Flashcard Study Calculator
SM-2 spacing priced per card — the ease factor, the next interval, and the ladder a card climbs.
Flashcard Study Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Single-card lane — deck intake is a budget question
- SM-2 classic, not FSRS or other newer schedulers
In short: SM-2 — the algorithm under Anki and SuperMemo — grows a card's interval by its ease factor: after the 1-day and 6-day steps, each successful review multiplies the last interval. A card at three successful repetitions, ease 2.5, rated 4, keeps its ease exactly (a 4 neither grows nor shrinks it) and returns in 15 days. Rate it 3 instead and the ease drops 0.14 to 2.360000, pulling the interval to 14 days; rate it below 3 and the card resets to tomorrow, reps zeroed. Spacing is the schedule memory actually obeys.
Formula
EF' = max(1.3, EF + 0.1 − (5−q)(0.08 + (5−q)·0.02)) ··· I(1)=1, I(2)=6, I(n)=round(I(n−1)×EF')
SuperMemo's SM-2 — Woźniak’s classic — is the algorithm Anki still defaults to. Each review is rated 0–5; the rating moves the card's ease factor by a fixed wedge — a 5 adds 0.1, a 4 changes nothing (0.1 minus exactly 0.10), a 3 costs 0.14, and anything below 3 is a failure that resets repetitions to zero and returns the card tomorrow. The ease floors at 1.3 so a hated card still spreads. Intervals boot at 1 day, then 6, then multiply by the updated ease — 6 → 15 → 38 → 95 at ease 2.5. The paper ancestor is Leitner's five boxes on 1/2/4/8/14-day rotations, wrong answers sending a card back to box one; SM-2 is the same idea with a dial instead of boxes.
Worked Example
- Count the card's successful repetitions.
- Carry its current ease factor.
- Rate today's recall honestly, 0 to 5.
- Read the next interval and the ladder.
Defaults: 3 reps, ease 2.5, rated 4 → ease holds at 2.500000 (a 4 is the neutral rating) and the next review lands in 15 days; the ladder runs 1 → 6 → 15 → 38 → 95. Drive the rating to 3 → ease 2.360000, interval 14. Drive it to 2 → the reset door: reps zero, back to 1 day.
Strengths & Limits Of This Model
Where this engine is strong
- Ease-factor wedge computed live, all five ratings
- Leitner ancestry kept beside the algorithm
Where it stops
- No review-date arithmetic — intervals in days only
Practical Use Cases
Anki scheduling
why the app picked that date
Paper decks
Leitner boxes, priced by SM-2
Exam triage
which cards still need you
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Flashcard Study Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
What does the ease factor actually control?
How fast the card's interval grows. Every card starts at 2.5; each review nudges it by the rating — a perfect 5 adds 0.1, a bare-pass 3 subtracts 0.14. Cards you find easy space out in big jumps; cards you struggle with keep returning in small ones. The floor at 1.3 keeps even the worst card's intervals growing eventually.
Why do a 4's intervals keep multiplying if the ease never moves?
Because a 4 is the neutral rating: 0.1 minus (1×0.10) is exactly zero, so ease holds while the interval still multiplies by it. A deck rated all 4s climbs 1 → 6 → 15 → 38 → 95 — the schedule you see in default Anki exports.
What happens when I fail a card?
Anything rated below 3 resets the card: repetitions to zero, next appearance tomorrow, ease reduced within the floor. The interval you had built is gone — which is the point, because a failure means the old spacing was lending memory you did not have.
Is SM-2 the same as the Leitner system?
Leitner is the paper ancestor of the seventies: five boxes on 1-, 2-, 4-, 8- and 14-day rotations, wrong answers sending the card back to box one. SM-2 replaces the fixed boxes with a per-card ease dial. Same principle — success stretches the gap, failure collapses it — with a finer gear.
How far out can a card get?
There is no ceiling — intervals compound. A card at ease 2.5 that keeps earning 4s and 5s passes a year between reviews within a dozen repetitions, which is how long-term decks stay reviewable: the mature cards barely ever come due.
Why 1 day and then 6?
Woźniak's original experiments fixed the first two intervals empirically: one day to consolidate the first contact, six to prove it stuck. Only from the third repetition does the ease multiplier take over. The 1-and-6 boot sequence survives in every SM-2 descendant unchanged.
What rating should I give myself?
The honest one. The algorithm only works if a 5 means effortless, a 3 means recalled with effort, and a 2 means failed. Inflating ratings buys longer intervals on cards that cannot carry them, and the debt arrives as failures exactly when the exam is close.
Does this tell me how many new cards a day to add?
No — it schedules one card's future, not a deck's intake. New-card load is a daily-budget question: every card you add today bills reviews for weeks. The exam countdown page prices the envelope; keep the intake inside it.