Spaced Repetition Calculator Formula

Understand the math behind the spaced repetition calculator. Each variable explained with a worked example.

Use the Spaced Repetition Calculator

Formulas Used

Next Interval (days)

next_interval = round(initial_interval * pow(ease_factor, review_number - 1))

Total Days Since First Study

total_days = round(initial_interval * (pow(ease_factor, review_number) - 1) / (ease_factor - 1))

Next Interval (weeks)

interval_weeks = round(initial_interval * pow(ease_factor, review_number - 1)) / 7

Variables

VariableDescriptionDefault
initial_intervalInitial Interval (days)1
ease_factorEase Factor2.5
review_numberReview Number4

How It Works

How Spaced Repetition Works

Spaced repetition increases review intervals over time as material is learned.

Formula

Next Interval = Initial Interval x Ease Factor ^ (Review Number - 1)

The ease factor determines how quickly intervals grow. Standard is 2.5, meaning each interval is 2.5x the previous one.

Typical Schedule

  • Review 1: Day 1
  • Review 2: Day 2–3
  • Review 3: Day 6–7
  • Review 4: Day 15–16

    • Worked Example

    Starting with a 1-day interval and ease factor 2.5, calculating the 4th review.

    initial_interval = 1ease_factor = 2.5review_number = 4
    1. 01Next interval = round(1 x 2.5^3) = round(15.625) = 16 days
    2. 02Review 1: 1 day, Review 2: 2.5 days, Review 3: 6.25 days, Review 4: 15.6 days
    3. 03Total days elapsed ≈ round(1 x (2.5^4 - 1) / 1.5) = round(25.4) = 25 days

    Ready to run the numbers?

    Open Spaced Repetition Calculator