The Best Spaced Repetition Intervals (And Why 1-3-7 Is Wrong)

The short answer

That proportional rule is the useful takeaway from the spacing literature, and it is almost never the thing interval articles tell you. It also explains why the famous ladder feels right to some people and fails badly for others — it happens to approximate the correct answer for a one-month horizon, and it is nowhere near correct for a one-year horizon.

If you use an app with a modern scheduler, the honest advice is to stop reading here and let it do the arithmetic. The rest of this page is for understanding what it is doing, deciding what to override, and for the minority of people genuinely working on paper.

Where 1-3-7-21 came from

This matters less as a debunking exercise than as a diagnosis. The ladder has two specific problems, and knowing them tells you when you can safely ignore the criticism.

It stops. Every version terminates somewhere between three weeks and two months. If the ladder is your whole schedule, then after the last rung you either review that card forever at a fixed frequency or you stop reviewing it and let it decay. Neither is what you want. Real schedules keep extending — a well-known card should eventually sit at intervals of one, two, four years, which is what makes a large mature deck cost so little per day.

It is identical for every card. The Japanese particle は and the year the Meiji period began are not equally hard for you, and a fixed ladder gives them the same treatment. In a deck of a thousand cards, perhaps sixty are genuinely difficult and perhaps four hundred are already solid. A single schedule over-reviews the four hundred and under-reviews the sixty, which is the main way people end up with an enormous daily queue and still fail the same handful of items.

The rule that does have evidence

That study is worth describing properly, because it is the closest thing to an answer that this question has. Over 1,300 participants learned a set of obscure facts, then had a second session after a gap ranging from a few minutes to several months, then were tested after a further delay of 7 days to 350 days. Crossing gap against test delay like that is what makes the result interpretable — it lets you see the optimum move.

What it showed:

• For a test 7 days out, the best gap was about 1 day.
• For a test 35 days out, the best gap was about 11 days.
• For a test 70 days out, the best gap was about 21 days.
• For a test 350 days out, the best gap was about 21–90 days — and the curve here is broad and flat rather than sharply peaked.

Two things follow. First, the ratio is not constant: it falls from roughly 15% at a week to something like 6–10% at a year. Second — and this is the practically important half — the penalty for spacing too widely is much smaller than the penalty for spacing too narrowly. The curves are asymmetric. Erring long costs you a little; erring short costs you a lot of time for very little retention.

That asymmetry is the single most actionable finding on this page. When you are unsure whether to review something in two weeks or six, choose six.

Notice the last row. Once the horizon is "forever", the proportional rule stops constraining you, because there is no target date to take a fraction of. What replaces it is simple multiplicative growth — which is exactly what SM-2 does, and approximately what FSRS converges to for an average card.

Expanding vs fixed intervals

The intuition for expanding schedules is appealing — a fresh memory is fragile, so test it soon; a durable one can wait. Landauer and Bjork's 1978 work made the case, and it became doctrine.

The follow-up work complicated it. When the final test comes shortly after study, expanding schedules do tend to win. When the test is delayed — which is the case anyone studying actually cares about — equal intervals do as well or better. The proposed explanation is that the first, long gap in an equal schedule is a harder retrieval, and hard successful retrievals build more durable memory. That is Bjork's desirable-difficulties principle again, and it is the same mechanism FSRS encodes in its stability update, where recalling something you had nearly forgotten increases stability more than recalling something fresh.

So why does everything expand anyway? Because of workload, not memory. A card on a fixed 10-day interval costs you 36 reviews a year, forever. The same card on an expanding schedule costs perhaps 8 reviews in year one and 2 in year three. Across a deck of two thousand cards that difference is the whole game — it is the difference between a sustainable 20-minute daily habit and an hour a day that grows without limit.

Expansion is a throughput optimisation that happens to cost very little retention. That is a perfectly good reason to use it. It is just not the reason usually given.

The first interval is the one people get wrong

The reason is that retrieval strengthens memory in proportion to how hard it was. A review you sail through is nearly free of benefit. This is the least intuitive thing about spacing, because a successful easy review feels productive, and it is the same illusion that makes rereading feel more effective than active recall.

Three practical consequences:

• Don't review the same day you learned it, beyond one quick pass to check the card makes sense. Same-day repetitions inflate your sense of mastery and cost real time.
• If you found the material easy, push the first gap out. Three or four days rather than one. In an app, this is what pressing Easy on the first review is for, and most people underuse it.
• If you found it genuinely confusing, the problem is not the interval. No gap makes a half-understood explanation stick. Go back and understand it, then card it. Cards are for retaining things you have understood, not for acquiring understanding you skipped.

Why real systems compute rather than choose

Once you accept that the right gap depends on the card and on your history with it, a published ladder can't express the answer. What a scheduler does instead is keep a small amount of state per card and derive the next interval from it.

SM-2 keeps one number, an ease factor, and multiplies. FSRS keeps three — difficulty, stability, retrievability — and solves for the day your predicted recall probability drops to a target you set. The comparison between them goes into the mechanics; what matters here is the shape of the output.

A card you keep answering correctly on a modern scheduler roughly follows this path:

Seven successful reviews buys roughly three and a half years. That is the compounding people mean when they say spaced repetition is efficient, and it is completely invisible in any ladder that stops at 21 days. It is also why the cost of a mature deck is so much lower than beginners expect — see how many cards to review per day for what that means for your daily queue.

The other thing a scheduler gives you that a ladder cannot is a single meaningful dial: desired retention. Rather than editing intervals, you state what fraction of due cards you want to get right, and every interval in the deck adjusts to hit it. Raising it from 0.90 to 0.95 will roughly double your workload for a few points of accuracy. Lowering it to 0.85 noticeably lightens the load. If you are tempted to hand-edit intervals, this dial is almost always the thing you actually wanted.

If you really are on paper

Some people have good reasons not to use an app — a closed-book professional exam, a preference for handwriting, a subject that resists typing. The Leitner box is the right answer, and it is the honest paper approximation of what software does.

Five boxes, each with a review frequency:

Two details that make the difference between a Leitner box that works and one that gets abandoned in a drawer:

• Demote to box 1, but promote failures from boxes 4 and 5 only to box 2. A card you have known for four months and just missed is not equivalent to a card you have never known. Sending it all the way back is the paper version of the reset problem below.
• Give each box a fixed weekday rather than counting days per card. Box 2 on Mondays and Thursdays, box 3 on the 1st and 15th, box 4 on the first Saturday of the month. Tracking per-card dates by hand is the thing that actually kills paper systems.

The Leitner box's real limitation is that it can't extend past box 5. For a deck you intend to keep for years, you will eventually want software; for a defined exam a few months out, it is entirely adequate.

Intervals after a failure

Full reset was SM-2's behaviour and it is one of the clearer improvements in modern schedulers, which compute a reduced post-lapse stability instead. If you are scheduling manually, approximate it: a card that was at 90 days when you missed it goes to about 30, not to 1.

The exception is a card you have failed repeatedly. If something has lapsed four or five times, the interval is not the problem — the card is. Either it packs two facts into one, or it is interfering with a similar card, or the front doesn't actually specify what answer it wants. Rewriting it will fix in one edit what no amount of interval adjustment will.

Five ways interval tinkering backfires

1. Shortening intervals because you failed something. The instinct is understandable and the effect is a queue that grows until you quit. If retention is genuinely too low, adjust the retention target once, globally — don't fight card by card.
2. Reviewing early because you feel unsure. Answering a card two days before it's due gives you a much easier retrieval, less durability, and a scheduler now working from corrupted evidence. The feeling of not being sure is not a reliable signal; that's the point of the system.
3. Different intervals per subject. Memory doesn't know what subject a fact belongs to. What varies is card difficulty, which a per-card scheduler already tracks.
4. Capping the maximum interval at something short. A one-year cap sounds cautious and quietly converts every mature card into a permanent annual obligation. Over a large deck this is a substantial standing cost for very little retention.
5. Changing settings more than once a month. The feedback loop here is weeks long. Change one thing, wait a month, look at your true retention rate and your daily count, then change the next thing.

Frequently asked questions

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