Learning Curve Calculator

The learning curve models unit time as a power function of cumulative output: the time for unit n equals the time for unit 1 multiplied by n raised to the exponent b, where b is negative. The learning rate is stated as the fraction of time retained each time cumulative output doubles, so b equals the natural log of the rate divided by the natural log of 2. An 80 percent rate gives b of minus 0.322, meaning unit 2 takes 80 percent of the time of unit 1, unit 4 takes 80 percent of unit 2, and unit 100 takes about 22 percent of the first. Because the relationship is a power law, plotting time against unit number on log-log axes yields a straight line whose slope is b, which is how an empirical rate is fitted from production records. Published rates cluster according to how much of the work is human-paced rather than machine-paced. Aerospace airframe assembly is conventionally modeled near 80 to 85 percent, electronics and machine-intensive operations nearer 90 to 95 percent, and complex manual tasks as low as 70 percent; a rate of 100 percent means no learning at all. Two caveats dominate practical use. First, the unit formulation used here and the cumulative-average formulation give different unit times for the same stated rate, so an estimate must declare which is meant. Second, the curve assumes uninterrupted production of an unchanged design: breaks cause forgetting, engineering changes reset progress, and every real curve eventually flattens against a floor set by tooling and process limits.

The relationship was documented by Theodore Paul Wright, an aeronautical engineer at Curtiss-Wright, in a 1936 paper in the Journal of the Aeronautical Sciences titled Factors Affecting the Cost of Airplanes. Examining airframe production records, Wright found that direct labor per aircraft fell by a consistent percentage each time cumulative output doubled, and reported a curve close to 80 percent. The finding became operationally important during the Second World War, when American aircraft and shipbuilding programs used it to forecast labor requirements and to schedule production, and postwar analyses of wartime shipyard output confirmed that the same pattern held across very different products. Two extensions followed. Work associated with Lockheed in the 1940s produced the unit formulation, in which the power law describes the time for an individual unit rather than the running average; it is usually credited to J. R. Crawford and remains the basis of most detailed production scheduling. In the 1960s the Boston Consulting Group, under Bruce Henderson, generalized the idea into the experience curve, extending declining cost per unit with cumulative volume from labor to total cost and using it as an argument for pursuing market share. Psychology had reached similar curves independently: Hermann Ebbinghaus charted practice and forgetting curves in his 1885 studies of memory, and the educational use of learning curves to model practice effects descends from that line of work rather than from Wright.