The Ebbinghaus forgetting curve
Memories fade fast at first, then more slowly. Each time you successfully recall something, the fade that follows is gentler. Try it: tap the chart to add or remove review days.
Model: recall R = e−t/S. Each review resets R to 100% and multiplies stability S. The numbers are illustrative, not a prediction for any specific fact.
What the chart is showing
Cramming two reviews right after learning gets you a high score tomorrow and not much a month later: the curve still collapses. Spaced reviews at 1, 3, 7 and 16 days use about the same effort but leave the last curve so flat that most of it survives day 30. Reviewing every day keeps recall high too, but spends far more time for little extra gain. That efficiency gap is the whole argument for spaced repetition.
Where the curve comes from
In Über das Gedächtnis (Memory, 1885), Hermann Ebbinghaus memorised lists of nonsense syllables such as “DAX” and “BOK” so meaning couldn’t help him, then measured how much faster he relearned each list after delays of 20 minutes, one hour, nine hours, one day, two days, six days and 31 days. The “savings” fell quickly and then levelled off. A 2015 replication by Murre and Dros (PLOS ONE) reproduced the same shape more than a century later.
The formula
Most apps model it as R = e−t/S: recall probability R decays exponentially with time t, at a rate set by stability S. Bigger S means a flatter curve. A successful recall doesn’t just reset R to 100%; it increases S, which is why the gaps between reviews can grow. Algorithms like SM-2 are rules of thumb for picking the next gap before R gets too low.
What changes the slope
- Meaning: material you understand and connect to what you know decays much more slowly than nonsense syllables.
- How you review: retrieving the answer (active recall) raises stability more than rereading it.
- Sleep: memories are consolidated during sleep, one reason spacing across days works better than spacing within one evening.
- Difficulty: reviews that feel a little effortful, just before you’d forget, tend to help most (“desirable difficulties”, Robert Bjork).
Want a dated plan for your exam? Use the spaced repetition schedule calculator, or let the study session schedule every card for you.
Questions people ask
What is the Ebbinghaus forgetting curve?
A graph of how much newly learned information you can still recall as time passes without review. Hermann Ebbinghaus measured it on himself in 1885 by learning lists of nonsense syllables and testing how much time relearning them saved after delays from 20 minutes to 31 days.
How fast do we forget?
In Ebbinghaus’s data the drop was steepest in the first hour and day, then flattened out; most of what was lost was gone within a day. The exact rate depends on how meaningful the material is and how well it was learned, so treat the famous “you forget 70% in a day” figures as rough illustrations, not laws.
What is the forgetting curve formula?
A common simplified model is R = e^(−t/S), where R is the chance of recall, t is time since the last review and S is the memory’s stability. Ebbinghaus himself fitted a slightly different logarithmic formula; the exponential version is used by many spaced-repetition apps because it is easy to work with.
How do you beat the forgetting curve?
Review at spaced intervals and make each review a retrieval attempt (active recall) rather than rereading. Each successful recall raises stability, so the curve after it is flatter and the next review can wait longer.