SM-2 Next Review Interval Calculator
Spaced repetition is one of the most evidence-backed techniques in learning science. The SM-2 algorithm, developed by Piotr Woźniak at SuperMemo in 1987, schedules flashcard reviews at precisely the right moment — just before you forget. The core mechanic: each time you recall a card correctly, the next review is pushed further into the future by multiplying your current interval by your ease factor (E-Factor). This calculator implements that exact formula so you can plan or verify your review schedule without needing a full SRS app.
In SM-2, the next review interval is calculated as: **Next interval = round(Current interval × E-Factor)**. With a 10-day interval and E-Factor of 2.5, the next review is in **25 days**. The E-Factor ranges from 1.3 (very hard) to 2.5 (very easy); Anki's default is 2.5.
When to use this calculator
- Language learners using Anki, Mnemosyne, or custom SM-2 decks who want to verify or predict future review dates.
- Developers building or testing an SRS application who need to confirm their interval calculation logic matches the SM-2 spec.
- Students learning about the SM-2 algorithm in courses on cognitive science or educational technology.
- Teachers designing paper-based spaced repetition systems and calculating manual review schedules.
Worked Example: A Spanish vocabulary card
- Current interval = 10 days (you reviewed the card 10 days ago).
- E-Factor = 2.5 (Anki rated it as Easy several times).
- Apply SM-2: Next interval = round(10 × 2.5) = 25 days.
- Enter: Current Interval = 10, E-Factor = 2.5.
How it works
2 min readHow SM-2 Calculates the Next Review
The SM-2 algorithm (SuperMemo 2), published by Piotr Woźniak in 1987, underlies apps like Anki and Mnemosyne. Its key insight is the forgetting curve: memory decays exponentially after learning, but each successful review extends the interval further.
The formula
// From the 3rd review onward:
Next interval = round(Current interval × E-Factor)
// First two reviews (fixed by SM-2 spec):
1st review: 1 day
2nd review: 6 days
// E-Factor update after each review (quality q from 0 to 5):
New EF = EF + (0.1 − (5 − q) × (0.08 + (5 − q) × 0.02))
Min EF: 1.3 // never drops below this---
SM-2 Interval Growth Table (by E-Factor)
How the interval grows over successive reviews with different E-Factors:
| Review # | EF = 1.3 (hard) | EF = 1.8 (average) | EF = 2.5 (easy) |
|---|---|---|---|
| 1 | 1 day | 1 day | 1 day |
| 2 | 6 days | 6 days | 6 days |
| 3 | 8 days | 11 days | 15 days |
| 4 | 10 days | 20 days | 38 days |
| 5 | 13 days | 36 days | 94 days |
| 6 | 17 days | 65 days | 235 days |
| 7 | 22 days | 117 days | 588 days (~1.6 yr) |
Key insight: With a high E-Factor (2.5), cards quickly reach months-long intervals. With a low E-Factor (1.3), intervals grow very slowly — a signal the card may need to be split into simpler pieces.
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Quick Reference: Interval × E-Factor → Next Review
| Current Interval | EF 1.3 | EF 1.8 | EF 2.1 | EF 2.5 |
|---|---|---|---|---|
| 1 day | 1 day | 2 days | 2 days | 3 days |
| 6 days | 8 days | 11 days | 13 days | 15 days |
| 10 days | 13 days | 18 days | 21 days | 25 days |
| 21 days | 27 days | 38 days | 44 days | 53 days |
| 30 days | 39 days | 54 days | 63 days | 75 days |
| 60 days | 78 days | 108 days | 126 days | 150 days |
| 90 days | 117 days | 162 days | 189 days | 225 days |
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Why the E-Factor matters
Cards with a high E-Factor (close to 2.5) grow into very long intervals quickly — eventually appearing only once every few months or years. Cards that remain difficult stabilize at low E-Factors and appear frequently until your recall improves.
Standard SM-2 E-Factor update formula
After a review with quality score q (0–5):
New E-Factor = E-Factor + (0.1 − (5 − q) × (0.08 + (5 − q) × 0.02))---
Common Mistakes
1. Manually editing the E-Factor: EF is computed by the algorithm based on your ratings. Editing it manually breaks the system.
2. Always rating 'Easy' (5): Intervals become so long you start forgetting. Rate honestly.
3. Using weeks or months instead of days: SM-2 works exclusively in whole days.
4. Failing a card without updating EF: When failing (quality < 3), SM-2 resets the interval to 1 day AND reduces EF. Only resetting the interval without updating EF causes the card to reappear with long intervals too soon.
Frequently asked questions
What does the E-Factor (Ease Factor) represent in SM-2?
The E-Factor is a per-card multiplier reflecting how easy the card is to recall. It ranges from 1.3 (very hard) to 2.5 (very easy). In Anki and other SM-2 apps, it adjusts automatically: 'Easy' raises it, 'Hard' or 'Again' lowers it. All new cards start at 2.5 by default.
How is the next SM-2 interval calculated step by step?
For reviews after the first two: Next interval = round(Current interval × E-Factor). The first review is always 1 day; the second is always 6 days. From the third review onward, the formula applies. Example: interval = 15 days, EF = 2.0 → next interval = round(15 × 2.0) = 30 days.
What are typical starting intervals in SM-2?
SM-2 prescribes 1 day for the first review and 6 days for the second (these are fixed). From the third review onward, the formula interval × EF applies. Anki slightly modifies this (1 day and 4 days by default), and users can adjust these in deck settings.
What happens if I forget a card (rate it 'Again' in Anki)?
When a card is failed (quality < 3), SM-2 resets its interval to 1 day and penalizes the E-Factor by roughly 0.2 (down to a minimum of 1.3). The card restarts the learning cycle. This calculator computes the success case — it assumes you recalled the card correctly.
Does Anki use exactly the SM-2 algorithm?
Anki uses a modified SM-2. The core interval formula (interval × ease factor) is the same, but Anki adds extra modifiers: an Interval Modifier per deck, a Hard interval multiplier, and an Easy bonus. Anki 23.10+ also introduced FSRS, a machine-learning-based algorithm that can replace SM-2 entirely and generally outperforms it.
What is the difference between SM-2 and FSRS?
SM-2 uses a fixed ease-factor-based multiplication. FSRS (Free Spaced Repetition Scheduler), introduced in Anki 23.10, uses a machine-learning model trained on real review data to predict the optimal next review date, taking into account estimated memory stability and retrievability. FSRS generally outperforms SM-2 on retention efficiency, but SM-2 is simpler to understand and implement manually.
What is a good E-Factor target for most cards?
A well-known rule of thumb in the SRS community: keep your E-Factor above 2.0 for most cards. If a card's E-Factor keeps dropping toward 1.3, it usually means the card is too complex and should be broken into smaller, simpler cards ('card splitting' or 'atomic notes').
Can I use this calculator for subjects other than language learning?
Yes. The SM-2 algorithm is content-agnostic — it schedules anything you want to memorize: vocabulary, formulas, historical dates, music theory, anatomy. As long as you can rate your recall on a card, SM-2 applies.
Why does this calculator not ask for a quality score (0–5)?
This calculator computes the next interval assuming a successful recall (score ≥ 3). The E-Factor update formula requires a quality rating, which changes the E-Factor for the next cycle. If you want to simulate a score-adjusted E-Factor, first compute: New EF = EF + (0.1 − (5 − q) × (0.08 + (5 − q) × 0.02)), then enter that updated EF into the calculator.