Operations Management & Manufacturing Costing
Wright’s Law Learning Curve Unit Cost Formula
Calculate N-th unit manufacturing cost C_N = C_1 * N^(LN(LR)/LN(2)) under Theodore Paul Wright’s (1936) learning-curve law across aerospace, semiconductors, and solar PV.
Forecast manufacturing cost declines per cumulative doubling of production via Wright’s Law!
First discovered in aircraft assembly by Theodore Paul Wright (1936) and famously validated across lithium-ion batteries, solar PV modules, and semiconductors, Wright’s Law states that every time cumulative production volume N DOUBLES, unit manufacturing cost multiplies by a constant Learning Rate LR in (0, 1] (where Progress Ratio LR = 0.80 means a 20% cost reduction per doubling)! Writing N = 2^(LN(N) / LN(2)) yields the exact power-law exponent b = LN(LR) / LN(2) <= 0 and N-th Unit Cost (Crawford unit model) C_N = C_1 * (N^(LN(LR) / LN(2)))!
Check by hand BEFORE trusting any power-law forecast: First_Unit_Cost_C1 = 1,000.00 (B2), Learning_Rate_LR = 0.80 (B3 = 80% curve), and Target_Unit_N = 8 (B4). Because 8 = 2^3 represents THREE exact doublings (1 -> 2 -> 4 -> 8), unit cost MUST equal 1,000 * 0.80 * 0.80 * 0.80 = 512.0000! Our formula computes Learning Exponent b = LN(0.80) / LN(2) = -0.3219 and C_8 = 1,000 * 8^(LN(0.80)/LN(2)) = 512.0000 — and then interpolates cleanly to non-power-of-two milestones such as N = 10 -> C_10 = 476.5099!
| Cumulative Volume Milestone (C_1 = 1,000, LR = 80%) | Doublings Completed | Verified Unit Cost C_N |
|---|---|---|
| First Prototype Unit (N = 1) | 0 Doublings | 1,000.0000 |
| Second Doubling (N = 4) | 2 Doublings (1,000 x 0.8^2) | 640.0000 |
| Third Doubling (N = 8) | 3 Doublings (1,000 x 0.8^3) | 512.0000 |
| Tenth Unit Milestone (N = 10) | LN(10)/LN(2) = 3.3219 Doublings | 476.5099 |
Wright Learning-Curve Exponent b = LN(LR) / LN(2) Formula
Avoid the common trap of plugging (1 - LR) = -0.20 directly as the exponent (N^(-0.20) gives ONLY a 12.94% drop per doubling instead of 20.00%!): ALWAYS use LN(LR) / LN(2) = -0.321928!
=IF(OR(B2 <= 0, B3 <= 0, B3 > 1, B4 < 1), "Require C_1 > 0, 0 < LR <= 1, and N >= 1", ROUND(LN(B3) / LN(2), 4))Exact Crawford / Wright N-th Unit Cost C_1 * N^(LN(LR) / LN(2)) Formula
Keep LN(LR) / LN(2) unrounded inside the exponentiation so powers of 2 hit their exact theoretical milestones without rounding drift.
=LET(c_1, B2, lr_p, B3, n_un, B4, IF(OR(c_1 <= 0, lr_p <= 0, lr_p > 1, n_un < 1), "Require C_1 > 0, 0 < LR <= 1, and N >= 1", ROUND(c_1 * (n_un^(LN(lr_p) / LN(2))), 4)))Try the example
Use the original values or change them to test your understanding.