Learning Curve Calculator

Model productivity improvements as you repeat a task. This calculator uses the classic learning curve model Y = aXb to estimate the time required for later units, the cumulative average time, and the total effort. Perfect for manufacturing, assembly, service operations and cost estimation.

same time unit for all

= average time halves to this % when volume doubles

which unit do you want to predict?

Exponent (b)

—

b = ln(r) / ln(2)

Time for unit X

—

Yx = a × X^b

Cumulative avg time

—

avg time per unit through X

Total time 1..X

—

= cum avg × X

Estimate learning rate from two observations

If you know the time of unit X₁ and the time of unit X₂ (X₂ > X₁), we can solve for b and the implied learning rate.

Learning curve formula

The most common formulation in industrial engineering is:

Y = a × Xb
where:
a = time for the first unit
X = unit number (1, 2, 3, ...)
b = ln(learning rate) / ln(2)

If your learning rate is 85%, this means: whenever total production doubles, the average time per unit falls to 85% of what it was before. A lower learning rate (like 70%) means faster improvement.

What this calculator does

  • Computes the exponent b from your learning rate.
  • Computes the time for the Xth unit.
  • Approximates cumulative totals (summing each unit from 1 to X).
  • Lets you reverse-engineer the learning rate from two observed data points.

FAQs

Which time unit should I use?

Any: minutes, hours, setup-minutes. Just be consistent across all inputs.

Why is the cumulative average useful?

Because costing and scheduling often need to know average labor per unit over a planned batch, not just the marginal unit.

Is this the same as experience curve?

Very close. Experience curves sometimes model cost instead of time, but the mathematics is the same.