Learning Curve

A learning curve shows how the time, cost, or resources required to perform a task decline as the task is repeated and proficiency increases. First described by Hermann Ebbinghaus in 1885, the concept is used to measure production efficiency and to forecast costs.

Key takeaways

• The learning curve charts how performance (time, cost, error rate) improves with experience.
• In business, the curve helps forecast unit costs, plan production, and schedule training.
• Learning curves are typically expressed as a percentage (e.g., 80%, 90%) that indicates the improvement rate when cumulative output doubles.

How it’s used in business

As employees repeat tasks, average time per unit typically falls, lowering unit costs. Managers use learning-curve estimates to:
* Forecast labor hours and production costs.
* Set prices and bids that reflect expected efficiencies.
* Plan staffing, training, and logistics to meet demand.

A learning curve is steepest early on (rapid gains) and flattens over time as further improvements become harder to achieve.

The formula

The commonly used model for the cumulative average time per unit is:
Y = a X^b

Where:
* Y = cumulative average time per unit (or batch)
* a = time to produce the first unit (initial quantity)
* X = cumulative number of units or batches
* b = learning exponent = log(p) / log(2), where p is the learning-rate percentage expressed as a decimal (for example, p = 0.8 for an 80% learning curve)

Interpretation: when X doubles, Y is multiplied by p (the learning percentage).

Worked example (80% learning curve)

Assume the first unit takes 1,000 hours and the learning rate is 80% (p = 0.8).

Using Y = a X^b with b = log(0.8)/log(2):

• X = 1: Y = 1000 × 1^b = 1000 hours (average for the first unit)
• X = 2: Y = 1000 × 2^b = 1000 × 0.8 = 800 hours (average per unit after two units)
• Cumulative time for 2 units = 2 × 800 = 1,600 hours → incremental time for 2nd unit = 600 hours
• X = 4: Y = 1000 × 4^b = 1000 × 0.64 = 640 hours (average per unit after four units)
• Cumulative time for 4 units = 4 × 640 = 2,560 hours → incremental time for units 3–4 = 960 hours

This shows diminishing incremental time per additional unit as experience increases.

Graphing learning curves

Common ways to visualize learning-curve data:
* Plot average time (or cost) per unit on the y‑axis against cumulative units on the x‑axis. This shows decreasing average time.
* Plot total cumulative time vs cumulative units—this rises, but the slope flattens as efficiencies accrue.
* Use log-log axes to linearize the power-law relationship; on a log-log plot, the slope equals the exponent b and makes trend estimation easier.

Be careful interpreting raw upward-sloping cumulative plots—they can obscure per‑unit efficiency gains unless you examine average or per‑unit metrics.

Practical interpretation and terminology

• Learning-rate percentage: If the curve is 90% (p = 0.9), average time per unit falls to 90% each time cumulative production doubles — a 10% improvement on doubling.
• “High” or “steep” learning curve: In technical terms, a steeper downward slope means faster improvement (greater efficiency gains). Colloquially, “steep learning curve” is often used to mean “hard to learn,” which is a different usage—clarify context when communicating.

Conclusion

Learning curves quantify how experience reduces time and cost per unit. They are a practical tool for forecasting labor and production costs, planning training and capacity, and understanding how efficiencies evolve as cumulative output increases.