What Is a Learning Curve? Formula, Calculation, and Example (2024)

What Is a Learning Curve?

A learning curve is a mathematical concept that graphically depicts how a process is improved over time due to learning and increased proficiency. The learning curve theory is that tasks will require less time and resources the more they are performed because of proficiencies gained as the process is learned. The learning curve was first described by psychologist Hermann Ebbinghaus in 1885 and is used as a way to measure production efficiency and to forecast costs.

A learning curve is typically described with a percentage that identifies the rate of improvement. In the visual representation of a learning curve, a steeper slope indicates initial learning that translates into higher cost savings, and subsequent learnings result in increasingly slower, more difficult cost savings.

Understanding a Learning Curve

The learning curve also is referred to as the experience curve, the cost curve, the efficiency curve, or the productivity curve. This is because the learning curve provides cost-benefit measurements and insight into all the above aspects of a company.

The idea behind thisis that any employee, regardless of position, takes time to learn how to carry out a specific task or duty. The amount of time needed to produce the associated output is high. Then, as the task is repeated, the employee learns how to complete it quickly, and that reduces the amount of time needed for a unit of output.

Thatis why the learning curve is downward sloping in the beginning with a flat slope toward the end, with the cost per unit depicted on the Y-axis and total output on the X-axis. As learning increases, it decreases the cost per unit of output initially before flattening out, as it becomes harder to increase the efficiencies gained through learning.

Learning curves are often associated with percentages that identify the rate of improvement. For example, a 90% learning curve means that for every time the cumulative quantity is doubled, there is a 10% efficiency gained in the cumulative average production time per unit. The percentage states the percentage of time that will carry over to future iterations of the task when production is doubled.

Learning Curve Formula

The learning curve has a formula to identify a target cumulative average time per unit or batch. The formula for the learning curve is:

$\begin{aligned}&{\bf Y = aX^b}\\&\textbf{where:}\\&\textbf{Y} = \text{Cumulative average time per unit or batch}\\&\textbf{a} = \text{Time taken to produce initial quantity}\\&\textbf{X} = \text{The cumulative units of production or the}\\&\qquad\ \text{cumulative number of batches}\\&\textbf{b} = \text{The slope or learning curve index, calculated}\\&\qquad\text{as the log of the learning curve percentage}\\&\qquad\text{divided by the log of 2}\end{aligned}$​Y=aXbwhere:Y=Cumulativeaveragetimeperunitorbatcha=TimetakentoproduceinitialquantityX=Thecumulativeunitsofproductionorthecumulativenumberofbatchesb=Theslopeorlearningcurveindex,calculatedasthelogofthelearningcurvepercentagedividedbythelogof2​

Learning Curve Calculation

Let's use an 80% learning curve as an example. This means that every time we double the cumulative quantity, the process becomes 20% more efficient. In addition, the first task we complete took 1,000 hours.

$\begin{aligned}Y &= 1000\times1^{\frac{\text{log}\, .80}{\text{log}\, 2}} \\&= 1000\times 1\\& = \text{an average of 1,000 hours per task}\\&\quad\ \,\text{to complete one task}\end{aligned}$Y​=1000×1log2log.80​=1000×1=anaverageof1,000hourspertasktocompleteonetask​

Now let's double our manufacturing output. The initial time spent on the first task will stay 1,000 hours. However, our value for X will now change from one to two:

$\begin{aligned}Y&= 1000\times2 ^{\frac{\text{log}\, .80}{\text{log}\, 2}}\\&= 1000\times .8\\& = \text{an average of 800 hours per task}\\&\quad\,\,\,\text{to complete two tasks}\end{aligned}$Y​=1000×2log2log.80​=1000×.8=anaverageof800hourspertasktocompletetwotasks​

This means that the total cumulative amount of time needed to perform the task twice was 1,600. Since we know the total amount of time taken for one task was 1,000 hours, we can infer that the incremental time to perform the second task was only 600 hours. This diminishing average theoretically continues as you advance along the learning curve. For example, the next doubling of tasks will occur at four tasks completed:

$\begin{aligned}Y &= 1000 \times 4^{\frac{\text{log}\, .8}{\text{log}\, 2}}\\& = 1000 \times .64\\& = \text{an average of 640 hours per task}\\&\quad\,\,\,\text{to complete four tasks}\end{aligned}$Y​=1000×4log2log.8​=1000×.64=anaverageof640hourspertasktocompletefourtasks​
In this final example, it took a total of 2,560 hours to produce 4 tasks. Knowing it took 1,600 hours to produce the first two tasks, the learning curve indicates it will only take a total of 960 hours to produce the third and fourth task.

Learning Curve Table

The learning curve can become complicated when trying to distinguish between the cumulative quantity, the cumulative production time, the cumulative average production time, and the incremental production time. Therefore, it is common to see a learning curve table that summarizes and neatly organizes each value. This type of information is very useful in cost accounting. The example above would have table as follows: