Origami Tessellation Grid Calculator
Calculate grid divisions, paper size, and pre-crease count for origami tessellation patterns and corrugations.
What are origami tessellations?
Tessellations are repeating patterns folded from a single uncut sheet of paper. They require a precise grid of pre-creases (mountain and valley folds) that serve as the foundation for collapsing the pattern. The grid type (square, triangular, or hexagonal) determines which tessellation patterns are possible.
Grid types and their uses:
| Grid Type | Divisions | Best Patterns | Difficulty |
|---|---|---|---|
| Square | Equal rows/columns | Hydrangea, waterbomb, box pleat | Beginner–intermediate |
| Triangular (60°) | 60° angled lines | Star puff, hex twist, flower tower | Intermediate–advanced |
| Hexagonal | From triangular grid | Snowflakes, Celtic patterns | Advanced |
| Diagonal square | 45° rotated grid | Pinwheel, sunk boxes | Intermediate |
Pre-crease count formula:
For a square grid of n × n divisions:
Horizontal creases = n - 1
Vertical creases = n - 1
Total creases = 2 × (n - 1)
Crease intersections = (n - 1)²
For a triangular grid of n divisions:
Horizontal creases = n - 1
Diagonal creases (left) = n - 1
Diagonal creases (right) = n - 1
Total creases = 3 × (n - 1)
Paper size formula:
The final tessellation shrinks significantly from the original paper size:
Shrink ratio = Final size / Original size
| Grid Divisions | Typical Shrink Ratio | 15 cm paper → Final |
|---|---|---|
| 8 × 8 | 50–60% | 7.5–9 cm |
| 16 × 16 | 40–55% | 6–8.25 cm |
| 32 × 32 | 30–45% | 4.5–6.75 cm |
| 48 × 48 | 25–40% | 3.75–6 cm |
| 64 × 64 | 20–35% | 3–5.25 cm |
Required paper size = Desired finished size / Shrink ratio
Example calculation (16 × 16 square grid):
- Grid: 16 × 16 divisions
- Horizontal creases: 15
- Vertical creases: 15
- Total pre-creases: 30
- Crease intersections: 225
- Paper: 30 × 30 cm (for ~14 cm finished piece)
- Time estimate: 30–45 minutes for pre-creasing
Paper weight recommendation:
| Grid Density | Recommended Weight | Paper Type |
|---|---|---|
| 8–16 divisions | 60–80 gsm | Standard kami, tant |
| 16–32 divisions | 50–70 gsm | Thin tant, tissue foil |
| 32–64 divisions | 30–50 gsm | Tissue foil, Nicolas Terry tissue |
| 64+ divisions | 20–35 gsm | Tissue, washi |
Thinner paper is essential for high-division grids because each fold adds thickness. A 64-grid on thick paper becomes impossibly bulky at the center where creases overlap.
Diagonal creases (for twist folds):
Many tessellations add diagonal creases within the grid cells:
Diagonal creases = 2 × (n - 1)² (both diagonals per cell)
This dramatically increases crease count. A 16 × 16 grid with diagonals has 30 + 450 = 480 total creases.