Definition:
SM-2 is a spaced repetition scheduling algorithm developed by Piotr Wozniak for SuperMemo in 1987. It calculates optimal review intervals for flashcards based on rated recall quality, using a per-card “easiness factor” that adjusts over time. SM-2 became the default algorithm in Anki and is the most widely deployed SRS scheduling algorithm in history.
Also known as: SuperMemo 2 algorithm, the Wozniak algorithm, the Anki algorithm (colloquially)
In-Depth Explanation
SM-2 is based on the observation that different items decay at different rates — some words are inherently easier to remember; some facts stick with little effort while others require constant re-exposure. SM-2 tracks this per-card using an “easiness factor” (EF), a floating-point number initialized at 2.5. After each review, the learner rates their recall quality:
- 0 — Complete blackout; no recall
- 1 — Incorrect response; correct answer recognized when shown
- 2 — Incorrect response; correct answer felt easy after seeing it
- 3 — Correct response with serious difficulty
- 4 — Correct response after hesitation
- 5 — Perfect response; immediate recall
The EF then updates using the formula:
$$EF’ = EF + (0.1 – (5 – q)(0.08 + (5 – q) imes 0.02))$$
where $q$ is the quality rating (0–5). A rating of 5 increases EF slightly; ratings below 3 decrease it. EF has a floor of 1.3 (the minimum interval multiplier). A card with EF = 2.5 running normally will see its interval multiply approximately 2.5× each successful review. A card stuck at EF = 1.3 (consistently difficult) will grow its intervals very slowly.
Interval schedule:
- First review: 1 day
- Second review: 6 days
- Subsequent reviews: previous interval × EF (rounded to nearest day)
Failure case: A quality rating of 0, 1, or 2 resets the card’s interval back to the first step (1 day) — the sequence restarts. The EF is reduced, meaning even after restart, the card will progress more slowly than a card never failed.
This algorithm is elegant in its simplicity: it is stateless between reviews except for EF and the last interval, which makes it easy to implement and fast to compute. Its weaknesses compared to modern algorithms:
- EF is adjusted on every review but has no principled calibration to actual forgetting curves — it is a heuristic.
- Ratings (0–5) are inconsistently applied by most users; most Anki users use a simplified Again/Good/Easy system.
- SM-2 has no concept of per-user calibration: every new card starts with EF = 2.5 regardless of how well that particular learner performs on that material type.
- Hard cards near the EF floor (1.3) receive very short intervals even when the learner is slowly improving, leading to inefficient “grinding.”
FSRS addresses all of these by directly modeling retrievability and stability per card per user from observed data.
Common Misconceptions
“SM-2 knows your true forgetting curve.”
SM-2 approximates a forgetting curve heuristically through the EF adjustment. It does not model the underlying memory trace directly. The algorithm was hand-calibrated to Wozniak’s own data in 1987 and generalized well enough to become dominant — but it does not adaptively fit to individual users’ actual memory behavior the way FSRS does.
“A rating of 3 (‘correct with difficulty’) is equivalent across all cards.”
EF adjustments accumulate over many reviews, so a rating of 3 on a card you’ve reviewed 20 times is functionally different from a rating of 3 on a card you’ve reviewed twice. The algorithm has no context for what “difficulty” means relative to the card’s history beyond the current EF value.
“Resetting a card to 1 day when you fail it is the right behavior.”
The SM-2 reset-to-start behavior is a documented limitation. A card you’ve successfully reviewed 15 times and then forgotten once should not be treated identically to a brand new card — considerable residual memory exists. FSRS handles this by modeling stability separately from current retrievability, so a lapse reduces stability moderately rather than catastrophically resetting the entire history.
“Everyone should use the default 0–5 rating scale in Anki.”
Anki’s default interface presents a 4-button scale (Again/Hard/Good/Easy). Most experienced Anki users effectively use only Again and Good. Research on rating reliability suggests finer distinctions (Hard/Good/Easy for correct answers) improve scheduling accuracy modestly, but only with consistent application — which most users don’t maintain.
Criticisms
SM-2 has been critiqued for its simplistic model of memory — the fixed interval multiplier and ease factor approach does not capture individual variation in memory strength or item difficulty as accurately as modern algorithms. The ease factor can enter a “death spiral” where a string of failures permanently reduces the ease factor to its minimum, creating an unsustainable review load. SM-2 also does not account for the actual time elapsed since last review when calculating the next interval.
Social Media Sentiment
SM-2 is widely discussed in the Anki community, where it was the default algorithm for years before being replaced by FSRS. Discussions often focus on “ease hell” — the tendency for the ease factor to decrease over time, creating ever-shorter review intervals. The transition from SM-2 to FSRS has generated extensive community discussion about algorithm performance, retention rates, and review load.
Last updated: 2026-04
History
- 1985–1987: Piotr Wozniak develops SuperMemo and iterates through SM-0 (paper) and SM-1 (software) toward a more general, mathematically cleaner algorithm. The empirical basis is his own multi-year self-study data. [Wozniak, 1990]
- 1987: SM-2 is finalized and implemented in SuperMemo. Its formula and easiness factor approach are deliberate choices for computational simplicity — SM-2 must run on early personal computers with limited resources. The formula is clean enough to be written in a few lines of any programming language.
- 1990: Wozniak publishes the SM-2 formula openly in his master’s thesis “Optimization of Learning.” This act of open publication is what enables the entire downstream SRS ecosystem.
- 2006: Damien Elmes implements a modified SM-2 as the core of Anki. Anki’s SM-2 variant differs slightly from the original (notably in how new cards are introduced and how the first two intervals are handled), but the fundamental EF and interval formula are faithful to the original.
- 2020s: Researchers and developers publish benchmarks comparing SM-2 to newer algorithms on real-world user data. SM-2 consistently underperforms on retention accuracy, motivating development of FSRS.
- 2022–present: FSRS becomes the preferred scheduler in Anki, superseding SM-2 for most use cases while remaining available for users who prefer the simpler system.
Practical Application
- Understand SM-2 as the foundational spaced repetition algorithm — it works but has known limitations that newer algorithms address
- If using SM-2 in Anki, be aware of the “ease factor problem” — avoid pressing “Hard” or “Again” excessively as it permanently reduces intervals
- Consider switching to FSRS which is now Anki’s recommended default algorithm and addresses many SM-2 limitations
- Sakubo uses FSRS natively, providing more accurate scheduling without the ease factor issues of SM-2
- Regardless of algorithm, consistent daily review is more important than algorithm optimization
Related Terms
See Also
Research
- Wozniak, P.A. (1990). Optimization of learning [Master’s thesis]. University of Technology, Poznan. https://www.supermemo.com/en/archives1990-2015/english/ol
Summary: The original documentation of SM-2 — formula, easiness factor, interval schedule, and the empirical basis from Wozniak’s self-study data. The primary reference for anyone implementing or evaluating SM-2.
- Anki documentation — Scheduling. https://docs.ankiweb.net/deck-options.html
Summary: Documents how Anki implements SM-2 and FSRS, including the specific differences between Anki’s SM-2 variant and Wozniak’s original. Essential for understanding what “SM-2 in Anki” actually means versus the original algorithm.
- Ye, J. et al. (2022). FSRS vs SM-2 benchmarks. https://github.com/open-spaced-repetition/fsrs-vs-sm2
Summary: Empirical comparison of SM-2 and FSRS performance on real-world Anki user data. Documents where SM-2 fails to accurately predict forgetting and how FSRS corrects for those failures. The clearest evidence for why SM-2 is being superseded.
- Wozniak, P.A., & Gorzelanczyk, E.J. (1994). Optimization of repetition spacing in the practice of learning. Acta Neurobiologiae Experimentalis, 54, 59–62.
Summary: Academic validation of SM-2’s interval optimization approach. Demonstrates measurable retention improvements from algorithmic scheduling compared to manual methods.