How FSRS Works: The Modern Spaced-Repetition Algorithm

Most people who use flashcard apps have no idea what is happening behind the scenes when an algorithm decides to show them a card tomorrow versus next month. For years the dominant answer was SM-2, a heuristic algorithm developed in the 1980s that has served millions of learners reasonably well. FSRS — the Free Spaced Repetition Scheduler — is a newer approach, and it takes a fundamentally different path: instead of using fixed rules, it builds a mathematical model of how your memory actually works. Understanding that model explains why FSRS schedules feel more accurate and why they tend to require fewer reviews for the same retention level. FSRS is open source and actively developed; you can explore the FSRS algorithm on GitHub. For the full range of spaced-repetition topics, visit the spaced repetition article collection.

The Three Components of Memory: D, S, and R

FSRS describes each piece of knowledge you are learning using three quantities. Together they form what researchers call the DSR model.

Retrievability (R)

Retrievability is the probability that you can successfully recall an item right now, at this exact moment. It starts at 1.0 (certainty) immediately after a review and decays over time following a forgetting curve. When the algorithm decides it is time to show you a card, it is because your retrievability has dropped to a target level — typically around 0.90, meaning roughly a 90 % chance of recall. The goal is to review right before you forget, not well before and not after.

Stability (S)

Stability describes how slowly your retrievability decays. A high-stability memory fades slowly; a low-stability memory fades quickly. After each successful review, your stability for that item increases, which is why review intervals can grow over time. The same item reviewed five times at the right moments will have much higher stability than an item reviewed five times in a single day — the algorithm captures this difference precisely.

Stability is the quantity that most directly corresponds to the colloquial sense of "knowing something well." High stability means that even if you skip a review, your memory will still be largely intact weeks later. Low stability means missing one review can drop your recall probability substantially.

Difficulty (D)

Difficulty is an estimate of the intrinsic hardness of a specific item for you. Some facts are just harder to remember than others, and that varies by person. The difficulty of an item affects how much stability increases after a successful review: easy items gain more stability per review; hard items gain less. Difficulty is not fixed — it is updated as you rate cards over time, so an item that initially seems difficult can gradually be reclassified as your familiarity grows.

How FSRS Predicts the Next Review Date

Given current values of D, S, and R for an item, FSRS can predict how retrievability will change over any future time interval. It uses this to answer a precise question: how many days from now will retrievability drop to the target threshold?

That day becomes the next scheduled review. Nothing more, nothing less — no fixed multipliers, no population averages, just a prediction derived from the model for this specific item and this specific learner.

After you complete a review and provide a rating — Again, Hard, Good, or Easy — FSRS updates the item's D and S values based on what your response reveals. A failed recall (Again) resets stability and slightly increases difficulty. An easy, confident recall (Easy) produces a larger stability gain than a slow, effortful one (Hard or Good). The next interval is then computed fresh from the updated parameters.

Adaptation: Why FSRS Improves Over Time

One of the most significant features of FSRS is that its underlying parameters can be calibrated to your review history. The model contains a set of weights that control how stability evolves in different situations. These weights have default values derived from large-scale research data, but they can also be fitted to the actual pattern of your historical reviews.

This means FSRS can learn that you tend to forget things more quickly than the population average, or that your recalls flagged as Hard are actually quite stable for you. The resulting schedules become personalised at a deeper level than any fixed-rule system can achieve.

This is conceptually different from just lowering an ease factor. Ease factors in older algorithms are per-card adjustments applied multiplicatively to intervals. FSRS learns the shape of your forgetting curves from data, then re-derives all intervals from first principles using that shape.

The Role of Your Ratings

Your ratings are the primary signal FSRS uses to update memory estimates. Getting them right matters.

• Again — you could not recall the answer. Stability resets to near zero; the card will reappear very soon.
• Hard — you recalled, but it was slow or required significant effort. Stability increases, but less than a Good rating would produce.
• Good — correct recall with normal effort. The expected and most common outcome.
• Easy — immediate, effortless recall. Stability increases substantially; the next interval jumps further into the future.

The key insight is that how you recalled matters, not just whether you recalled. A memory retrieved with effort is less stable than one retrieved instantly, and FSRS models that difference. Honest rating is therefore not just good practice — it is the data pipeline that keeps the model accurate.

FSRS and the Learning Loop

FSRS shines most when it is integrated tightly with how you consume and engage with material, not just how you review it. The quality of review scheduling is only as good as the quality of the flashcards being scheduled. Active recall during the initial reading phase — pausing to generate answers before checking — produces better-encoded initial memories, which gives FSRS a stronger starting point to work from.

For cross-material study, the algorithm treats each card independently regardless of what source it came from. This makes it possible to review vocabulary from a language-learning PDF, key concepts from a recorded lecture, and formulas from a textbook all in one session, with each item scheduled according to its own stability and difficulty rather than the category it belongs to.

FSRS does not ask "how hard is this topic?" — it asks "how stable is this specific memory in this specific learner, right now?" That shift from categories to individual memory traces is what separates model-based scheduling from heuristic scheduling.

What FSRS Does Not Do

It is worth being clear about the limits of the model. FSRS does not simulate the neurological details of memory consolidation. It does not know whether your fatigue level or study environment will affect performance on a given day. It does not guarantee retention — it targets a probability threshold, so some forgetting is expected and acceptable.

The model is also only as good as your ratings. If you consistently mark cards as Easy when they were actually effortful — perhaps to reduce the number of upcoming reviews — the algorithm will produce intervals that are too long and your actual retention will fall below target. The forgetting curve does not care about your preferences; it only responds to honest input.

Why FSRS Matters for Serious Learners

The practical payoff of a model-based approach is fewer total reviews for the same retention target. Because intervals are derived from an accurate prediction of when you will forget, rather than a conservative heuristic, the algorithm does not pad schedules unnecessarily. Items that are genuinely stable for you get long intervals. Items that are genuinely fragile get short ones. The net effect across a large deck over months of study can be substantial: the same retention level achieved with significantly less review time.

For anyone studying a large body of material — a language, a professional domain, an academic subject — that efficiency compounds into hours recovered and knowledge that actually sticks when it counts.

Your mastery trends and cross-book review queue are visible in the LearnBook dashboard — a live picture of how your memory is holding up across every source you are studying, all scheduled by the same FSRS model described above.