What Is SM-2 (SuperMemo 2)?
SM-2 (SuperMemo 2) is a spaced repetition algorithm developed by Polish researcher Piotr Woźniak in 1987. It calculates the mathematically optimal interval between each review of a vocabulary item — scheduling exactly when a learner should see a word again to maximize long-term memory retention. SM-2 is the foundation behind Anki, Mochi, and Wordrop. It remains the most widely implemented spaced repetition algorithm in the world, more than 35 years after its creation.
The core idea: each word in your library has its own _personalized_ review schedule, not a fixed one shared with every other word. That schedule is determined entirely by your past performance — how quickly and accurately you recalled the word each time you were tested.
Why Spaced Repetition Needs an Algorithm
The human brain follows a predictable decay pattern — the Ebbinghaus Forgetting Curve — that shows new information is lost exponentially unless reviewed at the right time:
- 20 minutes after learning: ~42% forgotten
- 24 hours after learning: ~67% forgotten
- 1 week after learning: ~75% forgotten
_(Source: Ebbinghaus, H. (1885). Über das Gedächtnis. Duncker & Humblot, Leipzig.)_
The key finding Ebbinghaus also documented: each successful retrieval resets the forgetting curve, but at a shallower slope — meaning the word becomes progressively harder to forget. The optimal strategy is to review a word just before it would be forgotten, then extend the next interval based on how well you recalled it.
Doing this manually for hundreds of words is impossible. SM-2 is the algorithm that automates it.
The SM-2 Algorithm: Exact Formula and Rules
Two Core Values Per Word
Every word in SM-2 is tracked by two numbers:
| Value | What It Means | Default Starting Value |
|---|---|---|
| I (Interval) | Days until the next review | 1 day |
| EF (Ease Factor) | Multiplier controlling how fast the interval grows | 2.5 |
The Ease Factor represents how easy that specific word is _for you_. Words you consistently recall quickly get a higher EF (longer intervals between reviews). Words you keep forgetting get a lower EF (shorter intervals, reviewed more often).
The Rating Scale
After every review, you rate your recall performance on a 0–5 scale:
| Rating | Label | Meaning |
|---|---|---|
| 0 | Complete blackout | No memory of the word at all |
| 1 | Incorrect, familiar | Wrong answer but the correct answer felt familiar when shown |
| 2 | Incorrect, easy | Wrong answer but the correct answer felt easy once revealed |
| 3 | Correct, difficult | Recalled correctly but with significant effort |
| 4 | Correct, hesitation | Recalled correctly after brief hesitation |
| 5 | Perfect recall | Recalled instantly and confidently |
Ratings below 3 are treated as failures. Any response rated 0, 1, or 2 resets the word's interval to 1 day and schedules it for relearning.
The Ease Factor Formula
After each _successful_ review (rating ≥ 3), SM-2 updates the Ease Factor using this formula:
``
EF' = EF + (0.1 − (5 − q) × (0.08 + (5 − q) × 0.02))
Where:
- EF' = new Ease Factor
- EF = current Ease Factor
- q = your recall rating (0–5)
The Ease Factor has a hard minimum of 1.3 — it can never drop below this floor, no matter how many times you fail a word.
Simplified table of EF changes by rating:
| Rating (q) | Change to EF | Explanation |
|---|---|---|
| 5 | +0.10 | Instant recall — word is getting easier for you |
| 4 | +0.00 | Good recall with hesitation — EF unchanged |
| 3 | −0.14 | Recalled with difficulty — EF decreases slightly |
| 2 | (relearning) | Failed — interval resets, EF not applied |
| 1 | (relearning) | Failed — interval resets, EF not applied |
| 0 | (relearning) | Failed — interval resets, EF not applied |
The Interval Calculation
The interval (days until next review) is calculated differently based on how many successful reviews a word has had:
- First review (n=1): I = 1 day
- Second review (n=2): I = 6 days
- Third review onward (n≥3): I = I(previous) × EF
The first two intervals are fixed. From the third review onward, each interval is the previous interval multiplied by the Ease Factor. This creates the exponential growth that is the hallmark of spaced repetition.
Step-By-Step Example: Tracing a Word Through SM-2
Let's trace the word "ephemeral" through a real SM-2 schedule.
Starting state: I = 1, EF = 2.5, review count n = 0
Review 1 — Day 0 (first learning)
You study the word. It's difficult — you recall it only with effort.
- Rating: 3 (correct but difficult)
- EF update: EF' = 2.5 + (0.1 − (5−3) × (0.08 + (5−3) × 0.02)) = 2.5 + (0.1 − 2 × 0.12) = 2.5 − 0.14 = 2.36
- New interval: I = 1 day (first-review rule)
- Next review: Day 1
Review 2 — Day 1
You see the word again. With one day of sleep consolidation, you recall it cleanly.
- Rating: 4 (correct with hesitation)
- EF update: EF' = 2.36 + 0 = 2.36 (rating 4 = no EF change)
- New interval: I = 6 days (second-review rule)
- Next review: Day 7
Review 3 — Day 7
Six days later. Recall is harder — but you get it.
- Rating: 3 (correct but difficult)
- EF update: EF' = 2.36 − 0.14 = 2.22
- New interval: I = 6 × 2.22 = 13.3 → 13 days
- Next review: Day 20
Review 4 — Day 20
Two weeks later. It comes back quickly.
- Rating: 4 (correct with hesitation)
- EF update: EF' = 2.22 (unchanged)
- New interval: I = 13 × 2.22 = 28.86 → 29 days
- Next review: Day 49
Review 5 — Day 49
Almost seven weeks later. Instant recall — you use this word in writing now.
- Rating: 5 (perfect recall)
- EF update: EF' = 2.22 + 0.10 = 2.32
- New interval: I = 29 × 2.32 = 67.28 → 67 days
- Next review: Day 116
By review 5, "ephemeral" reviews every 2–3 months. By review 7–8, it's reviewed once or twice a year. At that point, the word is in permanent long-term memory.
Summary of the "ephemeral" schedule:
| Review | Day | Rating | New EF | New Interval |
|---|---|---|---|---|
| 1 | 0 | 3 | 2.36 | 1 day |
| 2 | 1 | 4 | 2.36 | 6 days |
| 3 | 7 | 3 | 2.22 | 13 days |
| 4 | 20 | 4 | 2.22 | 29 days |
| 5 | 49 | 5 | 2.32 | 67 days |
| 6 | ~116 | 5 | 2.42 | ~160 days |
| 7 | ~276 | 4 | 2.42 | ~387 days |
What Happens When You Fail a Word
If you rate a word 0, 1, or 2 at any point, SM-2 initiates relearning:
- Interval resets to 1 day (you'll see it again tomorrow)
- The Ease Factor is updated using the formula — a low rating (e.g., 0) will lower the EF significantly, meaning even after relearning, the next interval growth will be slower
- The review count (n) does not reset — the algorithm remembers the word's history and accounts for it
This is important: failing a word doesn't erase your progress entirely. The EF carries the history of your struggles. A word you've failed five times will have a lower EF than a word you're seeing for the first time, even if both restart at a 1-day interval. That lower EF means the failed word will stay on a shorter review cycle longer — building deeper familiarity before extending its interval again.
SM-2 vs. Other Spaced Repetition Systems
| System | Based On | Key Difference |
|---|---|---|
| SM-2 (Wordrop, Anki) | Woźniak 1987 | Open formula, widely implemented, interval × EF growth |
| SM-17/18 (SuperMemo) | Woźniak 2006+ | Neural network-based, highly personalized but proprietary |
| FSRS (Anki optional) | Ye et al. 2022 | Machine learning model trained on 20B+ Anki reviews; higher accuracy but more complex |
| Leitner System | Leitner 1970s | Physical box system — fixed 5 intervals, no per-card EF |
| SuperSRS | Various | SM-2 variants with modified EF floor or fuzzing |
SM-2's advantages over newer alternatives:
- Transparent formula — every interval can be verified and understood
- Offline-first — no cloud training data required
- Proven at scale — 35+ years of independent implementation and validation
- Minimal data requirements — works well from the first session, no cold-start problem
For a vocabulary learning tool like Wordrop used by busy professionals, SM-2 is the right tradeoff: mathematically principled, computationally simple, and privacy-safe since all calculations happen on-device.
Why Wordrop Uses SM-2 for Vocabulary Learning
Wordrop implements a practical version of SM-2 with three adaptations designed for the way professionals learn vocabulary during a workday:
1. Micro-session delivery, not single daily sessions
SM-2 calculates _when_ to review each word, but not _how_ to present the session. Wordrop delivers 2–4 word quizzes per appearance rather than one long session. Research from Kornell & Bjork (2008) in _Psychological Science_ shows that interleaved and spaced micro-sessions produce stronger memory consolidation than blocked study of equivalent total time. Wordrop's overlay quiz format — appearing 4–8 times during your configured learning window — aligns with this finding.
2. Bidirectional recall on the same SM-2 schedule
Most SM-2 implementations track one direction: native-language prompt → English answer. Wordrop tracks both directions — native → English and English → native — as separate SM-2 items per word. This implements dual encoding (Paivio, 1986), which strengthens both the recognition and production pathways in memory, resulting in vocabulary you can both understand and use.
3. SM-2 ratings mapped to typed recall accuracy
Standard SM-2 implementations ask learners to self-rate (0–5). Self-rating is subjective and can be gameable. Wordrop's Recall and Reverse Recall modes require typed input rather than button clicks. The SM-2 rating is derived from response accuracy and latency — eliminating the self-rating bias and making the algorithm's interval calculations more honest.
The Research Base for SM-2's Effectiveness
SM-2's design draws on, and has since been validated by, a body of cognitive science research:
- Ebbinghaus (1885): Established the exponential decay of memory without reinforcement and the stabilizing effect of spaced retrieval.
- Cepeda et al. (2006), Psychological Bulletin: Meta-analysis of 254 studies showing spaced practice outperforms massed practice in 259 of 272 direct comparisons.
- Roediger & Karpicke (2006), Psychological Science: The testing effect — retrieval practice improves long-term retention by approximately 50% compared to re-study.
- Woźniak & Gorzelanczyk (1994), Acta Neurobiologiae Experimentalis: Original empirical validation of SM-2, showing >90% retention rates at 6-month intervals using the algorithm.
- Kornell & Bjork (2008), Psychological Science: Interleaved practice produces superior long-term retention compared to blocked practice, even when learners report blocked practice feeling more productive.
The SM-2 algorithm wasn't designed from theory alone — it was built iteratively by Woźniak using his own vocabulary learning data over years of experiments, then validated against independent learner populations. That empirical foundation is why it remains competitive with machine-learning alternatives despite being a deterministic formula.
Frequently Asked Questions
What does SM-2 stand for?
SM-2 stands for SuperMemo 2. It is the second major algorithm published by Piotr Woźniak for his SuperMemo learning software. Woźniak developed it in 1987 while studying biochemistry at Poznań University of Technology, originally to memorize biochemistry vocabulary and English words. The algorithm was published publicly, which led to its adoption in Anki, Mochi, and dozens of other spaced repetition applications.
How is SM-2 different from Anki's algorithm?
Anki originally used SM-2 exactly as published by Woźniak. Modern Anki (version 23+) optionally supports FSRS (Free Spaced Repetition Scheduler), a machine-learning-based algorithm that claims higher accuracy. However, SM-2 remains available in Anki and is still widely used. Wordrop uses a practical SM-2 implementation optimized for short micro-sessions and bidirectional vocabulary recall.
Does SM-2 work for all types of vocabulary?
SM-2 works well for any content with a clear question-and-answer structure — which covers nearly all vocabulary learning. It works best when the same word is tested consistently (same prompt, same expected answer). It is less suited for open-ended language production practice or grammar drills where correct answers are variable.
What is the minimum Ease Factor in SM-2?
The SM-2 algorithm enforces a hard minimum Ease Factor of 1.3. This prevents the interval from becoming stagnant for very difficult words — even at EF 1.3, intervals still grow (just slowly: ×1.3 per successful review). If EF dropped below 1.3, the algorithm could produce intervals of less than 1 day, creating review loops that don't allow consolidation time.
How long does it take for a word to reach long-term memory with SM-2?
Under SM-2 with consistent daily reviews, most words reach a review interval of 60+ days after approximately 5–7 successful reviews spanning 3–6 months. Research by Woźniak & Gorzelanczyk (1994) showed that words at intervals of 60+ days are retained at rates above 90% at the scheduled review point. Words at intervals of 1 year or more are effectively in permanent long-term memory for most learners.
Can I use SM-2 without a dedicated app?
The SM-2 formula is simple enough to implement in a spreadsheet. You need to track: the current Ease Factor, the last interval, the next review date, and your rating for each review. In practice, managing this for more than 50–100 words manually becomes unworkable. Purpose-built implementations like Wordrop handle all scheduling automatically.
Why does SM-2 use 2.5 as the default Ease Factor?
Piotr Woźniak chose 2.5 as the empirical starting point based on his own learning experiments and early user data from SuperMemo. A starting EF of 2.5 produces the canonical first intervals of 1, 6, and ~15 days, which aligned with the forgetting curve data he observed in his studies. The EF adjusts from 2.5 immediately based on your performance — so the initial value is a reasonable prior that gets personalized quickly.
Start Building Your Vocabulary with SM-2
SM-2 is the reason that a few minutes of well-timed vocabulary practice produces better results than hours of disorganized studying. The algorithm removes the guesswork from "when should I review this?" — replacing it with a mathematically precise schedule that works with how your memory actually functions.
Wordrop implements SM-2 natively in your Mac menu bar. The algorithm runs silently in the background, scheduling your vocabulary queue and delivering 2–4 word quizzes throughout your configured learning window — so reviews happen automatically, at exactly the right intervals, without any app-opening required.
No account needed. All SM-2 data stays on your device.
_Last updated: April 2026. References: Ebbinghaus (1885); Woźniak & Gorzelanczyk (1994), Acta Neurobiologiae Experimentalis 54(4); Cepeda et al. (2006), Psychological Bulletin 132(3); Roediger & Karpicke (2006), Psychological Science 17(3); Kornell & Bjork (2008), Psychological Science 19(6); Paivio (1986), Mental Representations. SM-2 algorithm specification: supermemo.com/en/articles/algorithm._