The Forgetting Curve, Measured: What FSRS Learns From 1.7 Billion Reviews

FSRS models memory with a power-law forgetting curve, fit on 1.7 billion real flashcard reviews. Here is how fast recall fades without review — and how spaced repetition stretches the curve by building memory stability.

Key findings

  • FSRS models forgetting as a power law, R(t) = (1 + (19/81)·t/S)^−0.5, fit on the open-spaced-repetition benchmark of ~1.7 billion Anki reviews from ~20,000 learners. Power-law decay fits real recall data better than the classic exponential forgetting curve.
  • A freshly-learned card (memory stability ≈ 1 day) decays fast: predicted recall falls to about 62% after a week and 35% after a month with no review.
  • Spaced repetition works by raising stability, not by changing the curve: the same card reinforced to ~30-day stability still holds ~90% recall at a month and ~77% at 90 days.
  • FSRS schedules each review as recall approaches the target (default 90%), so stability compounds with every successful review — which is why a few minutes a day beats cramming.
Predicted recall by Days since last review
Days since last reviewNewly learned card (1-day stability)Reinforced by spaced repetition (30-day stability)
10.90.996
30.7660.988
70.6150.974
140.4830.949
300.3530.9
600.2580.825
900.2130.766

Every card you learn starts fading the moment you stop reviewing it. Hermann Ebbinghaus first mapped this forgetting curve in 1885. Modern spaced-repetition research has since measured it at massive scale — and found that memory decays as a power law, not the smooth exponential curve from the textbooks.

The FSRS forgetting curve

Quizlar schedules reviews with FSRS (the Free Spaced Repetition Scheduler), the open-source algorithm now built into Anki. FSRS models the probability you still recall a card after t days as:

R(t) = (1 + (19/81) · t / S)−0.5

Here S is the card's memory stability — the number of days until recall is expected to fall to 90%. The curve above is plotted directly from this formula using FSRS's default, benchmark-fit parameters.

Stability is everything

The two lines tell the whole story of spaced repetition. A freshly-learned card (stability ≈ 1 day) decays fast — predicted recall drops to about 62% within a week and 35% within a month. The same card, reinforced by spaced reviews until its stability reaches ~30 days, still holds ~90% recall at a month and ~77% at 90 days.

Crucially, the shape of the curve never changes. Spaced repetition doesn't make you forget more slowly per card — it raises stability, stretching the same curve out over weeks and months. Each successful review compounds stability, which is why a few minutes a day beats one long cram before an exam.

Why power-law, not exponential

The classic Ebbinghaus curve is often drawn as exponential decay. Large-scale review data shows real forgetting has a heavier tail: you forget quickly at first, then forgetting slows. FSRS's power-law form captures this, which is part of why it predicts recall more accurately than older schedulers like SM-2.

Where this data comes from

The forgetting-curve parameters used here come from the open-spaced-repetition benchmark — an open dataset of roughly 1.7 billion flashcard reviews from about 20,000 Anki users, the largest public spaced-repetition dataset. The curve is the FSRS model fit on that data, not a measurement of Quizlar's own users. Because Quizlar runs the same FSRS engine, it is also exactly how Quizlar decides when to bring each of your cards back.

FAQ

Is the forgetting curve exponential or power-law?

Large-scale review data shows forgetting follows a power law, not a simple exponential. FSRS uses the power function R(t) = (1 + (19/81)·t/S)^−0.5, which fits real recall data more accurately than the classic exponential Ebbinghaus curve.

What is memory stability in FSRS?

Stability is the number of days until your predicted recall of a card drops to 90%. Every successful review increases stability, so the card can wait longer before its next review.

Does this data come from Quizlar users?

No. These curve parameters come from the open-spaced-repetition benchmark — about 1.7 billion reviews from ~20,000 Anki users. Quizlar uses the same FSRS algorithm, so the curve also describes how Quizlar schedules your reviews.

How does spaced repetition beat the forgetting curve?

It doesn't change the curve's shape — it raises stability. By reviewing each card right before you would forget it, FSRS stretches the same forgetting curve across longer and longer intervals.

Methodology & data

  • Predicted-recall curves plotted from the FSRS forgetting-curve formula for two representative memory-stability values (1 day and 30 days). Parameters are FSRS defaults fit on the open-spaced-repetition benchmark; this is the model curve, not an aggregate of Quizlar user data.
  • Learners in sample: ~20,000 learners
  • Reviews analyzed: ~1.7 billion reviews
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