How is the learning curve calculated?

A common model is Y = aX^b, where Y is time for the Xth unit, a is the time for the first unit, and b = ln(learning rate) / ln(2).

What is a learning rate of 85%?

It means that every time cumulative production doubles, the average time per unit falls to 85% of the previous average.

Can I estimate the learning rate from two time observations?

Yes. If you know the time of unit X1 and unit X2, you can solve for b and derive the implied learning rate. This calculator includes such a helper.

Learning Curve Calculator

Model productivity improvements as you repeat a task. This calculator uses the classic learning curve model Y = aX^b to estimate the time required for later units, the cumulative average time, and the total effort. Perfect for manufacturing, assembly, service operations and cost estimation.

Time for 1st unit (a)

same time unit for all

Learning rate (%) commonly 70–95%

= average time halves to this % when volume doubles

Target unit (X)

which unit do you want to predict?

Exponent (b)

—

b = ln(r) / ln(2)

Time for unit X

—

Yx = a × X^b

Cumulative avg time

—

avg time per unit through X

Total time 1..X

—

= cum avg × X

Estimate learning rate from two observations

If you know the time of unit X₁ and the time of unit X₂ (X₂ > X₁), we can solve for b and the implied learning rate.

Unit X₁

Time Y₁

Unit X₂

Time Y₂

Learning curve table (units 1–20)

Unit	Time (Y)	Cum. Avg	Total Time

Learning curve formula

The most common formulation in industrial engineering is:

Y = a × X^b
where:
a = time for the first unit
X = unit number (1, 2, 3, ...)
b = ln(learning rate) / ln(2)

If your learning rate is 85%, this means: whenever total production doubles, the average time per unit falls to 85% of what it was before. A lower learning rate (like 70%) means faster improvement.

What this calculator does

Computes the exponent b from your learning rate.
Computes the time for the Xth unit.
Approximates cumulative totals (summing each unit from 1 to X).
Lets you reverse-engineer the learning rate from two observed data points.

FAQs

Which time unit should I use?

Any: minutes, hours, setup-minutes. Just be consistent across all inputs.

Why is the cumulative average useful?

Because costing and scheduling often need to know average labor per unit over a planned batch, not just the marginal unit.

Is this the same as experience curve?

Very close. Experience curves sometimes model cost instead of time, but the mathematics is the same.

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

\[','\\]

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Formula (extracted text)

Y = a × Xb where: a = time for the first unit X = unit number (1, 2, 3, ...) b = ln(learning rate) / ln(2)

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
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