Kirigami Cut Calculator

Each fold stacks the current paper on top of itself, so every existing layer becomes two layers — that's exponential growth (2^foldCount), not additive. This is exactly why a small number of folds produces surprisingly detailed symmetric patterns when you cut and unfold: 3 folds gives 8 layers, but 6 folds already gives 64, which is why the calculator caps foldCount at 8 (256 layers) since cutting through more than that by hand becomes impractical.

A cut running the entire length of the folded section risks severing the piece completely once unfolded, since a full-length cut through all layers leaves no connective paper along that edge. The 10% margin (maxCutLength = min(foldedLength, foldedWidth) × 0.9) keeps a thin strip intact at the edges to hold the piece together, though it's a simplified guideline — always check that your specific cut pattern still leaves connected paper before cutting the final sheet.

In this calculator, no — popUpHeight is set directly equal to popUpSlitCm, and the standard pop-up angle is fixed at 90° rather than being derived from other inputs. The slit length is clamped to at most half the paper size, since a longer slit than that would extend past a stable card fold, but within that constraint it only feeds the height number and doesn't interact with layers, cuts, or the difficulty/integrity scores.

Cutting difficulty is 1 + (totalLayers × cutsPerSection) / 10, capped at 10 — it rises fastest when you combine high fold counts with many cuts per section, since that means cutting through many stacked layers repeatedly. Structural integrity works in the opposite direction: it starts at 10 and drops by 1 point for every 20 total unfolded cuts (max(1, 10 − totalCutsUnfolded/20)), reflecting that more total cuts leave less connected paper holding the piece together — both are relative heuristics from cut and layer counts, not measurements of an actual folded sample.