Why Memory Fades

After you review a flashcard, your ability to recall that information declines gradually unless you see it again. Psychologists often model this decline as an exponential decay. The forgetting rate can vary by subject and by individual, but the pattern is remarkably consistent. Spaced repetition systems take advantage of this by scheduling reviews just before you’re likely to forget, strengthening your memory each time.

The Decay Equation

If your retention after the first study session is $\mathrm{R\_0}$ (expressed as a decimal), and the daily forgetting rate is $f$, then after $t$ days your recall is $$R=\mathrm{R\_0}{e}^{-ft}$$. This calculator simplifies things by using percentages. You input your expected forgetting rate each day and the time until your next review. The result shows how much of the material you’ll likely remember when you sit down to study again.

Example Scenario

Suppose you finish learning a batch of vocabulary cards with a 90% immediate recall rate, and your personal forgetting rate is about 15% per day. If you wait three days to review, your projected recall is $$R=0.9e^{-0.15\times 3}$$, which equals roughly 65%. Seeing that drop-off can motivate you to schedule reviews sooner or adjust your study approach.

Keep in mind that actual retention varies based on how well you learned the material initially, how similar the concepts are, and distractions that may interfere with recall. Nonetheless, a decay model like this one offers valuable guidance when building a flashcard schedule.

Using the Result

If you find your predicted retention is lower than you’d like, shorten the interval before your next review or reduce the number of new cards you add at a time. Spaced repetition apps often adjust intervals automatically according to your performance. Reviewing cards while you still remember them reasonably well strengthens the neural connections and slows future decay.

By monitoring your retention percentage, you can fine-tune how often to study each deck so you spend less time relearning forgotten facts and more time building long-term memory.