Knowledge Concepts
The SM-2 algorithm is the mathematical formula that powers Anki and many other spaced repetition systems — it calculates precisely when to show you each flashcard based on how well you recalled it last time.
The SM-2 algorithm is the scheduling formula developed by Piotr Wozniak in 1987 that calculates when to show you each flashcard next based on how confidently you recalled it. Rate your recall from 0 to 5 after each card; the algorithm adjusts the next review interval up or down accordingly. Cards you know well are reviewed weeks or months from now; cards you struggled with appear tomorrow. SM-2 is the engine behind Anki and most spaced repetition software.
Understanding SM-2 helps you use Anki more effectively — and explains why the rating you give yourself on each card matters so much.
Piotr Wozniak is a Polish researcher who became fascinated with optimizing memory in the mid-1980s. He built the first version of his SuperMemo spaced repetition software in 1985-1986, and the SM-2 algorithm (SuperMemo algorithm version 2) was published in 1987. He published the algorithm publicly, and it became the foundation for virtually all subsequent spaced repetition software.
Wozniak's key insight was that spaced repetition needed a feedback loop: each review's outcome should determine when the next review happens. The Leitner system's fixed box intervals are approximate; SM-2 calculates a mathematically derived interval based on your specific performance history with each card.
The algorithm has been refined since (Wozniak himself developed SM-5, SM-11, FSRS), but SM-2 is what Anki implements and is what most learners encounter in practice.
The core inputs: After reviewing each card, you rate your recall quality on a scale of 0-5:
The core formula: The SM-2 algorithm calculates the next review interval based on:
The interval calculation:
Example with EF = 2.5:
The ease factor adjustment: After each review: EF = EF + (0.1 − (5 − q) × (0.08 + (5 − q) × 0.02)), where q is your rating.
In practice: consistently rating cards 4-5 makes their intervals grow quickly. Consistently rating 3 keeps intervals modest. Rating 0-2 resets the card to daily review and reduces the ease factor.
A student uses Anki to study Spanish vocabulary.
Card: "hablar" (to speak)
Day 1 — First review: Rated 4 (correct with minor hesitation). Next interval: 1 day. EF: 2.5.
Day 2 — Second review: Rated 5 (perfect recall). Next interval: 6 days. EF: 2.6.
Day 8 — Third review: Rated 4 (correct with minor hesitation). Next interval: 15 days (6 × 2.5). EF: 2.5.
Day 23 — Fourth review: Rated 5 (perfect). Next interval: 37 days (15 × 2.5). EF: 2.6.
Day 60 — Fifth review: Rated 3 (correct but struggled). Next interval: 36 days (reduced — EF decreased to 2.4; 37 × 0.98 ≈ 36). EF: 2.4.
The card reappears as intervals grow. Each successful review pushes the next review farther out. A single bad review reduces the ease factor and shrinks the next interval — but doesn't reset the card unless the rating is 0-2.
The SM-2 algorithm's quality depends entirely on your rating honesty. Common mistakes:
Rating too high (pressing 4 or 5 when you barely recalled it): This makes the algorithm give you longer intervals than your actual retention supports. Cards disappear from review too quickly. You forget them. On the next review (weeks later): surprised you can't remember it.
Rating too low (pressing 1 or 2 when you clearly recalled it): This resets the card and reduces the ease factor unnecessarily. The card will appear more often than needed. Your daily review load grows; you spend time on cards you already know.
The right calibration:
Consistent calibration makes SM-2 work well. Poor calibration undermines its scheduling.
| Algorithm | Where used | How it differs from SM-2 |
|---|---|---|
| SM-2 | Anki (default), many SRS apps | Simple, widely adopted, slightly imprecise |
| SM-5/SM-11 | SuperMemo | More complex, better models forgetting curves |
| FSRS | Anki (new option) | Machine learning model, more accurate than SM-2 |
| Leitner boxes | Physical flashcards | No calculation — approximate box intervals |
| Duolingo | Duolingo app | Proprietary, adapted for gamification |
For most learners, the difference between SM-2 and more sophisticated algorithms is small compared to the difference between using any spaced repetition vs. not using it. SM-2 is "good enough" for most purposes. FSRS (now available in Anki) produces meaningfully better scheduling at higher card counts.
Start with fewer new cards per day: Anki's default settings add 20 new cards per day. For most learners starting out: 5-10 new cards per day is more manageable. The daily review load grows proportionally to how many cards you've added; starting slowly keeps it sustainable.
Rate honestly: Your self-ratings are the algorithm's only feedback signal. Rate accurately based on the quality and speed of recall, not on how you want the schedule to look.
Don't skip reviews: The SM-2 algorithm's intervals are calculated to keep you just above the forgetting curve. Skipping reviews means cards mature past their optimal review date — you'll forget more before the next review. Missing a few days occasionally is fine; systematic skipping undermines the system.
Use suspension for cards that aren't working: If a card consistently gets rated 1-2 after many reviews: consider why. Maybe the card is too complex (split it into simpler cards). Maybe the question is ambiguous. Suspend and redesign cards that aren't converting to retention, rather than letting them accumulate and inflate your daily load.
Spaced repetition: The broader principle that SM-2 implements algorithmically — reviewing material at increasing intervals based on retention.
The forgetting curve: SM-2 schedules reviews to happen before the forgetting curve brings retention below a threshold — typically before you fall below 90% retention.
The Leitner system: The manual, pre-digital implementation of spaced repetition. SM-2 replaced it with precise interval calculation.
Anki: The most widely used implementation of SM-2 (with FSRS now available as an alternative).
Does Anki still use SM-2? Anki has used SM-2 as its default algorithm since its founding. In recent versions, Anki added FSRS (Free Spaced Repetition Scheduler) as an optional alternative, which many advanced users now prefer for its superior accuracy. SM-2 remains the default and works well for most learners.
Why does Anki's algorithm behave differently than the SM-2 formula describes? Anki implements a variant of SM-2 with some modifications: the button labels (Again, Hard, Good, Easy) map differently from the 0-5 scale, and Anki adds features (learning steps, relearning steps) not in the original SM-2. The core interval-growth logic follows SM-2.
Can I use SM-2 without Anki? Yes. The SM-2 formula is open and well-documented. Any spaced repetition system that calculates intervals based on recall quality and uses an ease factor is implementing SM-2 or a variant. Some learners implement it in spreadsheets; others use alternative apps.
The SM-2 algorithm is the hidden mechanism that makes spaced repetition effective — and the reason why how you rate your cards matters so much. It's not magic: it's a formula that grows intervals when you succeed and shrinks them when you struggle, keeping each card's review scheduled at roughly the last moment before you'd forget it. Understanding the formula helps you use Anki more deliberately: rate honestly, keep new card counts manageable, and trust the schedule even when the intervals feel surprisingly long.
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