See how fast a topic fades, and when to review it.

What Ebbinghaus measured

Hermann Ebbinghaus tested one person: himself. In 1879 and 1880 he learned lists of 13 nonsense syllables until he could recite each list twice without a mistake, relearned it after a delay of about 20 minutes to 31 days, and timed both. His measure, savings, is the share of the first learning time he saved the second time round.

Savings is not recall. Six days after learning, relearning a list still took 74.6% as long as learning it had, which says nothing directly about how many syllables he could have recited. In the 2015 replication below, Murre and Dros also scored the syllables recalled at the start of each relearning, and that curve fell far more gently than savings did.

The claim that we forget half of what we learn within an hour, 70% within a day and 90% within a week doesn't match his results. His numbers are about relearning time: an hour after learning, relearning took 55.8% as long as learning had, and a day after, 66.3%. None of his delays comes near 90%. After 31 days the figure was 78.9%.

The replication

In 2015 Jaap Murre and Joeri Dros repeated the experiment, with Dros as the only subject, and the curve came out close to Ebbinghaus's. The exception is 31 days, where Dros saved 4.1% against Ebbinghaus's 21.1%, and the authors could only speculate why.

They also found the curve isn't perfectly smooth. Savings after one or two days sat above a smooth curve, in Ebbinghaus's data and in each replication they compared. Research on sleep would predict a jump like that, they note, though for this kind of experiment it has yet to be shown.

A power curve, not an exponential

Ebbinghaus's formula isn't an exponential. Later work that compared shapes directly:

• Wixted and Ebbesen (1991) found a power function described forgetting better than five alternatives, an exponential among them, for recalled words, recognised faces and pigeons, and in Ebbinghaus's own savings.
• Rubin and Wenzel (1996) fitted 105 two-parameter functions to 210 published data sets. Logarithmic and power functions were among the four that fitted best, and the data could barely tell those four apart.
• Averell and Heathcote (2011) found an exponential fitted each person's data best, but once the analysis allowed for how easily one curve can imitate another, it favoured a power function.

The difference that matters is the tail. An exponential takes the same share of what is left in each equal stretch of time, so it runs down towards nothing. A power curve slows down: the longer something has lasted, the more slowly it goes. Ebbinghaus saw this in his own lists. A month after learning, relearning still took a fifth less time than learning had, and the loss by then was so slow that he expected the effect to vanish only after an indefinitely long time. The model behind the calculator is a power curve too.

Each review changes the curve

A review does more than top the curve back up. Get something right after a gap and it lasts longer, so the next fall is slower and the next gap can be longer. The gain from spreading study out like this is called the spacing effect. A 2006 review by Cepeda and colleagues found 839 assessments of spaced practice in 317 experiments, and that the best gap between study periods grew as the time to the test grew.

Their 2008 study put numbers on it. Over 1,350 people learned a set of facts and reviewed them once. When the test came 7, 35, 70 or 350 days after the review, the best gaps were 1, 11, 21 and 21 days, and a gap that was too long cost far less than one that was too short. There is more on choosing gaps in the forgetting curve, and how to get ahead of it.

What the calculator can't know

It knows dates and how each review felt, nothing else. It can't tell how meaningful the topic is to you, how you slept after learning it, or what you already knew, and each of those can change how fast something fades.

Ebbinghaus chose nonsense syllables because they have no meaning. Material you understand, and can connect to what you know, fades more slowly than his lists did. And FSRS was fitted to flashcards, one card at a time, while a topic is many facts and ideas that you may remember unevenly.