Understand SM-2 review intervals

Read the initial state

The simulation starts with ease 2.5 and no successful repetitions. Enter ratings separated by commas. Each rating represents a review completed on the previously scheduled day.

The state consists of three separate values: the interval in days, the ease factor, and the count of successful repetitions since a reset. At the default starting point these are zero, 2.5, and zero. The first rating is applied at the beginning of the simulation, and the displayed next-review day is measured from that starting point. Keep this convention in mind when reading the output: a row describes the consequence of a completed review, not an instruction to grade a card in the future. This simulator begins a new sequence from its defaults each time; it is not maintaining a calendar of your real cards.

Understand the ratings

Again maps to quality 1, Hard to 3, Good to 4, and Easy to 5. These labels are an interface choice for the simulator, not a universal mapping across study applications.

Use the labels consistently while exploring the calculation. In this implementation, Hard still counts as a successful review because its quality value is three. Again has quality one and resets the success count. The underlying helper accepts integer qualities from zero through five, but the text interface exposes the four named choices. If you are comparing this output with another application's buttons, do not assume matching labels imply matching algorithms. Write down the numerical quality as well as the name when doing a manual calculation. This makes it easier to locate a discrepancy in the mapping rather than incorrectly blaming the interval formula itself.

Follow successful intervals

The first successful repetition schedules one day; the second schedules six. Subsequent successful intervals multiply the previous interval by the existing ease factor and round to whole days.

The first two successful intervals are special cases. Starting from zero successful repetitions, a successful rating gives one day. The next successful rating gives six days even if the ease factor has changed. After that, the previous interval is multiplied by the ease value present before the current rating updates it. This order matters when using Easy or Hard. For example, if the prior interval is six and the existing ease is 2.6, the next successful interval is round(15.6), or sixteen days. The newly adjusted ease is retained for a later review rather than retroactively changing the interval just calculated in that row.

Update the ease factor

The update uses EF + 0.1 − (5 − q) × (0.08 + (5 − q) × 0.02), with a minimum of 1.3. The adjusted factor influences later intervals.

Work through the arithmetic for each exposed rating. Good has q equal to four, so its change is 0.1 minus 1 times 0.1, which is zero. Easy has q equal to five and adds 0.1. Hard has q equal to three and changes ease by 0.1 minus 2 times 0.12, or minus 0.14. Again has q equal to one and changes ease by 0.1 minus 4 times 0.16, or minus 0.54. The minimum clamp prevents ease from dropping below 1.3. These are model rules, not measurements of how much a particular learner has forgotten between sessions.

Handle a failed recall

A quality below three resets successful repetitions to zero and schedules a one-day retry. The simulator still updates ease. Failure is a signal to inspect the material as well as its schedule.

Consider a card whose state is an interval of fifteen, ease 2.5, and three successful repetitions. An Again rating produces interval one, ease 1.96, and zero successful repetitions. On the following Good rating, the success count starts over, so the interval is one day again. Another Good then gives six days. The reset does not mean the learner has no knowledge at all; it is simply how this model responds to a failed retrieval. If the failure came from an ambiguous prompt, repair the prompt too. A numerical penalty alone cannot distinguish a bad question from a genuine memory lapse.

Work through an example

Starting from the default state, three Good ratings produce intervals of one, six and fifteen days. Those intervals accumulate to next-review days one, seven and twenty-two.

Try the input Good, Good, Easy, Again, Good. The first two rows schedule intervals of one and six with ease 2.5. The Easy row uses the existing ease for a fifteen-day interval and then raises ease to 2.6. Again schedules one day, resets repetitions, and lowers ease to 2.06. The final Good schedules one day and keeps that ease. Adding intervals gives next-review days one, seven, twenty-two, twenty-three, and twenty-four. Compare every row with the tool output. If you instead multiply the six-day interval by 2.6 on the Easy row, you have applied the ease update in a different order from this implementation.

Interpret the limits

The model does not consider your calendar, overdue history, subject difficulty or exam date. It also does not prove that a particular retention rate follows from the suggested interval.

The cumulative days assume that each review happens when scheduled. If you skip a real review, the simulation does not automatically model the delay or revise its assumptions. It also omits card-specific history beyond the small state described here, and it does not allocate your daily workload. A growing interval is not a promise that the answer will remain available until that date. Use the model to understand the relationship between ratings, repetitions, and ease. For an actual exam plan, inspect the relevant deadlines and available sessions separately rather than treating the last simulated date as a complete study strategy.

Use the output thoughtfully

Compare rating sequences to learn how scheduling responds. Use your chosen study application's own controls for real due dates. Fix overloaded cards instead of treating every failure as a scheduling defect.

Compare two sequences that differ in just one rating so the effect is easy to trace. For example, contrast three Good ratings with Good, Hard, Good and inspect the ease after the second row. Keep the rest of the sequence identical. This is more informative than changing every rating at once and trying to explain the resulting dates. If a real card repeatedly attracts low ratings, check its scope, prerequisites, and answer criteria before changing your scheduling habits. Use honest ratings in the application that owns your actual review history. Manipulating a grade merely to obtain a preferred interval makes later scheduling evidence harder to interpret.

Keep interval and cumulative day in separate columns when checking a sequence manually. An interval of six days is a wait between reviews, while day seven is a position on the simulated timeline. Confusing those values can make an otherwise correct calculation appear inconsistent. Start again from the default state when comparing examples so an earlier experiment does not supply an unintended ease factor.

Copyable planning template

Topic: Understand SM-2 review intervals
Source and date:
What I need to recall or do:
First attempt without notes:
Error or uncertainty:
Correction and supporting source:
Next review or action:

Input example for SM-2 review simulator:
Good, Good, Easy, Again, Good

Frequently asked questions