Mathematical Psychology
Psychometrics & MeasurementDavid KrantzPatrick SuppesFrederic Lord
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Forgetting

Power Law of Forgetting

The power law of forgetting states that memory retention decreases as a power function of time, with rapid initial forgetting that progressively slows.

R(t) = a · t⁻ᵇ

The power law of forgetting, established empirically by Jost (1897) and formalized by Wixted and Ebbesen (1991), states that memory retention decreases as a power function of the retention interval. This function provides a better fit to forgetting data than the exponential function originally proposed by Ebbinghaus, across a remarkably wide range of memory tasks, materials, and time scales.

Power Law of Forgetting R(t) = a · t⁻ᵇ

R = retention (proportion recalled)
t = time since learning
a = initial memory strength
b = rate of forgetting

Why Power Rather Than Exponential?

Anderson and Schooler (1991) showed that the power law of forgetting mirrors the statistical structure of the environment: the probability that information from the past will be needed in the future follows a power function of the time elapsed. This suggests that forgetting is rationally adapted to the statistics of information relevance. The ACT-R cognitive architecture implements this principle directly, using base-level activation decay as a power function of time since last retrieval.

Interactive Calculator

Each row records delay (time since learning, in hours) and retention (proportion recalled, 0–1). The calculator fits both a power law R = a·t−b and exponential R = a·e−bt forgetting function and compares them.

Click Calculate to see results, or Animate to watch the statistics update one record at a time.

Related Topics

Memory ModelsExponential ForgettingMemory ModelsACT-R Declarative MemoryMemory ModelsSpacing Effect Models

References

  1. Wixted, J. T., & Ebbesen, E. B. (1991). On the form of forgetting. Psychological Science, 2(6), 409–415. https://doi.org/10.1111/j.1467-9280.1991.tb00175.x
  2. Anderson, J. R., & Schooler, L. J. (1991). Reflections of the environment in memory. Psychological Science, 2(6), 396–408. https://doi.org/10.1111/j.1467-9280.1991.tb00174.x
  3. Rubin, D. C., & Wenzel, A. E. (1996). One hundred years of forgetting: A quantitative description of retention. Psychological Review, 103(4), 734–760. https://doi.org/10.1037/0033-295X.103.4.734
  4. Ebbinghaus, H. (1885). Über das Gedächtnis: Untersuchungen zur experimentellen Psychologie. Duncker & Humblot. https://doi.org/10.1037/10011-000

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