The FSRS algorithm

What is the FSRS algorithm?

FSRS is a scheduling algorithm for flashcards: after each review, it decides how many days to wait before showing the card again. Jarrett Ye created it and develops it with the open-spaced-repetition community on GitHub. It grew out of his research at MaiMemo, a Chinese vocabulary app, published at the KDD conference in 2022 with Jingyong Su and Yilong Cao.^[1] That paper fitted a memory model to 220 million review logs from MaiMemo users, and a 2023 journal version extended it.^[1][2] The open-source project describes FSRS as based on the DHP model from this work.^[3]

Anki integrated FSRS in version 23.10, released in late 2023, as an option next to its older SM-2-based scheduler.^[4] Open-source libraries exist in Python, Rust, TypeScript and other languages, and the project's own list of apps using FSRS includes Mochi Cards, RemNote and Logseq.^[5] For how FSRS fits into Anki's settings, see the Anki algorithm.

How does FSRS model memory?

FSRS describes the memory of each card with three numbers, often shortened to DSR: difficulty, stability and retrievability.^[3] After every review, it updates difficulty and stability from your grade (Again, Hard, Good or Easy) and the time since the last review.

Retrievability falls as time passes, following a forgetting curve. Stability sets how fast: the higher it is, the more slowly the curve drops. A successful review raises stability, by more when difficulty is low and when retrievability was low at the time of the review.^[6]

How does FSRS decide when to show a card?

FSRS shows a card again when its estimated retrievability falls to your desired retention. In FSRS-6, the curve and the interval are:^[6][7]

R(t, S) = (1 + factor × t / S) ^ (−w20)
factor  = 0.9 ^ (−1 / w20) − 1

I(r, S) = (S / factor) × (r ^ (−1 / w20) − 1)

In words: t is the number of days since the last review and S is stability. The first line gives the probability of recall after t days. The factor makes that probability exactly 90% when t equals S. The decay w20 sets the shape of the curve and is fitted to each user. The last line solves the curve for t: the next interval I is the number of days until retrievability reaches the desired retention r. Implementations round it to whole days and cap it at a maximum interval.^[7]

A consequence: at a desired retention of 90%, the next interval equals the card's stability. FSRS does not know when you will forget a card. It estimates a probability, and at 90% you can expect to fail about one review in ten.

What does desired retention do?

Desired retention is the probability of recall you want at the moment a card comes up for review; it trades how much you remember against how many reviews you do. Anki's default is 90%. The Anki manual warns that the workload rises steeply as the setting approaches 100% and recommends staying below 97%.^[8] The FSRS documentation calls values between 70% and 97% reasonable.^[3]

For example, take a card with a stability of 10 days and the default FSRS-6 decay of 0.1542.^[7] The formula above gives these next intervals:

Raising the target from 90% to 95% more than halves the interval, so the card comes back more than twice as often. For how intervals add up over time, see the spaced repetition schedule.

How does FSRS adapt to your reviews?

FSRS adapts by fitting its parameters to your past reviews with an optimizer, a machine-learning step that finds the values which best predict whether you recalled each card.^[3] FSRS-6 has 21 parameters.^[6] They control, for example, the starting stability for each first grade, how much each grade changes difficulty, and the shape of the forgetting curve.

• Default parameters. Before you optimize, FSRS uses defaults fitted to several hundred million reviews from about 10,000 users.^[3]
• Optimizing in Anki. The “Optimize” button in the deck options runs the optimizer on your history. The manual flags collections with fewer than a few hundred reviews and says that optimizing once a month is enough.^[8]

Which version of FSRS is current?

FSRS-6 is the version in Anki: it arrived in Anki 25.07, and Anki's September 2026 release (26.09) ships version 6.6.2 of the FSRS library.^[9][10] Each version changed the model and the number of parameters:^[6][11]

The project's benchmark lists FSRS-7 as the newest version, with a more complex forgetting curve.^[11] Anki 26.09 still uses FSRS-6.^[10]

Is FSRS better than SM-2?

On the available evidence, FSRS predicts recall more accurately than SM-2, but that evidence comes mostly from the FSRS project itself. SM-2, from 1987, gives each card an ease factor and multiplies the interval by it; it does not estimate a probability of recall (see the SM-2 algorithm). The FSRS documentation reports, from simulations, 20–30% fewer reviews than SM-2 for the same retention.^[3] Benchmarks are covered in FSRS vs SM-2.

Keep three limits in mind:

• It needs history. With few reviews, FSRS runs on default parameters fitted to other people.^[8]
• The benchmark is the project's own. The open-spaced-repetition benchmark tests algorithms on about 10,000 Anki users' collections, filtered for outliers.^[11] It is large and public, but not independent, and Anki users may differ from other learners.
• It estimates, it does not know. Retrievability is a probability, not a forecast for one review: at 95%, about one review in twenty still fails.