How Many Times Can Paper Fibre Be Recycled? A Grade-by-Grade Bound on Fibre Shortening, Fines Loss, Virgin Top-Up and Deinking Cost

Paper recycling is often described as if fibre could circulate indefinitely. It cannot. Each repulping cycle shortens fibres, converts a fraction of the mass to fines that are lost in washing and forming, and removes further mass as rejects and deinking sludge. This paper models those three losses together for five grades — corrugated case material (old corrugated containers, OCC), printed office paper, old newsprint (ONP), mixed household paper, and tissue — and derives three quantities for each grade: the maximum number of useful cycles before fibre length or tensile strength falls below the grade requirement, the virgin top-up fraction a steady-state system needs in every cycle to hold its fibre inventory constant, and, for printed grades, the deinking yield and full cost per tonne of deinked pulp at stated 2025–26 prices. The bound is set by strength, not by length alone. OCC sustains 5 useful cycles and needs 12% virgin top-up per cycle; office paper sustains 4 cycles and needs 19% top-up; mixed household paper sustains 3 cycles and needs 28% top-up; newsprint sustains only 2 cycles and needs 22% top-up; tissue is a terminal use with 1 cycle at most. After its maximum number of cycles, only 52.8% of an original OCC fibre mass, 43.0% of office fibre, and 37.3% of mixed household fibre is still in circulation. Deinking chemicals cost $29.56 per tonne of feed in every printed grade, and deinked pulp costs $343 per tonne for office paper, $268 per tonne for newsprint and $238 per tonne for mixed paper, against $720 per tonne for virgin kraft pulp and $480 per tonne for virgin mechanical pulp. On cash cost alone, deinking pays against virgin pulp at the stated prices. On fibre mass, every grade is a net fibre loss in every cycle, and two uses are net losses in the stronger sense used here: tissue, which leaves the loop after a single use, and mixed household paper returned to a printing grade, which cannot meet its original grade after three cycles and survives only by downcycling into a lower grade. SIMULATED, NOT MEASURED: all cycle counts and costs are model outputs at stated parameters, not mill measurements.