The forgetting curve

What is the forgetting curve?

The forgetting curve is a graph of how much you still remember of something you learned, plotted against the time since you learned it. It falls steeply at first and then flattens out: much of the loss happens within hours, while what survives the first days fades far more slowly.^[1]

Hermann Ebbinghaus published the first forgetting curve in 1885.^[1] Since then, many studies have measured forgetting with other people, materials and tests, and a review by Rubin and Wenzel (1996) found that the same fast-then-slow shape fits most of their 210 data sets.^[4] The exact equation is still debated: a power function fit better than an exponential in Wixted and Ebbesen's experiments,^[3] and Rubin and Wenzel found several equations that fit about equally well.^[4]

How did Ebbinghaus measure forgetting, and does it hold up?

Ebbinghaus learned lists of nonsense syllables himself, then timed how long it took to relearn them after intervals from about 20 minutes to 31 days.^[1] Nonsense syllables are more uniform than real words, which makes lists easier to compare.^[2] The time saved on relearning, as a share of the first learning time, is called savings. It is not the share of syllables remembered: 33.7% savings after one day does not mean he had forgotten 66% of the list.

The method has limits. Ebbinghaus was his only subject, knew the purpose of each test, and called his own numbers individual and uncertain.^[1] But when Jaap Murre and Joeri Dros repeated the experiment in 2015, also with one subject, they found the same fast early loss and slower later loss, with lower savings overall.^[2]

What changes how fast you forget?

How fast you forget depends on what you learned, how well you learned it, and how you review it.

• Meaning. The same fast-then-slow pattern holds for words, faces and school knowledge,^[3][5] but meaningful material is learned much faster. Ebbinghaus learned stanzas of Byron's Don Juan with about a tenth of the readings that nonsense syllables needed.^[1]
• How well you learned it. Harry Bahrick (1984) tested people on the Spanish they learned in school, up to 50 years earlier. Retention fell for the first 3 to 6 years, then stayed nearly unchanged for up to 30 years, and how well people had first learned Spanish predicted how much they kept.^[5]
• Reviews. Recalling material, and spreading reviews over time, both slow later forgetting (see the next two sections).
• Sleep may play a role. In the 2015 replication, savings were higher after one day than after 9 hours. Sleep could explain this jump, but the link is not established.^[2]

How do reviews change the forgetting curve?

Each review restarts the forgetting curve, and the memory then fades more slowly than before. When Ebbinghaus relearned the same lists on six days in a row, the readings he needed fell from 158 on the first day to 31 on the last.^[1]

How you review matters too. In a study by Henry Roediger and Jeffrey Karpicke (2006), students who reread a passage did better on a test five minutes later. But two days and one week later, students who had instead taken recall tests remembered substantially more.^[6] This is the testing effect, the basis of active recall.

Do spaced reviews work better than massed ones?

Yes. Spreading reviews over time leads to better retention than massing them together in one session, an effect known as the spacing effect. Ebbinghaus found that 38 readings spread over three days prepared a list as well as 68 readings in a single session.^[1]

A meta-analysis by Nicholas Cepeda and colleagues (2006) combined 317 experiments. With the same total study time, spaced study beat massed study, and the longer you need to remember something, the longer the best gap between sessions.^[7] The same review found too little data to say whether gaps that keep growing beat equal gaps.^[7] Spaced repetition apps still lengthen the interval after each successful review.

Can you predict when you will forget something?

No. The forgetting curve describes how retention declines on average across many items, not the moment a particular memory will be lost. No algorithm can predict that moment, so spaced repetition apps do not schedule a review "just before you forget".

Instead, an algorithm such as FSRS estimates each card's retrievability: the probability that you can recall it now. It schedules the next review for when that probability falls to a target called desired retention.^[8] In Anki, desired retention defaults to 90%, meaning you should recall about 9 in 10 cards when they come due.^[9]

How can you use the forgetting curve when studying?

The research above suggests a few habits:

1. Review new material soon after learning it, since forgetting is steepest in the first hours.^[1]
2. Test yourself instead of rereading: try to recall the answer before you check it.^[6]
3. Spread reviews over days and weeks, with longer gaps for things you need to remember longer.^[7]
4. Let software keep track: flashcard apps such as Anki schedule each card on its own.

For example intervals, see the spaced repetition schedule.