How the SM-2 algorithm works

SM-2 was developed by Piotr Woźniak as part of SuperMemo, and published in 1987. It was not the first spaced repetition scheme — paper-based systems such as the Leitner box predate it by decades — but it was the first widely adopted algorithm to adapt intervals per card based on how the learner performed on that specific item.

Its influence is hard to overstate. Anki, Mnemosyne and a long list of successors all shipped SM-2 or a close variant, and for most people "the spaced repetition algorithm" means SM-2 even when they have never heard the name.

SM-2 keeps very little state. Each card has an ease factor — a multiplier representing how easy that card is for you, starting at 2.5 — and an interval, the number of days until it is next due. A repetition count tracks how many times in a row you have passed it.

That is the whole model. There is no record of your response times, no global difficulty estimate, no model of your memory as a whole. Its power comes from applying a simple adjustment consistently, thousands of times.

Anki-style implementations expose four grades. The exact constants below are the ones Language Flash uses, and they are the conventional SM-2 variant values — you can read them in the scheduler source, and they are covered by tests so they cannot drift.

Take a new card with the default ease of 2.50 and answer Good each time.

The first review schedules it 1 day out. The second, 6 days. The third multiplies: 6 × 2.50 = 15 days. The fourth: 15 × 2.50 ≈ 38 days. The fifth: roughly 94 days. By the sixth successful review the card is over eight months out, and it has cost you six reviews in total.

Now suppose you fail it at the 38-day mark. The ease drops from 2.50 to 2.30, the interval resets to zero, and the card comes back in ten minutes. Next time it passes, it starts the ladder again — but with a permanently lower ease, so it will grow more slowly than a card you have never failed. That is the algorithm learning that this particular card is hard for you.

Without a floor, a card you keep failing would drive its ease toward zero and become due constantly, crowding out everything else. The 1.30 minimum means even your worst card still grows its interval by 30% per successful review.

In practice, a card that has bottomed out at 1.30 is telling you something the algorithm cannot fix: the card is badly written, tests more than one thing, or is confusable with another card. The usual remedy is to rewrite or delete it rather than keep grinding.

SM-2 is nearly forty years old and its limits are well understood. It ignores how long you took to answer, treats all lapses alike, and its constants are hand-tuned rather than fitted to data.

FSRS — the Free Spaced Repetition Scheduler — is the leading modern alternative, and is now built into Anki. It models memory with retrievability, stability and difficulty, and fits its parameters to your actual review history, which lets it hit a retention target you choose. For large mature decks it generally schedules fewer reviews for the same retention.

Language Flash uses SM-2. It is predictable, needs no review history to start working, and behaves identically on every device — which matters here, because the web app and the mobile app write to the same cards and must agree on what happens when you press a button. FSRS is on the list.