1.0 or more.
Set the border margin in centimeters to leave unfolded space around the edges for finishing.
Read the number of repeats per axis and total molecules to know how many pattern units will fit.
Use the minimum paper size output to check whether your paper is large enough for the desired grid.

How the result changes with Paper size (cm)

Paper size (cm): Side length of the square paper in centimeters.
Molecule size (cm): Size of one tessellation repeat unit (molecule) in centimeters.
Pleat depth ratio: How much extra paper each pleat consumes as a ratio of molecule size. Shallow pleats ≈ 0.3, deep ≈ 1.0+.
Border margin (cm): Minimum untiled margin around the edges for finishing/anchoring.

Repeats per axis: Number of molecule repeats fitting along one side of the paper.
Total molecules: Total tessellation units in the grid (rows × columns).
Effective spacing (cm): Actual center-to-center spacing including pleat consumption.
Actual border (cm): Resulting border margin on each side after fitting the grid.
Visible area (cm²): Surface area of the visible tessellation pattern.
Coverage (%): Percentage of total paper area covered by the visible pattern.
Paper in pleats (cm²): Estimated paper area consumed by pleats underneath the surface.
Min paper for this grid (cm): Minimum paper side length needed for the calculated grid size.

Identify Input Parameters
4 parameters
Paper size (cm) = 25, Molecule size (cm) = 3, Pleat depth ratio = 0.5, Border margin (cm) = 1 = 4 input(s) provided
Calculate Repeats per axis
Repeats per axis
5 = 5
Calculate Total molecules
Total molecules
25 = 25
Calculate Effective spacing
Effective spacing = moleculeSize * (1 + pleatDepth)
4.5 = 4.5
Calculate Actual border
Actual border = (paperSize - gridCoverage) / 2
1.25 = 1.25