Spaced Repetition Algorithms Explained
A deep dive into FSRS, SM-2, and Leitner β the algorithms powering modern flashcard apps. Learn how each one works and which apps (Anki, RemNote, StudyGlen, Brainscape) implement them best.
In 1885, Hermann Ebbinghaus discovered that we forget 70% of new information within 24 hours β unless we review it at scientifically optimized intervals. Spaced repetition is now the #1 evidence-based study method, but the algorithm matters: FSRS can schedule 20-30% fewer reviews than SM-2 for the same retention. We break down how each algorithm works and which flashcard apps implement them.
Why the algorithm behind your flashcards matters
Spaced repetition works by showing you a flashcard just before you are predicted to forget it. The "just before" part is the whole game β and it is decided by an algorithm.
For most of spaced repetition's digital history, that algorithm was SM-2 (SuperMemo 2), a formula Piotr WoΕΌniak published in 1987. It powered the original SuperMemo, every Anki user before 2023, and is still the default scheduler in RemNote. SM-2 is battle-tested β but it is also rigid: every learner gets the same scheduling curves regardless of how their specific memory behaves.
In 2022 an open-source project called FSRS (Free Spaced Repetition Scheduler) changed that. FSRS fits a statistical model to your actual review history and schedules each card based on its predicted probability of recall. Benchmarks on 500+ million Anki reviews show FSRS needs 20-30% fewer reviews than SM-2 for the same retention rate. Anki adopted FSRS as the default in version 23.10 (November 2023).
This guide explains how FSRS, SM-2, and the classic Leitner box system work β and which flashcard apps implement each. If you are picking a study tool in 2026, the algorithm is the single biggest differentiator.
FSRS β the Free Spaced Repetition Scheduler
FSRS is a modern open-source scheduling algorithm developed since 2022 by Jarrett Ye and the open-spaced-repetition community. It was designed to beat SM-2 on accuracy and efficiency by treating memory as a statistical model that adapts to each individual learner. Anki, RemNote, and StudyGlen all implement it today.
How FSRS works β the DSR memory model
FSRS models the memory of a single flashcard using three values, updated after every review:
- Difficulty (D): How hard a specific card is for you. Ranges 1-10. Calibrated based on whether you press Again, Hard, Good, or Easy.
- Stability (S): How many days it takes for your probability of recalling this card to drop to your retention target (default 90%). Grows after correct reviews, resets after lapses.
- Retrievability (R): Your predicted probability of recalling this card right now β a function of D, S, and the days since your last review.
With these three values, FSRS answers one question for each card: given your retention target, what is the latest moment I can schedule this review and still expect you to remember it?
What makes FSRS different from SM-2
SM-2 uses fixed multipliers β everyone gets the same interval-growth curves out of the box. FSRS fits your personal parameters to your actual review history using gradient descent, typically after ~1,000 reviews. Once trained, it accounts for which card types you find harder, how quickly you forget, and how lapses affect long-term stability.
You also set a "Desired Retention" target β usually 0.80 to 0.97, with most users landing around 0.85-0.90. Higher retention means more reviews; lower means fewer. SM-2 has no equivalent control.
Which flashcard apps use FSRS
- Anki: Default scheduler since v23.10 (November 2023) across desktop, AnkiDroid, and AnkiMobile. SM-2 remains available as a fallback.
- RemNote: Available as an optional scheduler alongside SM-2.
- StudyGlen: Default algorithm for all AI-generated flashcard decks β no manual configuration required.
When FSRS wins clearly
Large decks (2,000+ cards), long-term retention goals, and heterogeneous difficulty (some cards easy, some hard). The more review data you accumulate, the more FSRS outperforms SM-2.
When FSRS does not matter
Under ~1,000 reviews, FSRS cannot fit a meaningful personal model yet β it falls back to default parameters and performs similarly to SM-2. For casual study or short-term cramming, algorithm choice is largely cosmetic.
SM-2 β Anki's classic algorithm
SM-2 was published by Piotr WoΕΌniak in 1987 as part of SuperMemo β the first commercial spaced repetition application. It powered Anki's default scheduler from the 2006 launch until late 2023, and it is still the default in RemNote. Four decades of real-world use have made it the baseline every other SRS algorithm is compared against.
How SM-2 works
SM-2 tracks two numbers per card:
- Ease factor (EF): A multiplier, initialized at 2.5, that controls how fast intervals grow.
- Interval: Days between reviews.
After every review:
- If you failed the card, reset the interval to 1 day and hold the EF.
- If you passed, multiply the current interval by the EF (raising EF slightly for Easy, lowering it for Hard).
A typical SM-2 card sequence might be: 1 day β pass β 6 days β pass β 15 days β pass β 37 days β pass β 92 days...
Strengths
SM-2 is simple, transparent, and needs no training data. It works from the first review. Its behaviour is predictable by hand β you can look at a card's EF and interval and explain exactly why it was scheduled where it was. 35+ years of real-world usage have made it the safest default for any SRS.
Limitations
SM-2's multipliers are universal β the algorithm does not adapt to individual learners. If your memory for geography facts decays faster than your memory for equations, SM-2 treats them identically. It also has no explicit retention target: you cannot ask for 95% retention instead of the implicit ~85% the multipliers produce.
Which apps use SM-2
- Anki: Available as a fallback scheduler. Was the default until v23.10 switched to FSRS.
- RemNote: Default scheduler.
- SuperMemo: Piotr WoΕΌniak's original app. Still actively developed β modern SuperMemo uses SM-18, a descendant of SM-2.
The Leitner system β spaced repetition on paper
The Leitner system, invented by German science journalist Sebastian Leitner in 1972, predates every digital SRS algorithm. It is a physical-card method that inspired the entire category β and it is worth understanding because some apps (including Quizlet's Learn mode) still use a simplified version of it.
How Leitner works
You have a set of numbered boxes (classically 5). All new cards start in Box 1.
- β’ Correct answer β move the card to the next higher box.
- β’ Wrong answer β send the card back to Box 1.
Each box has its own review frequency: Box 1 every day, Box 2 every two days, Box 3 every four days, and so on. Cards you consistently remember drift toward the higher boxes; cards you forget get pulled back into frequent review.
Strengths and limits
Leitner is the simplest possible SRS β it needs zero math and works with paper cards and a shoebox. Its scheduling is far coarser than SM-2 or FSRS, and the intervals do not adapt to individual memory or card difficulty. For short-term learning or study environments that reject digital tools, it is still fine. For most modern use cases, any digital SRS running SM-2 β and especially FSRS β will schedule reviews more efficiently.
FSRS vs SM-2: which algorithm performs better?
The Anki team ran benchmarks on over 500 million review logs comparing FSRS against SM-2. The headline result: for the same retention rate, FSRS requires roughly 20-30% fewer reviews. On a 2,000-card deck with daily reviews, that translates into hours saved per week.
Where FSRS wins clearly
- Long-term retention (30+ day intervals): FSRS's adaptive stability tracking schedules long intervals more accurately than SM-2's fixed multipliers.
- Mixed-difficulty decks: FSRS learns per-card difficulty; SM-2's universal multipliers over-schedule easy cards and under-schedule hard ones.
- Users with 1,000+ reviews: FSRS needs training data to personalize. Once it has it, the gap over SM-2 widens with every additional review.
Where SM-2 still holds up
- Small decks (under 500 cards): FSRS cannot fit a personal model yet; SM-2's defaults are competitive.
- Brand-new learners: SM-2 works from day one with zero setup. FSRS with default parameters is also fine, but the meaningful advantage appears only after you have accumulated data.
- Interpretability: SM-2's scheduling is predictable from (EF, interval). FSRS's fitted model is effectively a small neural network β harder to reason about by hand.
If your flashcard app offers FSRS, enable it. For most users, the 20-30% review reduction is the single biggest ergonomic gain available β which is why the Anki team made it the default in v23.10. The only reasons to stick with SM-2 are a very small deck, a thin review history, or a mid-deck migration you do not want to re-optimize.
Which algorithm should you use?
A quick decision framework:
- 1.
Large deck (1,000+ cards) and long-term retention goal β FSRS. Anki, RemNote, or StudyGlen all implement it.
- 2.
Small deck and short-term study (a single exam, a language phrasebook) β any algorithm works, including plain Leitner. Do not over-think it.
- 3.
You want zero setup plus AI-generated cards β StudyGlen (FSRS by default, AI generates cards from PDFs, notes, or images).
- 4.
You want maximum control plus access to community decks β Anki (FSRS default since v23.10, SM-2 available as a fallback).
- 5.
You take long-form notes and want flashcards built in β RemNote (SM-2 default, FSRS available).
- 6.
You want expert-curated flashcard sets with a simple confidence-based review β Brainscape (uses CBR, a proprietary non-FSRS scheduler).
- 7.
You need the largest existing library of flashcards and do not need true SRS β Quizlet (Leitner-style, not true SRS).
For most students in 2026, an FSRS-powered app is the right default. The algorithm has replaced SM-2 as the state of the art for a reason β and the infrastructure to train it is now built into every major flashcard tool.
Apps that implement these algorithms
Here are the five flashcard apps most commonly used for spaced repetition, grouped by which algorithm they run under the hood. The verdicts and pros/cons below help you compare them β but if you are still deciding between algorithms, jump back to the Which algorithm should you use section.
Pros
- FSRS algorithm adapts to your personal memory patterns for optimal review timing
- AI generates flashcards from PDF, text, and image input (no manual card creation needed)
- Set your target retention rate and FSRS schedules reviews mathematically
- Also generates quizzes, educational comics, and live quiz sessions
- 37 languages with automatic detection
- Free tier available with credit-based pricing (no subscription)
- AI-generated educational images on flashcards for visual memory aids
Cons
- Newer platform, growing community
- No mobile app yet (responsive web-based)
- No pre-made shared deck library
Pros
- Free and open-source (desktop and Android)
- Supports both FSRS and SM-2 algorithms (FSRS is default for new users)
- Highly customizable card templates, note types, and scheduling parameters
- Massive community with thousands of shared decks (AnKing for medical, etc.)
- Works fully offline on all platforms
- Powerful add-on ecosystem extends functionality
Cons
- Steep learning curve β intimidating for beginners
- No built-in AI card generation (requires manual creation or add-ons)
- iOS app costs $24.99 (one-time)
- Dated interface design
Pros
- Confidence-Based Repetition (CBR) adapts review frequency to your self-rated confidence (1-5 scale)
- Large marketplace of certified, expert-made flashcard classes
- Polished native mobile apps (iOS and Android)
- Detailed progress tracking and analytics dashboard
- Teacher and classroom tools built in
Cons
- No AI card generation from uploaded content
- CBR is proprietary β less transparent and research-backed than FSRS
- Pro subscription required for full library access ($9.99/mo)
- Limited card customization compared to Anki
Pros
- SM-2 spaced repetition integrated directly into the note-taking workflow
- AI generates flashcards from your notes automatically
- Bidirectional linking creates a knowledge graph of connected concepts
- PDF annotation and import for study materials
- Combines note-taking, flashcards, and review in one workspace
Cons
- SM-2 algorithm is less efficient than FSRS (requires ~20-30% more reviews for same retention)
- Steeper learning curve than a simple flashcard app
- Free tier limits AI features and storage
- Smaller community and fewer pre-made decks than Anki
Pros
- Massive library of 800M+ user-created flashcard sets
- Magic Notes AI converts notes into flashcards
- Polished mobile apps with offline access
- Multiple study modes (Learn, Test, Match game)
- Familiar interface with easy onboarding
Cons
- No true spaced repetition algorithm β uses basic Leitner-style box system
- AI features require Quizlet Plus subscription ($7.99/mo)
- Ad-heavy free tier
- Optimized for short-term cramming, not long-term retention
- No image OCR input
Feature Comparison Table
| Feature | StudyGlen | Anki | Brainscape | RemNote | Quizlet |
|---|---|---|---|---|---|
| SR Algorithm | FSRS | FSRS/SM-2 | CBR | SM-2 | Basic |
| AI Card Generation | Yes | Add-ons | No | Yes | Yes |
| PDF Upload | Yes | Add-ons | No | Yes | No |
| Card Types | Basic, Cloze, Image | Basic, Cloze, Custom | Basic only | Basic, Cloze | Basic, Diagram |
| Review Analytics | Yes | Yes | Yes | Limited | Limited |
| Free Tier | Free | Free | Limited | Limited | With ads |
| Mobile App | No | Yes | Yes | Yes | Yes |
See It in Action
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Frequently Asked Questions
FSRS stands for Free Spaced Repetition Scheduler. It is an open-source spaced repetition algorithm developed since 2022 by Jarrett Ye and the open-spaced-repetition community. Anki adopted it as the default scheduler in version 23.10 (November 2023), replacing SM-2.
FSRS models the memory of each flashcard using three values: Difficulty (how hard the card is for you), Stability (how many days before your recall probability drops to your retention target), and Retrievability (your current predicted probability of remembering the card). After every review, FSRS updates these values and schedules the next review at the optimal moment to hit your target retention rate. After roughly 1,000 reviews it can fit personalized parameters to your specific memory patterns using gradient descent.
SM-2, published by Piotr WoΕΌniak in 1987, uses fixed multipliers to grow intervals based on how you rate each review. FSRS, released in 2022, fits a statistical model to your review history and schedules each card based on predicted recall probability. Benchmarks on 500+ million Anki reviews show FSRS requires roughly 20-30% fewer reviews than SM-2 for the same retention rate, because it adapts to individual learners and card-level difficulty. SM-2 is simpler and needs no training data; FSRS is more accurate once it has enough review history to personalize.
For almost any modern digital use case, yes. The Leitner box system (1972) uses fixed box-to-box intervals (for example, 1 day, 2 days, 4 days) that do not adapt to individual memory or card-level difficulty. FSRS calculates interval length dynamically from your review history and explicitly targets a retention rate you choose. Leitner remains fine for paper flashcards or the simplest apps, but any SRS running FSRS β or even SM-2 β will schedule reviews more efficiently.
Per the Anki maintainers, re-optimizing 3-4 times per year is sufficient once your deck has 1,000+ reviews. More frequent re-optimization (for example, weekly) produces negligible improvements and is not worth the time. A good trigger is whenever your total reviewed cards roughly doubles.
Anki (default since v23.10), RemNote (as an alternative to SM-2), and StudyGlen (default for AI-generated flashcards) all support FSRS natively. The algorithm itself is open source β MIT-licensed Python and Rust implementations live at the open-spaced-repetition organization on GitHub β so expect more apps to adopt it over time.
FSRS needs review data to fit a personalized model. Under roughly 1,000 reviews it falls back to default parameters and behaves similarly to SM-2, so you will not see the 20-30% review reduction yet. That said, there is no downside to enabling FSRS early: Anki now does this automatically, and the personalized accuracy gains start showing up as soon as you have accumulated enough review history.
It depends on the destination app. StudyGlen accepts .apkg and .colpkg uploads directly and can opt-in convert your Anki SM-2 scheduling state β intervals, ease, lapses β into FSRS, so cards you've already learned don't reset to day zero. Most other tools either don't accept .apkg at all, or treat imported cards as fresh and lose your review history. If preserving years of Anki scheduling matters to you, check that the target app explicitly supports SM-2 β FSRS conversion before migrating. StudyGlen's free tier includes 5 imports per day; credit packs unlock unlimited.
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