Crease Pattern Analyzer Calculator

Flat-foldability check from crease pattern.

Mountain folds at vertex

Valley folds at vertex

Total crease lines in pattern

Paper thickness (mm)

Tab to move between fields

Maekawa's theorem (1=pass)

Kawasaki's check (1=pass)

Flat-foldable (1=yes)1

|Mountain - Valley|2

Total folds at vertex6

Estimated center layers16

Max thickness (mm)4.91

Crease density (per cm²)0.09

Simple Fold Thickness104,857.6

How to Use This Calculator

Count the mountain folds (convex ridges) meeting at the vertex you are analyzing and enter the number.
Count the valley folds (concave grooves) at the same vertex and enter that number.
Enter the total number of crease lines across the entire crease pattern.
Enter the paper thickness in millimeters (standard kami is ~0.06–0.08 mm; copy paper ~0.10 mm).
Check the Maekawa pass (1 = pass) — the absolute difference between mountain and valley folds must equal 2.
Check the Kawasaki pass and the flat-foldable result to confirm whether the pattern can lie flat.

What each input means

Mountain folds at vertex: Number of mountain (convex) folds meeting at the vertex you are analyzing.
Valley folds at vertex: Number of valley (concave) folds meeting at the same vertex.
Total crease lines in pattern: Total number of crease lines across the entire crease pattern.
Paper thickness (mm): Thickness of the paper in millimeters (standard kami ≈ 0.06-0.08 mm, copy paper ≈ 0.1 mm).

Maekawa's theorem (1=pass): Passes if |mountain - valley| = 2. Required for flat-foldability at a single vertex.
Kawasaki's check (1=pass): Passes if total crease count at vertex is even (necessary condition for Kawasaki's theorem).
Flat-foldable (1=yes): 1 if both Maekawa and Kawasaki conditions are met, 0 otherwise.
|Mountain - Valley|: Absolute difference between mountain and valley fold counts. Must equal 2.
Total folds at vertex: Sum of mountain and valley folds at the analyzed vertex.
Estimated center layers: Approximate paper layers at the center of the folded model.
Max thickness (mm): Estimated maximum thickness at the thickest point of the folded model.
Crease density (per cm²): Crease line density assuming a 15 cm standard square.

Identify Input Parameters
4 parameters
Mountain folds at vertex = 4, Valley folds at vertex = 2, Total crease lines in pattern = 20, Paper thickness (mm) = 0.1 = 4 input(s) provided
Calculate Maekawa's theorem
1 = 1
Calculate Kawasaki's check
1 = 1
Calculate Flat-foldable
1 = 1
Calculate |Mountain - Valley|
|Mountain - Valley|
2 = 2