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Rabin Poudyal
Page 10-1
10-1 Explainers

10.2The forgetting curve

Why you forget, and how to stop. Memory fades fast after you learn something, then more slowly. A review given while it is fading resets it and makes the next decline gentler, so when you review matters as much as how often. Turn the dials below and watch the same five reviews give very different results.

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  1. 1Read

    In 1879 and 1880 Hermann Ebbinghaus learned lists of 13 nonsense syllables, waited, then learned each list again and timed how much quicker the second learning was. That saving is his measure of what was left. This is his published table: most of the loss comes in the first hours, and what survives a day fades slowly after that.

    0%25%50%75%100%1 hour1 day1 week1 monthTime until relearning (log scale)20 minutes: 58.2% saved1 hour: 44.2% saved8.8 hours: 35.8% saved1 day: 33.7% saved2 days: 27.8% saved6 days: 25.4% saved31 days: 21.1% saved58.2%21.1%
    0%25%50%75%100%1 hour1 day1 week1 monthTime until relearning (log scale)20 minutes: 58.2% saved1 hour: 44.2% saved8.8 hours: 35.8% saved1 day: 33.7% saved2 days: 27.8% saved6 days: 25.4% saved31 days: 21.1% saved58.2%21.1%
    Show as a table
    Ebbinghaus 1885: work saved in relearning, by time since learning
    Relearned afterWork saved
    20 minutes58.2%
    1 hour44.2%
    8.8 hours35.8%
    1 day33.7%
    2 days27.8%
    6 days25.4%
    31 days21.1%

    In 2015 Jaap Murre and Joeri Dros repeated the experiment on one person and found the same shape, with a jump upwards at the one day point that they think may come from the first night's sleep. A saving is not the same as a chance of recall, and these are one person's nonsense syllables, not your facts. The rest of the page uses a model with the same shape.

  2. 2Set

    On the rest of this page memory follows a simple model. Each fact has a stability: the number of days it takes your chance of recalling it to fall to about a third. Chance of recall after t days is e to the power of minus t over stability, so it drops fastest at the start, like Ebbinghaus's curve. Set how well the fact was learned in the first place.

    Recall after 1 day
    61%
    After 1 week
    3%
    After 30 days
    0%
  3. 3Place

    You learn a fact on day 0. Add review sessions on the timeline: tap the chart, or use the button and move each review with its slider (arrow keys move a day, Shift and an arrow an hour). Each review resets recall to 100% and raises stability, by how much depends on how hard the recall was at that moment.

    Load a set of reviews
    0%25%50%75%100%015304560Days since you learned itDay 30Day 60
    0%25%50%75%100%0102030405060Days since you learned itDay 30Day 60
    Show as a table
    Chance of recall over 60 days with 0 reviews
    DayChance of recall
    0100%
    58%
    101%
    150%
    200%
    250%
    300%
    350%
    400%
    450%
    500%
    550%
    600%
    Reviews
    0
    Recall on day 30
    0%
    Recall on day 60
    0%
    1. 4Compare

      Five reviews, evenly spaced, starting one gap after you learn. Turn the gap from one hour (cramming in one evening) up to six days, and read recall a month later.

      0%25%50%75%100%015304560Days since you learned itDay 30Day 60
      0%25%50%75%100%0102030405060Days since you learned itDay 30Day 60
      Show as a table
      Recall over 60 days with five reviews 1 hour apart, against five reviews one hour apart
      DayChance of recall
      0100%
      520%
      104%
      151%
      200%
      250%
      300%
      350%
      400%
      450%
      500%
      550%
      600%
      Recall on day 30
      0%
      Recall on day 60
      0%
      Best gap for day 60
      4.5 days
      Recall on day 60, for every gap
      0%50%100%1h1d3d6d
      0%50%100%1h1d2d3d4d5d6d
      Note

      Same five reviews, same total effort. One hour apart they leave 0% on day 60; 4.5 days apart they leave 41%. Only the timing changed. A review straight after another one finds the memory at full strength and has nothing to repair, so it adds almost nothing. In the words of Elizabeth and Robert Bjork, “when some skill or knowledge is maximally accessible from memory, little or no learning results from additional instruction or practice.” Reviews that feel hard, where you nearly fail, are the ones doing the work.

      Push the gap too far and the curve turns down again: the fact is gone by the next review and you are relearning it. Real people show the same rise and fall. In a study of more than 1,350 people learning obscure facts, Cepeda and colleagues found the best gap before a test 35 days later was about 8 days, and that the best gap grows as the test gets further away.

    2. 5Run

      This is the real scheduler behind this site's flashcards (src/lib/srs.ts), modelled on the SM-2 algorithm Piotr Wozniak published for SuperMemo in 1990. A new card that you get right comes back the next day; after that each gap is the last one times the card's ease, which starts at 2.5. Pick how you answer every review and the scheduler places them.

      Answer every review with
      0%25%50%75%100%015304560Days since you learned itDay 30Day 60
      0%25%50%75%100%0102030405060Days since you learned itDay 30Day 60
      Show as a table
      Recall over 60 days with the scheduler's 4 reviews, answering good every time
      DayChance of recall
      0100%
      590%
      1054%
      1587%
      2070%
      2555%
      3044%
      3594%
      4085%
      4577%
      5069%
      5562%
      6056%
      Reviews in 60 days
      4
      Recall on day 30
      44%
      Recall on day 60
      56%

      Review days: 1, 4, 12, 32next due day 82

      Note

      The scheduler never sees this model. On /flashcards it learns from your grades instead: a Hard answer shrinks the next gap and lowers the card's ease, an Again sends it back to be relearned, so cards you find difficult come back sooner. That is the honest limit of this page too: the curves are a model of the mechanism, not a measurement of you.

    3. 6Try

      Three cards on what you just read, graded with the same scheduler. This deck lives only on this page and saves nothing.

      Mini deck0 of 3 done

      What did Ebbinghaus measure to track forgetting?

    4. 7Go

      The decks on this site are scheduled this way. Pick one and give it five minutes a day.

    10.2.1How the model works

    Chance of recall t days after the last study is e−t/S, where S is stability in days. A review is a recall attempt that succeeds with chance R, the recall at that moment. If it succeeds, stability grows more the harder the recall was; if it fails, you relearn the fact and stability stays put. Averaged over the two, a review multiplies stability by 1 + G × R × (1 − R), with G set to 5. The boost is largest when recall is a coin flip and near zero when it is certain or long gone.

    That is a sketch of the mechanism, not a measurement. The numbers it prints are the model's, not yours, and real schedulers fit far richer models to millions of reviews. The shape it produces (fast early loss, cramming that fades, a best gap that is neither tiny nor huge) is the part the research supports.

    10.2.2Sources

    1. Hermann Ebbinghaus, Memory: A Contribution to Experimental Psychology (1885; translated by H. A. Ruger and C. E. Bussenius, 1913), chapter 7, section 29. The seven savings in step 1 are from its results table.
    2. Jaap M. J. Murre and Joeri Dros, Replication and Analysis of Ebbinghaus' Forgetting Curve, PLOS ONE 10(7), 2015.
    3. Nicholas J. Cepeda, Edward Vul, Doug Rohrer, John T. Wixted and Harold Pashler, Spacing Effects in Learning: A Temporal Ridgeline of Optimal Retention, Psychological Science 19(11), 2008.
    4. Elizabeth L. Bjork and Robert A. Bjork, Making Things Hard on Yourself, But in a Good Way: Creating Desirable Difficulties to Enhance Learning, in Psychology and the Real World (2011).
    5. Piotr Wozniak, SuperMemo 2: Algorithm (1990), the SM-2 scheduler.