Spaced Repetition Explained: Learning with Spacing

You know this: vocabulary test on Friday, cramming everything in on Thursday night, barely passing on Friday, and by Monday it's all gone. The problem was not your memory. The problem was the schedule.

Spaced repetition means revisiting the same material at intervals of time. With flashcards, active recall almost always comes with it: you answer the question yourself first and then check. These are two different ingredients that work well together. We explain retrieval in the guide Active Recall. This article is about the spacing.

Ebbinghaus: what the forgetting curve actually shows

Every article on spaced repetition begins with Hermann Ebbinghaus, and almost every one tells it a little wrong. Ebbinghaus published his memory studies in 1885. He was his own only test subject and learned meaningless syllable sequences.

What he measured was not how much he could still recall freely, but the savings in relearning: how much faster the second time went compared with the first. A saving of 40% therefore does not mean that 40% of the content was still retrievable.

In 2015 Murre and Dros repeated the experiment, again with exactly one test subject who invested around 70 hours. Testing took place after 20 minutes, one and nine hours, and after one, two, six and 31 days. The authors interpret the curve's shape as a successful replication. The 31-day value did, however, deviate considerably from the historical result.

What you can take from this: forgetting happens quickly and then more slowly. What you cannot take from this: sentences like "After one day everyone forgets X percent". Those appear in countless guides and cannot be derived from this data.

The spacing effect: well supported

The evidence for the spacing effect itself is much more solid. Cepeda et al. published a meta-analysis in 2006: 184 articles, 317 experiments, 839 comparisons, mainly on verbal learning material. For the comparison "all at once" versus "distributed", learners averaged 36.7% versus 47.3% correct answers. This was based on 271 comparisons with a combined 14,811 participants.

A surprising number from the same work: steadily growing intervals were not significantly better than constant intervals (62.0% versus 58.6%, p = 0.61, from 22 comparisons). Distributing clearly helps. That the intervals must always grow larger is less well supported than most apps suggest.

How large should the gap be?

Cepeda et al. examined exactly this in 2008, this time as an experiment. 1,354 people learned 32 facts over the internet. They were randomly assigned to 26 combinations: gap until the repetition of up to 105 days, gap until the final test of up to 350 days.

The result is a hill. With larger gaps between study sessions, things first get better and then, beyond a point, worse again. "The longer the pause, the better" is therefore not correct. The best gap yielded 64% more freely recalled answers than a repetition on the same day (d = 1.1). These are relative percentages, not percentage points.

As a rough guide, the study gives: for a test one week later, the best gap was about 20 to 40% of that time; for a test one year later, only about 5 to 10%. The further away the exam, the longer you may wait, but relatively speaking not indefinitely. What the study does not provide is a complete schedule for all further repetitions. That requires an algorithm.

From the card box to the algorithm

Leitner: cardboard compartments

The analog variant is the Leitner system. All cards start in the first compartment. Answered correctly, the card moves one compartment forward. Answered incorrectly, in the basic variant it goes back to the first compartment. Because cards in later compartments come up less often, longer gaps arise automatically for what you already know.

Sebastian Leitner's book "So lernt man lernen" is bibliographically documented for 1972, though already in its fourth edition; other sources give 1973. We have not found a controlled comparison between the Leitner box and modern algorithms.

SM-2: the formula from 1987

Piotr Woźniak developed the SuperMemo method in the 1980s and in December 1987 wrote the first computer implementation. The associated algorithm SM-2 is still the basis of many flashcard apps. The original rule:

• First repetition after 1 day, second after 6 days.
• Afterwards: new interval = old interval × ease factor.
• The factor starts at 2.5 and changes depending on the rating on a scale from 0 to 5.
• Rated below 3, the sequence starts again from the beginning.

With a constant factor of 2.5 this gives approximately 1 → 6 → 15 → 38 → 95 days. After five repetitions you therefore see a card again only after roughly three months. This is a worked example, not a prescribed study plan, and Woźniak's parameters are not independently established as optimal for everyone.

Anki and FSRS

Anki is attributed to Damien Elmes and dated to 2006. Anki's SM-2 is not an unchanged copy: it has four answer buttons, adjustable learning steps, and late repetitions are taken into account. Since Anki 23.10, FSRS is additionally available as an option; with Anki 25.07 came FSRS-6.

FSRS describes each card by three quantities: difficulty, stability of memory and current recall probability. Instead of a fixed multiplier, your repetition history, your ratings and your desired retention rate plan the next interval. The Anki manual names 90% as the default target. Higher targets mean shorter gaps and more work. The parameters can be adapted to your own history. All details are in the guide FSRS explained.

What happens if you miss repetitions?

Eventually it happens: holiday, illness, three days at a festival. When you come back, a mountain of due cards awaits. Three things on this from the official Anki FAQs:

1. There is no pausing. While you are away, forgetting continues. Pushing all due dates back does not stop your memory and can even increase the risk of forgetting.
2. Just carry on. The FAQ recommends continuing to study normally after a break instead of resetting the deck. Cards you still know despite being overdue receive a longer following interval, because you demonstrably retained them longer. An example from the FAQ for SM-2: a card was due after five days and is answered correctly 20 days late. Under the settings there, this gives roughly 6 days for "Hard", 37.5 for "Good" and 81.25 for "Easy".
3. Rate honestly. If you have forgotten it, press "Again". For FSRS, "Hard" means: recalled, but with effort. Anyone who rates errors this way distorts the scheduling.

How much time does it cost per day?

The honest answer: it depends on you. The Anki manual gives a rule of thumb. With a sustained 20 new cards per day you end up at roughly 200 repetitions daily. If you need on average ten seconds per answer, that is arithmetically around 33 minutes of pure answering time. This is a back-of-the-envelope estimate, not a study result, and creating cards is not included.

You have the biggest lever through the number of new cards per day and through the desired retention rate. Anki offers a simulator for this. We have not found a reliable average of how many minutes Anki users actually study per day.

What do studies with real students show?

This is where it gets interesting, and where skepticism pays off. Most studies come from medical school:

• Deng et al. (2015) surveyed 72 students retrospectively. More Anki cards worked through went with a higher USMLE Step 1 score; around 1,700 additional cards statistically corresponded to one point. This is a correlation. More diligent students probably also do more otherwise.
• Lu et al. (2021) compared 132 intensive Anki users with 69 other students: Step 1 means 241.10 versus 235.51 (d = 0.38). But only 36.9% of those contacted responded, and the respondents overall had better results. No causal proof.
• Levy et al. (2023) observed 45 students over eight weeks in four usage groups. No statistically reliable difference, though with very small groups.

The fair summary: distributed learning improves later recall under many of the conditions studied. Studies of Anki use in medical school yield positive but also non-significant results, and many do not allow causal conclusions. Moreover, "using Anki" bundles several things together: retrieval, spacing, card selection and simply more study time. These studies do not isolate which part does what. We have not found a randomized comparison of FSRS against SM-2 with real exam grades.

Spaced repetition with checkst

checkst plans your repetitions with FSRS and starts with a target retention rate of 90%. You don't need to calculate intervals, sort compartments or adjust anything to get started. A widget shows you how many cards are due today, and the streak helps turn "once in a while" into "a little every day".

For the week before the exam there is exam mode: you study deliberately toward a date without your long-term intervals being permanently thrown into disarray. And if you already have Anki decks, you can import them as .apkg. How, is explained in the article Importing Anki decks on iPhone.