The SM-2 algorithm, step by step
SM-2 decides when you should see a flashcard again. It needs only three numbers per card and one grade per review. Change the grade below and watch each part of the formula update.
1. Easiness factor. EF′ = EF + (0.1 − (5 − q)(0.08 + (5 − q) × 0.02))
= 2.50 + (0.1 − 1 × (0.08 + 1 × 0.02)) = 2.50 + 0.00 = 2.50
2. Next interval. first successful repetition: interval = 1 day.
The three rules of SM-2
- Grade recall from 0 to 5 right after you answer.
- Set the interval. If q ≥ 3 the repetition counts: 1 day after the first, 6 days after the second, then the previous interval × EF. If q < 3, start over at 1 day.
- Update the easiness factor with the formula above. A 5 raises EF by 0.10, a 4 leaves it unchanged, a 3 lowers it by 0.14, and anything under 3 lowers it more. EF starts at 2.5 and never drops below 1.3, so even the hardest card’s gaps keep growing slowly.
Woźniak also suggested repeating any card graded below 4 at the end of the day’s session until it scores at least 4.
How Cardsmith maps four buttons to SM-2
Choosing among six grades is slow, so the Cardsmith study session uses four buttons: Again = 1, Hard = 3, Good = 4, Easy = 5. “Again” also brings the card back about ten minutes later in the same session, matching Woźniak’s advice above. Everything else is textbook SM-2, so the intervals you see under each button are exactly what this calculator would give.
Where SM-2 came from, and what came after
Piotr Woźniak developed SM-2 in 1987 while studying at Poznań University of Technology, after years of hand-scheduling his own paper flashcards. It became the basis of SuperMemo and, in modified form, Anki’s long-standing scheduler, Mnemosyne and many others. Later SuperMemo versions (SM-15 onwards) and the open-source FSRS model estimate each card’s stability and difficulty from your review history instead of using fixed rules. They can cut review load, but the idea underneath is unchanged: review just before the forgetting curve drops too far. See it in context on the spaced repetition page.
Questions people ask
What is the SM-2 algorithm?
SM-2 is a spaced-repetition scheduling algorithm published by Piotr Woźniak in 1987 for the SuperMemo program. After each review you grade recall from 0 to 5; the algorithm updates an “easiness factor” for the card and uses it to set the number of days until the next review.
What is the SM-2 formula?
Intervals: I(1) = 1 day, I(2) = 6 days, I(n) = I(n−1) × EF. Easiness factor update: EF′ = EF + (0.1 − (5 − q) × (0.08 + (5 − q) × 0.02)), with EF never allowed below 1.3. If q < 3, repetitions restart from I(1) without changing EF in the original; many apps still apply the EF update.
Does Anki use SM-2?
Anki’s classic scheduler is a modified SM-2 (four buttons, learning steps, different ease adjustments). Since 2023 Anki also offers FSRS, a newer model based on memory stability and difficulty fitted to review data.
Is SM-2 still good?
It is simple, transparent and works well for most learners. Newer algorithms (later SuperMemo versions, FSRS) predict forgetting more precisely and can save some reviews, but consistent daily study matters far more than the algorithm choice.