As cumulative output doubles, the time per unit falls by a fixed percentage — the heart of Wright's learning curve. Enter the time for the first unit and a learning rate to find the time for any unit, the cumulative total, the cumulative average, and the labor time or cost for a production run. Everything recomputes live in your browser.
The learning curve (or experience curve) captures a robust empirical fact: as people repeat a task, they get faster. Wright's model formalizes it — every time cumulative output doubles, the time to produce a unit drops by a constant percentage, the learning rate. This calculator uses Wright's unit model to find the time for any specific unit, the cumulative total and average time, and the labor time or cost for a production run, all live in your browser.
T. P. Wright observed in 1936 that the labor hours to build the Nth airplane followed Tₙ = T₁ · nᵇ, where T₁ is the time for the first unit, n is the cumulative unit number, and b is the learning exponent. The exponent is derived from the learning rate: b = ln(rate) / ln(2). For an 80% learning curve, b = ln(0.80)/ln(2) ≈ −0.322. Because b is negative, unit time decreases as n grows. The defining property: doubling cumulative output multiplies unit time by exactly the learning rate — the 100th unit takes 80% as long as the 50th, which takes 80% as long as the 25th, and so on.
A learning rate of 80% is steep, common in aerospace and complex assembly; a 90% rate is gentler, typical of more automated or already-refined processes. A lower percentage means faster learning and steeper cost reduction. The complement (100% − rate) is sometimes called the learning slope or progress ratio improvement. Estimate your rate from historical data by plotting log(unit time) against log(unit number) — the slope is b, and rate = 2ᵇ. Note that a 100% learning rate means no learning at all (b = 0, every unit takes T₁), which is why the rate must be strictly below 100%.
There are two common formulations. The unit model (used here) treats Tₙ as the time for the specific Nth unit and computes the cumulative total by summing the individual unit times. The cumulative-average model instead treats T₁ · nᵇ as the average time over the first n units, so the cumulative total is n · T₁ · nᵇ. The two give different totals from the same inputs, so always confirm which convention a textbook, contract, or estimating system uses. This calculator reports the unit-model cumulative total (an exact sum of T₁·iᵇ) and divides by n to give the cumulative average.
Learning curves are widely used to bid jobs, plan capacity, and price production runs. Use the production-run feature to total the labor hours between any two unit numbers — for example, units 51 through 100 of a follow-on order — and multiply by a labor rate to estimate cost. Because early units are far more expensive than later ones, ignoring the learning effect badly overestimates the cost of large runs and underestimates the cost of small ones. Caveats: learning eventually plateaus as a process matures, and any disruption (design change, new workers, a production gap) can reset or flatten the curve, so revalidate the rate periodically against actuals.
A learning curve describes how the time or cost to produce a unit declines as cumulative production experience grows. Wright's model states that each doubling of cumulative output reduces unit time by a fixed percentage (the learning rate), following Tₙ = T₁ · nᵇ.
b = ln(learning rate) / ln(2), with the rate as a decimal. For an 80% curve, b = ln(0.80)/ln(2) ≈ −0.3219. The exponent is negative because unit time decreases as the unit number increases.
It means that every time cumulative output doubles, the time per unit falls to 80% of its previous value. So if the 10th unit takes 50 hours, the 20th takes about 40 hours, the 40th about 32 hours, and so on. A lower percentage indicates faster learning and steeper cost reduction.
In the unit model, T₁ · nᵇ is the time for the specific Nth unit, and the cumulative total is the sum of individual unit times. In the cumulative-average model, T₁ · nᵇ is the average time over the first n units, so the total is n times that. They produce different totals, so identify which one your source uses. This calculator uses the unit model.
Learning typically continues but slows as a process matures, eventually approaching a plateau or "standard time" where further improvement requires process or technology changes rather than repetition. The curve can also be disrupted by design changes, new or retrained workers, long production gaps, or automation — any of which may flatten, reset, or steepen the curve, so estimates should be revalidated against actual data.