How FSRS Works

FSRS (Free Spaced Repetition Scheduler) is a modern spaced repetition algorithm developed by Jarrett Ye. It's based on the DSR model (Difficulty, Stability, Retrievability) and uses principles from memory research to optimize when you should review each card.

The Science of Forgetting

The Forgetting Curve

When you learn something new, your memory of it decays over time following a predictable pattern called the forgetting curve. This phenomenon was first discovered by German psychologist Hermann Ebbinghaus in 1885. FSRS models this with the formula:

R(t) = (1 + t / (9 × S))^(-1)

The Components

R(t) = Retrievability — "what's the chance I can recall this right now?" Ranges from 0 to 1 (0% to 100%).
S = Stability — how "durable" the memory is. Higher stability means the memory decays more slowly. Each successful review increases stability.
t = Time since last review (in days).

Why This Formula?

The formula R(t) = (1 + t/(9·S))^(-1) is a power-law decay, which empirically fits human memory better than exponential decay for longer time intervals.

A few intuitions:

Condition	Calculation	Meaning
t = 0 (just reviewed)	R = 1/(1+0) = 1	Perfect recall (100%)
t = S (stability time)	R = 1/(1+1/9) ≈ 0.90	90% chance of recall
t = 9·S	R = 1/(1+1) = 0.5	50% chance of recall

The constant 9 is calibrated so that when t equals S, retrievability is about 90%. This is FSRS's definition of stability: the time it takes for recall probability to drop to 90%.

Concrete Example

If your stability S = 10 days:

After 10 days → ~90% chance of recall
After 90 days (9 × 10) → 50% chance of recall
After 180 days → ~36% chance of recall

This is why FSRS schedules reviews around the stability point—catching you at ~90% retrievability maximizes efficiency.

The goal of spaced repetition is to review cards just before you forget them, which strengthens the memory and increases stability. This leverages the spacing effect—the finding that information is better retained when learning is spread out over time.

Optimal Review Timing

FSRS schedules reviews to maintain a target retrievability (typically ~90%). This means:

Review too early → wasted effort, the memory was still strong
Review too late → you've already forgotten, need to relearn
Review at the right time → maximum efficiency, memory gets stronger

This approach is supported by research on the testing effect, which shows that actively recalling information strengthens memory more than passive review.

Core Concepts

Stability (S)

Stability measures how long a memory will last before decaying below the recall threshold. It's measured in days. This concept comes from the two-component model of memory, which distinguishes between memory stability (how long it lasts) and retrievability (current recall probability).

Stability	Meaning
0.5 days	Very fragile memory, needs review within hours
5 days	Moderate memory, review within a week
30 days	Strong memory, can wait a month
365 days	Very stable, annual review sufficient

How stability changes:

Again: Stability decreases significantly (memory reset)
Hard: Stability increases slightly
Good: Stability increases normally
Easy: Stability increases substantially

After each successful review, stability grows—this is why intervals get longer over time.

Difficulty (D)

Difficulty represents how hard a particular card is for you to learn. It ranges from 1 (easiest) to 10 (hardest).

Difficulty	Meaning
1-3	Easy cards, quick to learn
4-6	Average difficulty
7-10	Challenging cards, require more repetition

How difficulty changes:

Pressing Again increases difficulty (the card is hard for you)
Pressing Easy decreases difficulty (the card is easy for you)
Pressing Good keeps difficulty roughly stable

Difficulty affects how much stability increases after each review. High-difficulty cards gain stability more slowly. This aligns with research on desirable difficulties—harder items require more effort but can lead to stronger learning.

Retrievability (R)

Retrievability is the probability that you can recall a card at any given moment. It starts at 100% right after a review and decays over time following the power law of forgetting.

Day 0: 100% (just reviewed)
Day 3: ~85% (starting to fade)
Day 7: ~70% (time to review)
Day 14: ~50% (likely forgotten)

FSRS schedules reviews to catch cards when retrievability drops to around 90%.

The Four Ratings

Each rating affects stability and difficulty differently:

Rating	Stability Effect	Difficulty Effect	When to Use
Again	Decreases significantly	Increases	You forgot completely
Hard	Small increase	Slight increase	You struggled but recalled
Good	Normal increase	No change	Normal recall
Easy	Large increase	Decreases	Effortless recall

Rating Examples

Again: You see "ephemeral" and have no idea what it means. Press Again. The card resets to a 1-minute interval.

Hard: You see "ubiquitous" and after 10 seconds of thinking, remember it means "present everywhere." Press Hard.

Good: You see "serendipity" and recall "happy accident" within a couple seconds. Press Good.

Easy: You see "hello" and instantly know it. Press Easy to skip ahead.

Learning vs Review Phase

Learning Phase

New cards start in the Learning state with short intervals (minutes). This phase uses your configured learning step:

New Card → Good (10m) → Good → Graduate to Review

During learning:

Intervals are short (minutes)
Cards don't affect your retention statistics
The goal is initial memorization

This phase leverages massed practice initially before transitioning to spaced practice.

Review Phase

Once a card graduates, it enters the Review state with longer intervals (days/weeks/months):

Review → Good → (interval doubles or more) → Review again later

During review:

Intervals grow with each successful recall
Cards contribute to your retention statistics
The goal is long-term memory retention

Relearning Phase

If you press Again on a Review card, it enters Relearning:

Review → Again → Relearning (1m) → Good → Back to Review

The card goes through short intervals again before returning to review with reduced stability.

The 19 FSRS Parameters

FSRS uses 19 internal parameters (w₀ to w₁₈) that control the algorithm's behavior. These were optimized using machine learning on millions of real review records:

w₀₋₃: Initial stability for each rating on new cards
w₄₋₅: Difficulty calculation
w₆₋₈: Stability increase factors
w₉₋₁₀: Difficulty-stability interaction
w₁₁₋₁₄: Failure and relearning behavior
w₁₅₋₁₈: Short-term scheduling

Anglio uses the default parameters, which are optimized from millions of Anki reviews and work well for most learners. For technical details, see the FSRS algorithm documentation.

Interval Calculation

When you press a rating button, FSRS calculates the next interval using:

Current stability of the card
Your rating (Again/Hard/Good/Easy)
Target retrievability (90%)
The 19 parameters

The formula ensures that when you next see the card, your retrievability will be around 90%—the optimal point for memory strengthening according to research on optimal retention.

Example Progression

A typical card might progress like this (pressing Good each time):

Review	Interval	Stability
1	10 min	0.5 days
2	1 day	2 days
3	3 days	6 days
4	8 days	15 days
5	21 days	40 days
6	2 months	100 days
7	5 months	250 days

Notice how intervals grow faster than linearly—this is the power of spaced repetition.

FSRS vs SM-2

Anglio uses FSRS instead of the older SM-2 algorithm (used by Anki by default). Here's why:

Aspect	SM-2	FSRS
Ratings	2 (Again, Good)	4 (Again, Hard, Good, Easy)
Core metric	Ease Factor	Stability + Difficulty
Adaptability	Fixed formula	Based on memory model
Accuracy	Good	Better (proven in studies)
Theoretical basis	Empirical	Memory science

FSRS has been shown to achieve the same retention with fewer reviews, or better retention with the same number of reviews. See the FSRS benchmark comparisons for detailed data.

Tips for Optimal Learning

Be Honest with Ratings

The algorithm only works if you rate honestly:

Don't press Good when you actually struggled (use Hard)
Don't press Easy just to skip ahead
Press Again when you genuinely forgot

Research on metacognition shows that accurate self-assessment is crucial for effective learning.

Review Consistently

FSRS assumes you review cards around their due time. Large backlogs reduce efficiency because:

Overdue cards have lower retrievability
The algorithm's predictions become less accurate

Trust the Process

It might feel wrong to wait days or weeks between reviews, but that's the point. The spacing effect shows that spacing creates stronger, more durable memories than cramming.

The Science of Forgetting​

The Forgetting Curve​

The Components​

Why This Formula?​

Concrete Example​

Optimal Review Timing​

Core Concepts​

Stability (S)​

Difficulty (D)​

Retrievability (R)​

The Four Ratings​

Rating Examples​

Learning vs Review Phase​

Learning Phase​

Review Phase​

Relearning Phase​

The 19 FSRS Parameters​

Interval Calculation​

Example Progression​

FSRS vs SM-2​

Tips for Optimal Learning​

Be Honest with Ratings​

Review Consistently​

Trust the Process​

Further Reading​