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Vocab Vault implements the SuperMemo 2 (SM-2) spaced repetition algorithm to help you learn vocabulary more efficiently and retain it for the long term.

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What is Spaced Repetition?

Spaced repetition is a learning technique that schedules reviews at increasing intervals. Instead of cramming information all at once, you review material just before you’re about to forget it. This technique is backed by decades of cognitive science research and is proven to:
  • Improve long-term retention by up to 200%
  • Reduce study time by focusing on difficult material
  • Build stronger neural pathways through optimally-timed reviews
  • Combat the forgetting curve discovered by Hermann Ebbinghaus
The Science: Each time you successfully recall a term, the memory becomes stronger and the interval before the next review increases. This exploits the psychological spacing effect to encode information into long-term memory.

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The SM-2 Algorithm

Vocab Vault uses the SM-2 algorithm developed by Piotr Wozniak in 1987. This algorithm calculates optimal review intervals based on your performance.

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How It Works

Each flashcard has three key metrics:
  • Ease Factor: How easy this card is for you (starts at 2.5)
  • Interval: Number of days until the next review
  • Repetitions: Successful reviews in a row

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Quality Ratings

When reviewing a card, you rate your recall using simplified buttons:

Again

You didn’t remember it. The card resets to review tomorrow.

Hard

You remembered it with serious difficulty.

Good

You remembered it with some hesitation.

Easy

Perfect recall! You knew it instantly.
These buttons map to the SM-2 quality scale: 
const SIMPLE_RATINGS = [
  { value: 1, label: "Again", sm2Quality: 1 },
  { value: 2, label: "Hard", sm2Quality: 3 },
  { value: 3, label: "Good", sm2Quality: 4 },
  { value: 4, label: "Easy", sm2Quality: 5 },
];

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Interval Scheduling

The algorithm calculates your next review date based on your performance:
1

First Review

If you answer correctly, the card comes back in 1 day.
2

Second Review

If you answer correctly again, it comes back in 6 days.
3

Subsequent Reviews

The interval multiplies by your ease factor. For example, with ease factor 2.5:
  • Third review: 15 days (6 × 2.5)
  • Fourth review: 37 days (15 × 2.5)
  • Fifth review: 92 days (37 × 2.5)
If you answer incorrectly (quality < 3), the card resets to 1-day interval and you start over.

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Ease Factor Adjustment

Your ease factor adjusts based on how well you recall the card: 
// The ease factor formula
newEaseFactor = easeFactor + (0.1 - (5 - quality) * (0.08 + (5 - quality) * 0.02));
newEaseFactor = Math.max(1.3, newEaseFactor);
  • Easy answers (quality 5) increase the ease factor → longer future intervals
  • Hard answers (quality 3) slightly decrease it → shorter intervals
  • Wrong answers (quality < 3) significantly decrease it → more frequent reviews
  • The minimum ease factor is 1.3 to prevent cards from getting stuck

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Mastery Levels

As you review cards, they progress through mastery levels:

New

Never reviewed before. These appear in your study queue alongside due cards.

Learning

Interval less than 7 days. You’re actively building this memory.

Reviewing

Interval between 7-21 days. The memory is getting stronger.

Mastered

Interval 21+ days. This term is in your long-term memory!

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Study Queue Algorithm

Vocab Vault intelligently combines due cards and new cards in your study queue: 
// Interleave: 3 due cards, then 1 new card
while (dueIdx < dueCards.length || newIdx < newCards.length) {
  // Add up to 3 due cards
  for (let i = 0; i < 3 && dueIdx < dueCards.length; i++) {
    queue.push(dueCards[dueIdx++]);
  }
  // Add 1 new card
  if (newIdx < newCards.length) {
    queue.push(newCards[newIdx++]);
  }
}
This ensures you:
  • Review due cards before they’re forgotten
  • Steadily introduce new material (10 new cards per day by default)
  • Don’t get overwhelmed with only new content
Due cards are sorted by overdue date first, then by ease factor (harder cards come first).

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Retention Statistics

Track your learning progress with detailed statistics:
  • Learned: Total cards you’ve reviewed at least once
  • Learning: Cards with intervals < 21 days
  • Mature: Cards with intervals ≥ 21 days (long-term memory!)
  • Due Today: Cards scheduled for review today
  • Average Ease: Your overall ease factor across all cards

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Implementation Details

The SRS system is implemented in /src/lib/sm2.ts: 
export interface SRSCard {
  termId: number;
  easeFactor: number;      // How easy this card is (starts at 2.5)
  interval: number;        // Days until next review
  repetitions: number;     // Number of successful reviews in a row
  nextReviewDate: string;  // ISO date string
  lastReviewDate: string | null;
  quality: number;         // Last quality rating
}
Key functions include:
  • initializeCard(termId): Creates a new SRS card with default values
  • processReview(card, quality): Updates card based on your rating (0-5)
  • isDue(card): Checks if a card needs review today
  • getDueCards(cards): Gets all cards due for review
  • getStudyQueue(allTermIds, cards, newCardsPerDay): Builds your study session

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Best Practices

Don’t mark a card as “Easy” if you hesitated. Accurate ratings ensure optimal scheduling.
Consistency is key. Even 5-10 minutes daily is more effective than hour-long sessions once a week.
Cards you struggle with need more reviews. Embrace the “Again” button—it’s helping you learn!
Start with 10 new cards per day. Increase gradually as you get comfortable with your review load.

Daily Goals

Set daily study targets to stay consistent

Streaks

Build momentum with daily practice streaks

Achievements

Unlock achievements as you master categories

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