Most people learn vocabulary the wrong way.
They study a word.
They forget it two days later.
They study it again. Forget it again. Study. Forget. Repeat — until they give up and decide they're "just bad at languages."
But here's what nobody tells you: the problem isn't your memory. It's the timing.
There's a 37-year-old algorithm — built by one researcher working alone in Poland — that solved this problem completely. It's called SM-2. It powers Anki, Mochi, and Wordrop. It's behind why some people can permanently memorize hundreds of words with just a few minutes of daily practice, while others spend hours and remember almost nothing.
This is the full breakdown of how it works.
What Is SM-2?
SM-2 (SuperMemo 2) is a spaced repetition algorithm developed by Piotr Woźniak in 1987.
Woźniak was a biochemistry student at Poznań University of Technology who needed to memorize enormous amounts of vocabulary and scientific terminology. He was frustrated by how quickly he forgot what he studied. So he did something unusual: he turned himself into a test subject, collected his own memory data over years, and used it to build a mathematical model of forgetting.
The result was SM-2 — a formula that tells you exactly when to review each word to maximize how long you retain it, while minimizing the total time you spend studying.
The core idea is deceptively simple:
> Each word in your library has its own personalized review schedule. That schedule is built entirely from your past performance on that specific word — not from a fixed calendar, not from how long you've been studying, not from how other words are performing. Just your history with that one word.
This is why SM-2 feels different from flashcard systems. It's not showing you cards — it's managing memory.
Why the Timing of Review Changes Everything
Your brain doesn't store memories like a hard drive. It lets them decay.
In 1885, Hermann Ebbinghaus spent years memorizing nonsense syllables and measuring how quickly he forgot them. His findings — the Ebbinghaus Forgetting Curve — revealed something uncomfortable:
- 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.)_
That's not a learning problem. That's biology.
But Ebbinghaus also found the solution embedded in the same data: every successful retrieval resets the forgetting curve — at a shallower slope. Review a word at the right moment, and it becomes harder to forget. Review it again, even harder to forget. After 5–7 well-timed reviews, a word can reach an interval of months, then years. It's effectively permanent.
The brutal truth is this: review too early and you waste time. Review too late and you've already forgotten — the review doesn't count. You need to review the word at exactly the moment your brain is about to lose it.
For hundreds of words simultaneously, with everyone's memory decaying at different rates... doing that manually is impossible.
SM-2 is the algorithm that makes it automatic.
The SM-2 Algorithm: Exact Formula and Rules
Two Numbers Per Word
Every word tracked by SM-2 has exactly two variables:
| Value | What It Means | Starting Default |
|---|---|---|
| I (Interval) | Days until the next review | 1 day |
| EF (Ease Factor) | Multiplier that controls how fast the interval grows | 2.5 |
The Ease Factor is what makes SM-2 personal. Words you recall quickly develop a higher EF — their intervals grow faster, so you see them less often. Words you struggle with get a lower EF — intervals grow slowly, and you encounter them more frequently until they stick.
Think of EF as the algorithm's confidence score for you and that word. High confidence = longer gap. Low confidence = back soon.
The 0–5 Rating Scale
After every review, you rate your recall 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 0, 1, or 2 are failures. Any failed review resets the word's interval back to 1 day. You'll see it again tomorrow.
The Ease Factor Formula
After each successful review (rating ≥ 3), SM-2 updates the Ease Factor:
EF' = EF + (0.1 − (5 − q) × (0.08 + (5 − q) × 0.02))Where:
The Ease Factor has a hard floor of 1.3 — it can never drop below this, no matter how many times you fail a word.
What this looks like in practice:
| Rating (q) | Change to EF | What it means |
|---|---|---|
| 5 | +0.10 | Instant recall — word is getting easier for you |
| 4 | +0.00 | Good recall — EF unchanged |
| 3 | −0.14 | Hard recall — EF decreases slightly |
| 2, 1, 0 | (relearning) | Failed — interval resets, EF formula still applies |
The Interval Calculation
The number of days until the next review follows three rules:
- Review 1 (n=1): Interval = 1 day (fixed)
- Review 2 (n=2): Interval = 6 days (fixed)
- Review 3+ (n≥3): Interval = Previous Interval × EF
The first two intervals are fixed regardless of your rating. From the third review onward, every interval is the previous interval multiplied by your current Ease Factor. This is the exponential growth that makes spaced repetition so powerful over time — gaps that start at days eventually stretch to months, then years.
Step-By-Step: Tracing One Word Through the Algorithm
Let's follow the word "ephemeral" through a real SM-2 schedule.
Starting state: Interval = 1 day, EF = 2.5, review count = 0
Review 1 — Day 0
You encounter the word for the first time. It's new and difficult.
- Rating: 3 (correct, but with significant effort)
- EF calculation: 2.5 + (0.1 − 2 × 0.12) = 2.5 − 0.14 = 2.36
- Next interval: 1 day (first-review rule)
- Next review: Day 1
Review 2 — Day 1
One day later. One night of sleep helped consolidate it. You recall it with some hesitation.
- Rating: 4 (correct with hesitation)
- EF update: 2.36 + 0 = 2.36 (rating 4 = no change)
- Next interval: 6 days (second-review rule)
- Next review: Day 7
Review 3 — Day 7
Six days later. It takes a moment, but you get it.
- Rating: 3 (correct, difficult)
- EF update: 2.36 − 0.14 = 2.22
- Next interval: 6 × 2.22 = 13.3 → 13 days
- Next review: Day 20
Review 4 — Day 20
Two weeks later. It comes back more naturally this time.
- Rating: 4 (correct with hesitation)
- EF update: 2.22 (unchanged)
- Next interval: 13 × 2.22 = 28.86 → 29 days
- Next review: Day 49
Review 5 — Day 49
Almost seven weeks later. Instant. You use this word in your writing now.
- Rating: 5 (perfect recall)
- EF update: 2.22 + 0.10 = 2.32
- Next interval: 29 × 2.32 = 67.28 → 67 days
- Next review: Day 116
By review 5, "ephemeral" is scheduled every 2–3 months.
By review 7, it's once or twice a year.
After that — it's not scheduled. It's just yours.
Full schedule summary:
| 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
Failing is not as bad as it sounds.
When you rate a word 0, 1, or 2, SM-2 does this:
- Interval resets to 1 day — you'll see it tomorrow
- The Ease Factor formula still runs — a rating of 0 drops EF significantly, meaning future intervals after relearning will grow more slowly
- Review count (n) does NOT reset — the word keeps its history
Here's the part most people don't realize: failing a word doesn't erase your progress. The Ease Factor carries the memory 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.
Lower EF means that failed word stays on shorter intervals longer. The algorithm is being more careful with it. More repetitions. More reinforcement. It's not punishing you — it's giving that word the extra attention it needs.
SM-2 vs. Other Spaced Repetition Systems
| System | Based On | Key Difference |
|---|---|---|
| SM-2 (Wordrop, Anki) | Woźniak 1987 | Open formula, widely implemented, deterministic 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 trained on 20B+ Anki reviews — higher precision, more complex |
| Leitner System | Leitner 1970s | Physical flashcard boxes — fixed 5 intervals, no per-card personalization |
Why SM-2 still wins for most use cases:
- Fully transparent — every interval is calculable, auditable, explainable
- No cold-start problem — works from your very first session, zero training data needed
- Offline-first — no cloud, no data dependency, no privacy concerns
- 35+ years of independent validation — not a theory, an empirical track record
For vocabulary learning during a real workday — on a commute, between meetings, over coffee — SM-2 is the right tradeoff. Mathematically precise. Computationally simple. Fast enough to run on-device on a watch.
Why Wordrop Uses SM-2 (And What We Changed)
Wordrop implements SM-2 with three practical adaptations:
1. Micro-sessions instead of single daily blocks
SM-2 calculates when to review — not how to present the session. Wordrop breaks reviews into 2–4 word quizzes delivered 4–8 times during your configured learning window, rather than one long session.
Research from Kornell & Bjork (2008) in Psychological Science found that interleaved, distributed micro-sessions produce stronger memory consolidation than blocked study of equivalent total time — even when learners felt blocked practice was more effective. The overlay quiz format is designed around this finding.
2. Bidirectional recall on the same SM-2 schedule
Most SM-2 apps track one direction: your native language → English. Wordrop tracks both directions as separate SM-2 items — native → English and English → native.
This implements dual encoding (Paivio, 1986), strengthening both your recognition pathway (reading comprehension) and your production pathway (speaking and writing). The goal isn't vocabulary you understand — it's vocabulary you can use.
3. Typed input replaces self-rating
Standard SM-2 asks you to rate yourself 0–5. Self-rating is subjective, inconsistently calibrated, and gameable.
Wordrop's Recall and Reverse Recall modes require you to type the answer. The SM-2 rating is derived from response accuracy and response latency — not a button you pressed. This removes self-rating bias and makes interval calculations reflect your actual memory state, not your mood.
The Research Base Behind SM-2
SM-2 wasn't invented from theory. It was built from data — and that data has been independently validated for decades:
- Ebbinghaus (1885): Exponential memory decay without reinforcement; the stabilizing effect of spaced retrieval — the foundational observation SM-2 was built to address.
- Woźniak & Gorzelanczyk (1994), Acta Neurobiologiae Experimentalis: Original empirical validation of SM-2. Showed retention rates above 90% at 6-month intervals using the algorithm with real learners.
- Cepeda et al. (2006), Psychological Bulletin: Meta-analysis of 254 studies. Spaced practice outperformed massed practice in 259 of 272 direct comparisons.
- Roediger & Karpicke (2006), Psychological Science: The testing effect — active retrieval practice improves long-term retention by approximately 50% compared to re-reading the same material.
- Kornell & Bjork (2008), Psychological Science: Interleaved practice produces superior retention even when learners rate it as less productive in the moment.
The uncomfortable finding from all of this: the study strategies that feel most productive are usually the least effective. Rereading your notes feels productive. Massed practice feels productive. They are not. Effortful, spaced retrieval feels frustrating. That's exactly why it works.
SM-2 is the mechanism that automates the frustrating-but-effective approach.
Frequently Asked Questions
What does SM-2 stand for?
SM-2 stands for SuperMemo 2. It's 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. He published the algorithm openly, 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. Modern Anki (version 23+) optionally supports FSRS — a machine-learning algorithm trained on over 20 billion Anki reviews that claims higher precision. SM-2 is still available in Anki and widely used. Wordrop uses an SM-2 implementation specifically 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 with the same prompt and expected answer. It's less suited for open-ended language production or grammar drills where multiple correct answers are possible.
What is the minimum Ease Factor in SM-2?
The SM-2 algorithm enforces a hard minimum Ease Factor of 1.3. Even at EF 1.3, intervals still grow after each successful review — just slowly (×1.3 per review). The floor exists because if EF dropped below 1.3, intervals could theoretically become shorter than 1 day, creating review loops that don't allow the overnight memory consolidation that makes spaced repetition work.
How long does it take for a word to reach long-term memory with SM-2?
With consistent reviews, most words reach an interval of 60+ days after approximately 5–7 successful reviews spanning 3–6 months. Research by Woźniak & Gorzelanczyk (1994) showed words at intervals of 60+ days are retained 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 an app?
The SM-2 formula is simple enough to implement in a spreadsheet. You need to track: current Ease Factor, last interval, next review date, and your rating for each review. In practice, managing this manually for more than 50–100 words becomes unworkable quickly. Purpose-built implementations like Wordrop handle all scheduling automatically.
Why does SM-2 start with an Ease Factor of 2.5?
Woźniak chose 2.5 as the starting point based on his own learning experiments and early SuperMemo user data. A starting EF of 2.5 produces the canonical first intervals of 1, 6, and ~15 days — which aligned with the forgetting curve observations in his studies. The EF adjusts immediately from 2.5 based on your performance, so it gets personalized within the first few reviews.
The Bottom Line
You're not bad at remembering vocabulary.
You've just been reviewing at the wrong times.
SM-2 calculates the right times. Not for an average learner on an average word. For you, on that specific word, based on every review you've done with it. The algorithm works because it mirrors how memory actually functions — not how we think it should function.
That's why a word reviewed 7 times over 9 months using SM-2 is more reliably retained than the same word reviewed 30 times over 2 weeks using a fixed flashcard deck.
Less time. More memory. Permanently.
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 — no app-opening required, no session to schedule, no habit to build.
No account needed. All SM-2 data stays on your device.
_Last updated: June 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._