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2.5 on a card you have never reviewed
The 0 to 5 scale is SM-2’s own wording. Anything below 3 counts as a failure.
2026-09-29
in 15 days
A projection, not a schedule. Real grades vary, and a single failure puts the card back on a one-day interval and starts the ladder again from there.
This is Algorithm SM-2, from P. A. Woźniak’s 1990 master’s thesis “Optimization of learning” at the University of Technology in Poznań, as SuperMemo has published it. The ladder is one day, then six days, and thereafter the previous interval multiplied by the card’s E-Factor. The factor starts at 2.5, moves by 0.1 - (5 - q) * (0.08 + (5 - q) * 0.02) after each graded repetition, and never falls below 1.3.
Two things the paper leaves open are settled here and named rather than hidden. The interval is worked out from the E-Factor in force at the time of the review and the factor is updated afterwards, which is the order the published steps are numbered in. And because a card is due on a day rather than on a fraction of one, the interval is rounded to the nearest whole day and the rounded figure is what the next multiplication uses.
Tell the scheduler when you last looked at a card, how many times you have recalled it successfully, what gap it was sitting on, what its ease value currently is, and how the recall went on a scale of nought to five. It returns the gap before the next attempt, the date that falls on, the new ease value, and a projection of the next several reviews if the card keeps earning the same grade. It handles a single card rather than a deck, which makes it a way to understand what your flashcard application is doing to you.
The method is SM-2, described by Piotr Woźniak in his 1990 master’s thesis at the University of Technology in Poznań and carried by the first computerised version of SuperMemo in 1987. It is the ancestor of nearly every scheduler since, and it is short enough to state completely: a card carries an ease value beginning at 2.5, the first gap is one day, the second is six days, and every gap after that is the previous one multiplied by the ease.
The ease itself moves after each graded attempt by nought point one, minus a penalty that grows faster than in proportion to how far the grade fell short of five, and it is never allowed under 1.3. A grade of four leaves it exactly where it was, a five raises it by a tenth, and a three costs it fourteen hundredths. A grade under three is a failure: the card returns to a one-day gap and begins the ladder again, and the thesis is explicit that the ease value is left untouched when that happens.
The published steps are numbered in an order that schedules the gap from the ease value already in force and updates that value afterwards, and that is the order used here. Some implementations update first and multiply by the new figure. On a grade of four the two agree exactly, because four moves nothing, and elsewhere they part company by a fraction of a day at first and by more later.
The second gap is rounding. Multiplying by an ease value produces fractions, and cards fall due on days rather than on 37.5 of one. The figure is rounded to the nearest whole day, and the rounded figure is what the following multiplication uses, so the ladder you are shown is the ladder the arithmetic actually ran on. Both decisions are stated because a scheduler that quietly picked one and called itself SM-2 would be impossible to check.
The other genuinely documented method is older. Sebastian Leitner set out a physical card box in his 1972 book So lernt man lernen, with compartments of increasing width — one, two, five, eight and fourteen centimetres — where a card answered correctly moves forward a compartment and a card missed goes back. Reviews were triggered by a compartment filling up, not by a calendar.
This matters, because the tidy ladder of one, two, four, eight and sixteen days that circulates under Leitner’s name appears nowhere in his book. It is a later convenience that someone invented and everyone repeated. That is precisely why SM-2 is what runs here: it was published as arithmetic, so it can be implemented rather than approximated.
Often some descendant of it, usually with modifications the developers have documented separately. SuperMemo itself has moved through many later algorithms, and several popular applications have replaced their SM-2 variant with a scheduler fitted to collected review data, so treat this as the classical baseline rather than as a simulation of your particular deck.
The correction term works out at exactly zero when the grade is four, which is a deliberate feature of the formula rather than a coincidence. A card recalled correctly after a slight hesitation is behaving exactly as the schedule predicted, so there is nothing for the schedule to learn from it.
Runaway shortening. Without a floor, repeated poor grades would drive the multiplier toward zero and the card would come back daily forever. Woźniak’s advice when a card sinks that far is not to schedule it harder but to rewrite it, since a card that resists memorising is usually asking two questions at once.
Only as an illustration of the shape. It assumes every future attempt earns the identical grade, which never happens across a real deck, and one failure anywhere in the sequence sends the card back to a single day and restarts the whole ladder from that point.