---
title: "The Cutting Stock Problem, Explained Simply"
description: "What the cutting stock problem is, why it is NP-hard, and how 1D and 2D optimizers (guillotine vs true nesting) find good solutions fast."
image: "https://nestingcalc.com/og-default.png"
url: "https://nestingcalc.com/guides/cutting-stock-problem/"
locale: "en"
---

# The Cutting Stock Problem, Explained Simply

What the cutting stock problem is, why it is NP-hard, and how 1D and 2D optimizers (guillotine vs true nesting) find good solutions fast.

## What is the cutting stock problem?

Given stock lengths (bars, boards, sheets) and a list of requested pieces, cut all pieces from as little stock as possible. It sounds trivial; mathematically it is NP-hard — the number of combinations explodes as the piece list grows.

## 1D, 2D and guillotine cuts

1D means one dimension: pipes, profiles, studs. 2D adds width — plywood, glass, sheet metal. Guillotine cuts run edge to edge (what a panel saw does); true nesting allows any rotation and non-guillotine layouts (what lasers and routers do).

## Why exact solutions are rare

Only small instances can be solved exactly (dynamic or integer programming). Industry relies on heuristics — First Fit Decreasing, Best Fit Decreasing, shelf algorithms — which usually land within a few percent of the optimum in milliseconds.

## Kerf and other real-world traps

Every cut consumes material: a 3 mm blade kerf adds 3 mm per cut, and 50 cuts silently eat 150 mm of stock. Offcut reuse, grain direction and trim losses matter just as much as the packing itself.

## Try it on your own cut list

The [Linear cutting calculator](https://nestingcalc.com/linear-cutting-calculator/) optimizes bar and profile lists; the [Sheet cutting calculator](https://nestingcalc.com/sheet-cutting-calculator/) handles guillotine sheet layouts with rotation and kerf. Paste your list and compare total stock before and after.

[Linear cutting calculator](https://nestingcalc.com/linear-cutting-calculator/) [Open the linear cutting calculator](https://nestingcalc.com/linear-cutting-calculator/)

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