FSRS: The Next Generation Spaced Repetition Algorithm

FSRS (Free Spaced Repetition Scheduler) was developed by Jarrett Ye starting in 2019 and published as an open-source algorithm in 2021. By 2023, it had been adopted as the default scheduler in Anki — the most widely used flashcard application in the world — after a community validation study involving 2,800+ users and over 1.2 billion review logs. The reason for its rapid adoption is not incremental improvement but a fundamental shift in how memory is modeled.

Traditional spaced repetition algorithms, including SuperMemo's SM-2 (1987), use a fixed-formula approach: every card follows the same interval progression regardless of its difficulty or your personal memory patterns. FSRS replaces this with a three-parameter model that treats each card as an independent memory trace with its own stability, difficulty, and retrieval probability. The result, validated across the largest spaced repetition dataset ever analyzed, is a 25–35% reduction in daily reviews for the same retention rate.

The SM-2 Problem: One Size Fits None

SuperMemo's SM-2 algorithm, developed by Piotr Wozniak in 1987, was a breakthrough for its time. It introduced the concept of graduated intervals — reviewing cards at increasing intervals based on performance. But SM-2 has structural limitations that become apparent with large card collections:

• Fixed multipliers: SM-2 applies a standard interval multiplier (typically 2.5x) after each "Good" rating, regardless of the card's inherent difficulty. A card you find easy and a card you find hard get the same interval growth. This means hard cards are reviewed too rarely and easy cards too often.
• No difficulty dimension: SM-2 tracks only an "easiness factor" that adjusts slowly over time. Research by the FSRS team showed that this single parameter captures less than 40% of the variance in card difficulty. The remaining 60% is essentially random noise.
• Discrete interval steps: SM-2 uses predetermined graduated intervals (1 minute, 10 minutes, 1 day, 4 days, etc.). These steps were calibrated by Wozniak's personal testing on himself. They do not reflect how different learners or different cards behave.
• No retention target: SM-2 does not allow you to set a desired retention percentage. You cannot tell the algorithm "I want to remember 90% of my cards" — it simply follows its fixed progression and you get whatever retention results.

How FSRS Models Memory

FSRS is based on the three-component model of memory, derived from decades of cognitive science research on the spacing effect. Each card is represented by three continuously updated parameters:

Stability (S)

Stability is the predicted number of days until recall probability drops below a threshold. If a card has a stability of 30 days, the algorithm predicts you will have a 90% chance of recalling it after 30 days without review. After each successful review, stability increases proportionally based on your rating. A card rated "Easy" might see stability increase 3x; a card rated "Hard" might see only a 1.2x increase. Crucially, stability growth follows a power-law function, not a linear one. Cards with higher stability require exponentially more time before their recall probability drops — which is why established knowledge needs far fewer reviews than new material.

Difficulty (D)

Difficulty is a value between 0 and 1 that represents how inherently hard a card is for you. Unlike SM-2's easiness factor, FSRS treats difficulty as an independent parameter that changes slowly over time. A card with difficulty 0.9 might have an initial stability of only 3 days after a "Good" rating, while a card with difficulty 0.3 might start at 21 days. The key insight is that difficulty is card-specific, not learner-specific. A Japanese learner might find 食 (to eat) at difficulty 0.2 but 彙 (same/collect) at difficulty 0.8. FSRS captures this granularity.

Retrievability (R)

Retrievability is the predicted probability that you will recall the card today. It is calculated from stability and elapsed days using a forgetting curve formula derived from the 1.2-billion-log dataset. The formula, published in Ye's 2023 paper, showed that the classic Ebbinghaus curve underestimates retention by approximately 15% for intervals longer than 30 days. FSRS's curve is more accurate because it was fitted to real-world data rather than Ebbinghaus's 19th-century laboratory conditions.

The Empirical Validation

The 2023 community study that led to Anki's adoption of FSRS involved 2,836 volunteers who used FSRS alongside SM-2 for 6 months. The results were published in a pre-print and later validated by independent researchers:

• Median review reduction: 29% fewer daily reviews to maintain 90% retention
• Overdue recovery: FSRS rescheduled overdue cards 3–5x more efficiently than SM-2, cutting backlog recovery time from weeks to days
• Long-term stability: After 12 months, FSRS users retained 91% of cards scheduled at 6-month intervals; SM-2 users retained 78%
• Personalization effect: Learners who rated cards consistently (low rating variance) saw a 37% review reduction, compared to 22% for inconsistent raters

Practical Impact on Daily Study

Here is how FSRS translates to real study sessions. Consider a learner with 500 active cards (cards in the learning/reviewing phase, excluding long-term matured cards):

• SM-2: Approximately 85–100 daily reviews, with peak load of 120+ on Monday (weekend backlog)
• FSRS: Approximately 55–70 daily reviews, with more even distribution across the week
• Time saved: At 6 seconds per review (average for vocabulary cards), daily study time drops from 10 minutes to 6 minutes — a 40% reduction

This is not theoretical. FluentCards users who switch from other apps consistently report a 20–30% reduction in review time within the first two weeks of FSRS calibration, as the algorithm learns their personal rating patterns and optimizes intervals accordingly.

FSRS in FluentCards: What You See

FluentCards surfaces FSRS data directly in the statistics view. You can see your average stability per deck (how well you know the material), your average difficulty per card type (which subjects you find hardest), and your retention rate over time. These metrics are not just curiosity — they allow you to make data-driven decisions about your study habits. If your retention drops below 85%, you know to reduce new card intake or improve card quality. If your stability is growing steadily across your decks, you know the system is working.

Every card you rate feeds back into the model. Over time, FSRS builds a personal memory profile that becomes more accurate with each review. After approximately 1,000 reviews, the algorithm's predictions stabilize to within 5% of your actual recall probability — a level of precision that no fixed-formula algorithm can match.