Spaced Repetition Algorithm Explained (2026 Guide)
Spaced Repetition, Explained: The Algorithm Behind Effortless Memorization
If you have ever crammed for an exam and forgotten everything a week later, you have already met the problem that the spaced repetition algorithm was designed to solve. Spaced repetition is a learning technique that schedules reviews at increasing intervals so each card is seen exactly when you are about to forget it — no sooner, no later.
This guide is for learners and builders who want to understand what is actually happening underneath apps like Anki, RemNote, and SmartRecall. We will walk through the science, the history, the four main algorithms, and a worked example you can run on paper.
The 1-minute mental model
Spaced repetition stands on two well-replicated findings from cognitive psychology:
- The testing effect. Actively retrieving information from memory strengthens that memory more than re-reading or highlighting. Every flip of a flashcard is a retrieval attempt, which is why flashcards beat passive review even when total study time is held constant.
- The spacing effect. Memories consolidate better when reviews are distributed across time rather than packed into one session. Two 10-minute sessions one day apart beat a single 20-minute session, and seven sessions across a month beat seven in a row.
A spaced repetition algorithm is just a scheduler that combines these two ideas: it decides when the next retrieval attempt should happen so that the long-term memory trace gets the maximum boost per minute of study.
Where it came from: from Ebbinghaus to SuperMemo
The story spans 140 years and three big jumps.
- 1885 — Hermann Ebbinghaus ran the first systematic memory experiments on himself, memorizing nonsense syllables and plotting how recall decayed over hours and days. The resulting curve — the forgetting curve — is the empirical foundation everything else rests on.
- 1932 — C. A. Mace suggested in Psychology of Study that reviews could be scheduled at expanding intervals to fight the curve.
- 1972 — Sebastian Leitner published the Leitner box system in his book So lernt man lernen: physical card boxes where cards graduated to a slower box on success and demoted on failure.
- 1985–1987 — Piotr Wozniak ran self-experiments at a Polish university and published the SM-2 algorithm, the first practical computational scheduler. SM-2 introduced the ease factor — a per-card multiplier that adapts to how hard each item is for you. (1987 paper)
- 1990s–2010s — SuperMemo SM-4 through SM-18 added two-component memory models, optimal factor matrices, and stability/retrievability tracking. Most stayed proprietary.
- 2006 — Anki shipped a polished open-source implementation of SM-2+ and brought spaced repetition to a mass audience.
- 2023–2024 — FSRS (Free Spaced Repetition Scheduler) by Jarrett Ye became the first widely-adopted open algorithm to beat SM-2 in head-to-head benchmarks. Anki adopted it as a built-in option in version 23.10.
The four major algorithms compared
| Algorithm | Difficulty to implement | Accuracy vs. target retention | Best use case |
|---|---|---|---|
| Leitner (1972) | Trivial — 5 paper boxes | Low; intervals are fixed regardless of card difficulty | Beginners, paper flashcards, kids learning vocab |
| SM-2 (1987) | Easy — ~50 lines of code | Good; adapts per-card via ease factor | Most apps for the last 30 years; Anki default until 2023 |
| Anki SM-2+ | Moderate — adds learning steps, lapses, fuzz | Good; production-hardened SM-2 with UX patches | Daily drivers who want stability over optimality |
| FSRS (2024) | Hard — three-parameter DSR model, optimizer | Best in published benchmarks; ~20–30% fewer reviews at the same retention | Power users who track thousands of cards and want minimal review time |
A deeper benchmark and migration notes live in SM-2 vs FSRS vs Leitner vs Anki — 2026 comparison.
How a single review changes your schedule
Let us trace one card through SM-2 to make this concrete. SM-2 stores three values per card: interval (days until next review), repetitions (consecutive successful recalls), and EF (ease factor, starts at 2.5).
Day 0 New card created.
interval = 0, repetitions = 0, EF = 2.50
Day 0 First review → "Good" (q = 4)
repetitions = 1 → interval = 1 day
EF stays ≈ 2.50
Day 1 Second review → "Good" (q = 4)
repetitions = 2 → interval = 6 days
EF ≈ 2.50
Day 7 Third review → "Good" (q = 4)
repetitions = 3 → interval = round(6 × EF) = round(6 × 2.5) = 15 days
EF ≈ 2.50
Day 22 Fourth review → "Good" (q = 4)
interval = round(15 × 2.5) = 38 daysIf you had answered "Hard" (q = 3), EF would drop slightly and the next interval would shrink. A "Again" answer (q < 3) resets repetitions to 0 and the card re-enters the learning queue from scratch — that is the lapse penalty.
The exact constants and formulas SmartRecall uses live in How SM-2 Works in SmartRecall.
Picking the right tool for you
There is no single best app. Each one optimizes for a different user.
- Anki — Free, open-source, FSRS-capable, infinitely customizable. Best for hardcore users (med students, language learners) who do not mind a steep UX. Mobile app on iOS costs $25 one-time.
- RemNote — Spaced repetition wired into a notes-and-outliner workflow. Best if you want flashcards to emerge from your notes rather than be authored separately.
- SmartRecall — AI-assisted card generation from text, PDFs, or audio, with SM-2 scheduling and a clean mobile-first UI. Best if you want to skip manual card authoring and study on the phone. Free tier available.
- Quizlet — Huge shared library, social study modes, great for casual users. The spaced repetition layer (Learn mode) is weaker than the others — fine for short-term test prep, less ideal for multi-year retention.
If you already enjoy authoring cards, start with Anki. If authoring is the bottleneck that has stopped you before, try an AI-assisted tool.
FAQ
Does spaced repetition really work? Yes. The spacing effect is one of the most replicated findings in cognitive psychology, with meta-analyses across more than a century of studies. The practical effect size in real-world learning (vocabulary, medical facts, code APIs) is large — typically 2–3× more retained per hour of study compared to massed re-reading.
How much time should I spend per day? Most users sustain 15–30 minutes per day. The algorithm self-throttles: if you keep adding new cards, daily review time grows; if you stop adding, it shrinks toward zero. A good rule is to add new cards only at a pace that keeps daily reviews under your target time budget.
Can I do spaced repetition without an app? Yes — the Leitner box system uses five physical card boxes and works fine for a few hundred cards. Above that, manual scheduling becomes a chore and an app pays for itself within a week.
Is FSRS better than SM-2? On published benchmarks FSRS reaches the same retention with roughly 20–30% fewer reviews. For most learners that translates to a few minutes saved per day. SM-2 remains a perfectly reasonable default — the gap matters most for users with thousands of mature cards.
What is the best spaced repetition app for beginners? For absolute beginners we suggest a tool that removes the friction of authoring cards, since most people quit during the card-creation phase rather than the reviewing phase. SmartRecall, RemNote, and Quizlet all qualify; Anki is excellent but expects you to enjoy the editor.
Ready to try a science-backed review schedule without authoring cards by hand? Create a free SmartRecall account and generate your first deck from any document in under a minute. See pricing for what is included on the free tier.