Vocabulary Retention Calculator
Why New Vocabulary Fades on a Predictable Curve
In 1885, psychologist Hermann Ebbinghaus tested his own memory by learning nonsense syllables and re-testing himself at intervals, and found that forgetting follows a remarkably consistent exponential decay rather than a linear one — most of the loss happens fast, in the first day or two, and then the rate of loss slows. That curve is the mathematical backbone behind spaced repetition study systems, and this calculator applies it directly: given how many days have passed since you studied a word and how durable that memory currently is, it estimates what fraction you still retain.
The Formula
Where t is days elapsed since the word was last reviewed and S is memory strength in days — a rough measure of how durable the memory currently is. A freshly learned word might have a memory strength of just 1–2 days, while a word reviewed successfully several times through spaced repetition can have a memory strength stretching into weeks or months.
Where This Matters
- Deciding when to re-review — if estimated retention has dropped below a comfortable threshold, that word is due for review before it's forgotten entirely.
- Understanding why cramming fails long-term — the curve shows why a single study session produces rapid, front-loaded forgetting unless it's reinforced by follow-up review.
- Calibrating spaced repetition intervals — the same exponential relationship underlies how apps like Anki schedule review intervals as memory strength increases with each successful recall.
| Memory strength | 1 day | 2 days | 5 days | 10 days | 30 days |
|---|---|---|---|---|---|
| S = 1 day | 36.8% | 13.5% | 0.7% | 0.0% | 0.0% |
| S = 2 days | 60.7% | 36.8% | 8.2% | 0.7% | 0.0% |
| S = 5 days | 81.9% | 67.0% | 36.8% | 13.5% | 0.2% |
| S = 10 days | 90.5% | 81.9% | 60.7% | 36.8% | 5.0% |
This is a simplified model of a well-documented general phenomenon; individual memory decay varies with word difficulty, personal association, and review history.
How to Use This Calculator
- Enter the number of days since last review for the word or item.
- Enter the current memory strength in days (defaults to 2, appropriate for a recently learned item).
- Select Calculate to see the estimated percentage of the memory still retained.
Related Calculations
Plan your next review with the Spaced Repetition Calculator, or track overall progress with the Language Proficiency Level Calculator.