How to use the learning curve cost calculator
- Enter the cost of the first unit, in dollars. This can be a cost or a time, valued at an hourly rate.
- Enter the learning rate. An 80 percent rate means that each time total output doubles, the cost falls to 80 percent of what it was.
- Enter the units produced and choose a curve model: unit cost falls, or average cost falls.
- Read the cost of the last unit, the average, the total, and the table at each doubling.
Formula
b = log2(learning rate / 100)
unit cost model: cost of unit n = first cost x n^b, total = sum of all units from 1 to n
average cost model: average of the first n units = first cost x n^b, total = n x average
The exponent b is negative for any rate below 100 percent. At a rate of 100 percent there is no learning and every unit costs the same.
An 80 percent curve over 16 units
The first unit costs $1,000 and the learning rate is 80 percent, so b = log2(0.8) = -0.32193. In the unit cost model the second unit costs $800, the fourth $640, the eighth $512 and the sixteenth $409.60. Each doubling multiplies the cost by 0.8.
The sum of all 16 unit costs is $8,920.14, an average of $557.51 per unit. In the average cost model the same inputs give an average of $409.60 over the 16 units, so the total is $6,553.60 and the sixteenth unit alone costs about $280.61.
Unit cost or average cost
Two versions of the learning curve are in use. In the unit cost version the cost of each single unit falls as output doubles. In the cumulative average version the running average falls instead, which makes later units cheaper than the average. The same learning rate gives a lower total in the average version, so check which one your data followed before you plan.
To find a learning rate from your own data, divide the cost of unit 2n by the cost of unit n for any n. The result is the rate, for example 640 / 800 = 0.8.
Using the result in a quote or plan
Learning effects are strongest in hand work, early in a product’s life and with a stable crew. They flatten once a process is routine, so do not run the curve out to very large quantities without a reason. For a price, add overhead and margin to the average cost with the Cost Plus Pricing Calculator, and test the volume with the Break-Even Calculator.
Assumptions and limits
- The learning rate stays the same through the whole run.
- Every unit is the same product made by the same process.
- Costs are in one currency and ignore inflation and changes in material prices.
- The learning rate shown when the page opens is an example, not a measured value for any industry.
Frequently asked questions
What does an 80 percent learning curve mean?
Each time cumulative output doubles, the cost per unit falls to 80 percent of its earlier level. The 4th unit costs 80 percent of the 2nd, and the 8th costs 80 percent of the 4th.
Can the learning rate be above 100 percent?
The page accepts rates from just above 0 up to 100. A rate above 100 would mean costs rise as output doubles, which is not a learning effect, so it is not allowed.
How many units can I enter?
Up to 1,000,000. The unit cost model adds up every unit, which takes a moment for very large runs, but the answer is exact to the cent.
Why is the total lower in the average cost model?
In the average cost model the whole average falls with output, so even the early units are priced as if they were cheap. In the unit cost model only the latest unit follows the curve and the early units stay expensive.