Learning curve calculator
Project how long each unit takes as the work is repeated, or calculate your learning rate from two measurements.
1. Project the curve
Time of unit 32
3.93 min
Cumulative time
176.1 min
Average per unit
5.50 min
Unit that reaches the target
31
| Unit | 1 | 2 | 4 | 8 | 16 | 32 | 64 |
|---|---|---|---|---|---|---|---|
| Minutes | 12.00 | 9.60 | 7.68 | 6.14 | 4.92 | 3.93 | 3.15 |
2. What learning rate do I have? (from two measurements)
Learning rate
75.0%
Slope (n)
-0.415
Time of the 1st unit
101.4 min
The preloaded values come from Niebel and Freivalds: 12 min for the first unit at 80% gives 9.60, 7.68, 4.92 and 3.93 min for units 2, 4, 16 and 32 (table 18.1); and in example 18.1, 20 min at unit 50 and 15 min at unit 100 give 75%. This is Crawford's unit model; cumulative time is added up unit by unit (the book approximates it by integration and the result differs little).
How it works
The tool uses the Crawford unit model, the one developed by Niebel and Freivalds: the time of unit number x is y = k · xn, where k is the time of the first unit and n is the slope. Each time the cumulative quantity doubles, the time per unit drops by a fixed percentage (the learning rate).
Section 1: project the curve. You enter the time of the first unit, the learning rate (for example 80%), the unit number N you are interested in and, optionally, a target time.
- The slope is n = log₂(learning rate), a negative number: for 80% it is −0.322 and for 90% it is −0.152.
- The time of unit N is k · Nn.
- The cumulative time is the sum of the times of units 1 to N, added one by one. The book approximates it by integration: the results differ very little.
- The unit that reaches the target is the first one whose time drops to the target: x = (target ÷ k)1 ÷ n, rounded up. If the target is greater than the time of the first unit, it is already met from unit 1; with a 100% learning rate (no learning) it is never reached.
Section 2: what rate do I have? With two measurements (unit x₁ took y₁ and unit x₂ took y₂) it solves for the slope n = (log y₂ − log y₁) ÷ (log x₂ − log x₁), the learning rate 2n and the time of the first unit k. This is the procedure of example 18.1 in the book.
How to read it. The lower the percentage, the faster the learning: 70% is the highest rate of learning and 100% means there is no learning, as in a fully automated operation. The typical rates the book gives are 70 to 80% for large or assembly work (aircraft), 80 to 90% for welding and 90 to 95% for machining. The book's examples are preloaded: 12 minutes for the first unit at 80% gives 9.60 minutes for unit 2 and 3.93 for unit 32; and 20 minutes at unit 50 with 15 at unit 100 gives 75%.
What it does not do. It is an average learning rate, not a prediction for a particular person. It assumes continuous repetition: if the operator is interrupted (on holiday, for example) they forget part of what they learned, the "regression" that the book models separately and that this calculator does not compute. The learning rate must be between 0 and 100.
If you prefer to work in Excel, there is a learning curve spreadsheet in Excel with these same calculations.
Sources
These are the ones from the article where the theory behind this tool is developed.
Which models exist and how are they used to set standards? It is in the article Learning curves.