Flashcard Spaced Repetition Calculator

Spaced repetition is one of the most effective learning techniques backed by cognitive science. It exploits the “spacing effect”: memories last longer when you review material at increasing intervals over time, rather than cramming it all at once.

The most widely used algorithm is SM-2 (SuperMemo 2), developed by Piotr Wozniak in 1987. This algorithm forms the basis of popular apps like Anki, Duolingo, and many others.

How SM-2 works:

Each card has two key values:

• Interval (I): how many days until the next review
• Ease factor (EF): a multiplier that adjusts the interval based on how easily you remembered the card (starts at 2.5)

Review schedule with SM-2:

• First correct answer: review again in 1 day
• Second correct answer: review again in 6 days
• Third and subsequent: next interval = current interval × EF

After each review, you rate how well you remembered it (0–5 scale):

• 5: Perfect response
• 4: Correct with slight hesitation
• 3: Correct with difficulty
• 2: Incorrect: would have remembered
• 1: Incorrect: hint helped
• 0: Complete blackout

If you rate 0–2, the card resets to day 1 (goes back to the beginning). If you rate 3–5, the interval grows according to the formula.

The ease factor updates after each review: EF_new = EF_old + (0.1 − (5 − grade) × (0.08 + (5 − grade) × 0.02))

This keeps well-known cards with long intervals and keeps hard cards appearing frequently.

Practical implications:

• A card reviewed 5 times with all grade-4 answers has intervals of 1, 6, 15, 38 and 95 days. Grade 4 is the case where the ease factor does not move at all: the update term works out to exactly zero, so EF stays at 2.5 and each interval after the second is simply the last one multiplied by 2.5.
• After 1 year, mature cards may appear only once every 3–12 months.
• Studying 20 new cards per day settles at roughly 150 to 200 reviews per day. Each card comes back around eight times in its first couple of months, and that multiplier is what makes a deck feel manageable in week one and punishing in week five.

This calculator simulates future review dates given the current stage, review history, and ease factor. The forgetting curve planner runs the same 1, 6, 15, 38, 95 ladder from the other direction, starting from how much you still remember rather than from the card’s history.

One thing SM-2 gets criticised for, fairly. The 6-day second interval and the 2.5 starting ease are fixed constants that Wozniak chose in 1987 from his own data, and they are not tuned to you or to your material. Anki’s newer FSRS scheduler fits the parameters per user instead, and typically ends up with shorter early intervals and longer late ones. SM-2 is still what most implementations ship and it is close enough to be worth planning against, but do not treat the numbers below as precise to the day.