What Is the SM-2 Algorithm?

SM-2 is a spaced repetition algorithm that decides when you should next review each flashcard. After every review you grade your answer, and the algorithm multiplies the card's previous interval by an ease factor that reflects how hard the card is for you. Created by Piotr Woźniak in 1987, it is one of the most widely copied algorithms in learning software and the basis of Anki's classic scheduler.

Origin

Woźniak, then a student in Poznań, Poland, had been experimenting with spaced review on paper since the mid-1980s. In 1987 he implemented SM-2 in the first computer version of SuperMemo. He published the algorithm's description, and its simplicity made it easy to reimplement. Later SuperMemo versions use much more complex algorithms (SM-17, SM-18), but SM-2 lived on in open-source tools including Anki and Mnemosyne.

How SM-2 works: the formula

After each review you rate recall quality q from 0 to 5 (5 = perfect, 3 = correct with serious difficulty, 0–2 = incorrect).

Intervals (in days), where n is the number of successful reviews in a row:

• I(1) = 1
• I(2) = 6
• I(n) = I(n−1) × EF, for n > 2

Ease factor update after each review:

EF' = EF + (0.1 − (5 − q) × (0.08 + (5 − q) × 0.02))

• Every card starts with EF = 2.5. EF never goes below 1.3.
• q = 5 adds 0.1; q = 4 leaves EF unchanged; q = 3 subtracts 0.14.
• If q < 3, the card's repetitions restart from I(1), with EF left unchanged.
• Within a day's session, cards graded below 4 are repeated until they reach at least 4.

A worked vocabulary example

You can generate a schedule like this with the spaced repetition scheduler.

Why it matters for learning words

SM-2 made spaced repetition personal. Unlike the Leitner system, where every card in a box shares one interval, SM-2 lets an easy word like happy race ahead to monthly reviews while a slippery word like ambivalent stays on shorter intervals. That means far fewer wasted reviews in a deck of thousands of words.

Known weaknesses

• "Ease hell." Repeated low grades push EF down toward 1.3, and in implementations like Anki's there is little mechanism to raise it again, so hard cards can get stuck on short intervals.
• Fixed assumptions. The constants (2.5, 1, 6, 1.3) are not fitted to your memory.
• Delays are ignored. Reviewing a card late, and still remembering it, is not credited as evidence of a stronger memory.
• Six grades are hard to use consistently. Most apps reduce them to three or four buttons.

These issues motivated newer algorithms, most notably FSRS, which models memory stability directly from your review history.

SM-2 and Wordie

Wordie does not implement SM-2. Its recall mode uses a simpler Forgot / Hard / Easy rating that updates a 0–100% mastery score per word, and its main review mechanism is highlighting saved words when they reappear on web pages. If you want strict SM-2 scheduling, export your words to CSV and import them into Anki; see how to import words into Anki.

Sources: Woźniak, P. A. (1990). Optimization of learning (master's thesis, Poznań University of Technology), describing the SM-2 algorithm developed in 1987.