The SM-2 Algorithm Explained Simply

Every time you rate a flashcard in Anki — or in any serious spaced repetition app — a formula runs in the background and decides when you'll see that card again. That formula is called SM-2. Understanding how it works helps you use it better.

Why the Algorithm Matters

Most people think of flashcard apps as digital index cards. They're not — or at least, the good ones aren't. What makes spaced repetition apps valuable isn't the cards themselves, it's the scheduling engine behind them.

Without spaced repetition, reviewing flashcards is like studying the night before an exam: you can load information into short-term memory, but it fades quickly and requires constant re-loading. With spaced repetition, the algorithm ensures each card surfaces at the precise moment you're about to forget it — which makes each review maximally efficient and builds genuinely durable memory.

SM-2 is the algorithm that makes this happen. It was developed by Piotr Woźniak in 1987 and is remarkably good considering its age. Anki uses SM-2. Repetrax uses SM-2. Understanding it will help you work with it rather than against it.

The Two Core Concepts

1. The Forgetting Curve

Hermann Ebbinghaus, a 19th-century psychologist, was the first to systematically measure memory decay. His finding: memory of new information drops steeply at first, then levels off. You forget roughly half of new material within a day, and most of the rest within a week — unless you review it.

Crucially, each successful review resets the curve at a higher baseline. Review something once, and it lasts a few days. Review it again, and it lasts a few weeks. Review it again, and it might last months. Each review extends the interval.

2. The Spacing Effect

Reviewing material spread out over time (spaced practice) produces far better long-term retention than reviewing it multiple times in a short period (massed practice). Studying a word five times over five weeks beats studying it five times in one afternoon — by a large margin.

SM-2 is designed to exploit both of these: it schedules reviews at intervals calibrated to keep you just ahead of forgetting, and it uses your own performance to adjust those intervals.

How SM-2 Actually Works

Every card tracked by SM-2 has two properties:

Interval (I): How many days until the next review.

Ease Factor (EF): A multiplier that determines how quickly the interval grows. Starts at 2.5 for every new card. Can decrease to a minimum of 1.3.

The First Two Reviews

For any new card:

• After the 1st successful review: next review in 1 day
• After the 2nd successful review: next review in 6 days

These first two reviews are fixed — the algorithm doesn't yet have enough data to adapt.

Subsequent Reviews

After the second review, the new interval is calculated as:

New Interval = Previous Interval × Ease Factor

So for a card with EF = 2.5 and current interval of 6 days:

• New interval = 6 × 2.5 = 15 days

And if that review goes well:

• New interval = 15 × 2.5 = 37.5 days (rounded to 38)

And again:

• 38 × 2.5 = 95 days — about three months

You can see how a word moves from daily review to monthly review to quarterly review as you demonstrate you know it.

How Your Rating Affects the Ease Factor

When you rate a card, SM-2 adjusts the ease factor based on your response:

• Perfect recall (5): EF increases slightly (you're finding this easy)
• Correct with hesitation (4): EF unchanged
• Correct with difficulty (3): EF decreases by 0.14
• Incorrect, answer was easy (2): EF decreases by 0.20; interval resets
• Incorrect (1 or 0): EF decreases by 0.32; interval resets to beginning

Most modern apps (including Repetrax) simplify this to a 4-button rating: Again, Hard, Good, Easy — which map roughly to these SM-2 response grades.

The practical implication: cards you consistently find hard gradually get scheduled more frequently. Cards you find easy get pushed further and further out. The algorithm personalizes to your actual memory, not some theoretical average.

What "Mature" Cards Mean

In Anki and similar apps, cards are classified by interval:

• New: Not yet seen
• Learning: In the first few reviews, interval under 21 days
• Mature: Interval of 21 days or more
• Mastered/Suspended: Some apps add a "mastered" state for cards with very long intervals

A "mature" card is one the algorithm has built significant confidence about — you've proven you know it reliably, so it schedules it months apart. This is the goal: getting words to mature status means they're in long-term memory.

Why Ease Factor Decay Is a Problem (And How to Manage It)

SM-2 has a well-known issue that the Anki community calls "ease hell." Here's what happens:

When you consistently rate cards as "Hard" (or fail them), the ease factor drops. A card with EF = 1.3 (the minimum) grows its interval very slowly — even when you're reviewing it successfully. It gets stuck in a loop of being seen frequently even after you've learned it, because the algorithm has marked it as genuinely difficult for you.

How to avoid this:

1. Don't rate cards as "Hard" or "Again" unless you genuinely failed them. If you remembered it but it took a few seconds, that's "Good," not "Hard." Reserve "Hard" for real struggles.

2. Use the "Easy" button occasionally. If a card is genuinely trivially easy — you knew it instantly and it feels stable — marking it "Easy" raises the ease factor back up.

3. Don't add too many new cards at once. Overwhelm leads to failure ratings, which leads to ease decay across your entire deck.

The Practical Implications for Learners

Don't Cram the Night Before

SM-2 is useless for cramming. It's designed for long-term retention, not short-term memory loading. If you have a language exam in two days, reviewing your Repetrax deck won't magically prepare you — the algorithm will show you whatever is due, not whatever is most relevant to the exam.

Spaced repetition is a marathon tool, not a sprint tool.

Daily Review Is Non-Negotiable

The algorithm only works if you show up every day. If you skip a week, cards will pile up in review backlog. The algorithm doesn't know you were on vacation — it just knows reviews are overdue, and it'll show them all to you when you return.

The backlog effect is real: skip 7 days, and you might return to 200+ pending reviews. At that point, many people give up. The solution is to either do a small amount every day (even 5 minutes), or to bury/reschedule the backlog when you return rather than trying to clear it all at once.

More New Cards = More Future Work

Every new card you add today becomes future review burden. Adding 50 cards a day feels productive — but in two weeks, you'll have hundreds of reviews due per day. Start slow (10–15 new cards per day) and increase only if you're consistently clearing reviews without feeling overwhelmed.

The Algorithm Is Smarter Than Your Intuition

A common urge is to review cards that feel important or that you think you might forget, rather than the cards the algorithm schedules. Resist this. The algorithm knows which cards are actually at risk of being forgotten — that's what the interval and ease factor track. Reviewing "important" cards you already know is inefficient. Trust the schedule.

SM-2 vs. Newer Algorithms

SM-2 was designed in 1987 and is remarkably effective for its age. But newer algorithms have been developed:

SM-17 / SM-18 (SuperMemo's current versions): Much more sophisticated, but complex and proprietary. SuperMemo's app implements them, but they're not widely available elsewhere.

FSRS (Free Spaced Repetition Scheduler): A modern algorithm developed by Jarrett Ye and the Anki community. It's available as an Anki add-on and is mathematically superior to SM-2 in several ways — particularly in handling lapses and ease decay. Anki now supports FSRS natively.

The practical difference: For most learners, SM-2 is good enough. The gains from more sophisticated algorithms are real but incremental. If you're doing your reviews consistently and managing ease decay appropriately, SM-2 will serve you well.

A Quick Reference

The Bottom Line

SM-2 is not magic — it's math applied to memory science. It works because it forces reviews at the right time (exploiting the spacing effect) and personalizes the schedule based on your actual performance (tracking each card's difficulty individually).

The best thing you can do to make it work for you: show up consistently, rate cards honestly, and resist the urge to add more new cards than you can sustainably review. The algorithm handles the rest.

Repetrax uses the SM-2 algorithm for Italian vocabulary learning and general flashcard study. Try it free →