Industrial Engineering & Operations Lab

Learning Curve & Wright's Law Calculator

Model manufacturing learning curves, Wright's Law, progress ratios, Nth unit direct labor costs, cumulative batch totals, and margin expansion.

Learning Curve Engine Volume Matrix Wright's Law Theory FAQ

Manufacturing Presets

Load calibrated Wright's Law production profiles.

Step 1: First Unit Cost (T1), Learning Rate %, Target Quantity & Contract Price

Wright's Law & Production Parameters

⚙️ First Unit & Progress Ratio

💰 Forward Contract Pricing & Economics

Wright's Law Formulation: Unit Cost Y_N = T1 × N^b, where b = ln(Learning Rate) / ln(2). Whenever cumulative volume doubles, cost drops by (100% - LR%).

N-th Unit Cost (Y_N)
$20,111
Unit #250 requires 236.6 hrs (vs 1,411.8 hrs on Unit #1)
Cumulative Average Cost
$29,663
Average cost across first 250 units (Index b = -0.3219)
Total Batch Cost
$7.42M
Total manufacturing cost to produce batch of 250 units
Batch Gross Margin
68.8% Margin
Total Gross Profit: $16.33M on $23.75M revenue

Wright's Law Matrix: N-th Unit Cost vs. Progress Ratio

Simulates N-th unit cost ($) and cumulative average batch cost ($) across production scale milestones and learning rates.

Production Scale 75% Learning Rate 80% Learning Rate 85% Learning Rate 90% Learning Rate 95% Learning Rate

Industrial Operations Principles

Understanding Wright's Law & Learning Curves

Key principles from industrial engineering, aerospace, and cost accounting:

  • The Experience Effect: Repetitive task learning, specialized fixturing, tooling improvements, and scrap reduction reliably drive cost down with cumulative volume.
  • The Doubling Rule: Under an 80% curve, Unit #2 costs 80% of Unit #1; Unit #4 costs 64%; Unit #8 costs 51.2%; Unit #16 costs 40.96%.
  • Forward Pricing Strategy: Early contract bids intentionally take negative margins on early prototype units to capture volume and dominate the cost curve.
  • Diminishing Absolute Reductions: Going from Unit 1 to 2 saves $24K; going from Unit 500 to 501 saves only pennies.

Calculate standard variances in the Standard Costing Lab.

Mathematical Formulation

Wright's Law learning curve equations

b = ln( Learning_Rate_% ) / ln( 2 )

Y_N = T_1 × N^b

Total_Batch_Cost = ∑ [ T_1 × i^b ] ≈ [ T_1 / ( 1 + b ) ] × N^( 1 + b )

Cumulative_Average_Cost = Total_Batch_Cost / N

Batch_Profit = ( Selling_Price × N ) - Total_Batch_Cost

Batch_Margin_% = ( Batch_Profit / Total_Revenue ) × 100%

Calculate production batch sizes in the EPQ Production Lab.

FAQ

Learning curve & Wright's Law questions

What is Wright's Law in manufacturing?

Wright's Law states that for every doubling of cumulative production volume, direct labor and production cost decreases by a constant percentage (the learning rate). Discovered by T.P. Wright in 1936, it is foundational in aerospace, automotive, semiconductor, and clean tech manufacturing.

How do you calculate the Learning Index (b)?

The learning index b is calculated as: b = ln(Learning Rate) ÷ ln(2). For an 80% learning curve, b = ln(0.80) ÷ ln(2) = -0.3219. The N-th unit cost is Y_N = T_1 × N^b.

What is the difference between Unit Cost and Cumulative Average Cost?

The unit cost is the direct cost to produce a specific single unit (the N-th unit). The cumulative average cost is the total manufacturing cost of all units produced up to N divided by N.

How is the Learning Curve used in forward pricing and bidding?

Manufacturers bidding on multi-unit contracts price based on the lower cumulative average cost rather than the expensive first unit (T1), using volume to achieve profitability as workers gain experience.

Can I export the learning curve audit and sensitivity matrix to CSV?

Yes. You can export complete Wright's Law formulas, milestone doubling schedules, batch cost totals, and 6x5 sensitivity tables as a UTF-8 CSV spreadsheet with formula defense.

Continue Exploring Operations & Quality Tools

Explore our Operations & Quality Hub, analyze production batches in the EPQ Production Lab, evaluate target costing in the Target Costing Lab, model equipment reliability in the MTBF & MTTR Lab, or calculate standard variances in the Standard Costing Lab.