Spaced Repetition Calculator Formula
Understand the math behind the spaced repetition calculator. Each variable explained with a worked example.
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)) / 7Variables
| Variable | Description | Default |
|---|---|---|
initial_interval | Initial Interval (days) | 1 |
ease_factor | Ease Factor | 2.5 |
review_number | Review Number | 4 |
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
Worked Example
Starting with a 1-day interval and ease factor 2.5, calculating the 4th review.
- 01Next interval = round(1 x 2.5^3) = round(15.625) = 16 days
- 02Review 1: 1 day, Review 2: 2.5 days, Review 3: 6.25 days, Review 4: 15.6 days
- 03Total days elapsed ≈ round(1 x (2.5^4 - 1) / 1.5) = round(25.4) = 25 days
Frequently Asked Questions
What is the ideal ease factor?
The default 2.5 works well for most material. Reduce to 2.0 for difficult cards or increase to 3.0 for easy material.
What apps use spaced repetition?
Anki, SuperMemo, Quizlet (partially), and Memrise all implement spaced repetition algorithms.
How does spaced repetition compare to cramming?
Spaced repetition leads to much better long-term retention. Cramming may work for a test the next day but leads to rapid forgetting.
Ready to run the numbers?
Open Spaced Repetition Calculator