Forgetting Curve Calculator
Estimate how much you still remember as time passes without review.
Drops to 50% after about 1.386 days (t = S·ln2). Each review resets the curve.
Without review, retention falls fast at first, then levels off. A review lifts the line back toward 100% and flattens the next decline.
Memory decays exponentially without review. The forgetting curve estimates retention as R = e^(−t ÷ S), where t is time elapsed and S is memory strength. With S = 2 days, after t = 2 days you retain e^(−1) ≈ 36.8% — and you cross 50% at about 1.39 days.
What the forgetting curve shows
In the 1880s Hermann Ebbinghaus tested his own recall of nonsense syllables and found that memory fades fast at first, then slows down. That shape is the forgetting curve: retention drops steeply in the hours and days after learning, then flattens as the memories that survive become more stable.
This calculator uses the common exponential form R = e^(−t ÷ S). R is the fraction of material you still hold (shown as a percent), t is the time since you learned it, and S is the memory strength — a larger S means the curve falls more slowly. At t = S the exponent is −1, so R = 1/e ≈ 36.8%. This is a simplified model: real retention varies by person, by how meaningful the material is, and by how well you sleep.
R = fraction retained · t = time elapsed · S = memory strength (same time units)
Worked example
You set memory strength S = 2 days and check retention after t = 2 days:
- 1 Pick a memory strength S. Use days. Fresh, unrehearsed material is roughly S = 1; well-learned material holds longer, around S = 7.
- 2 Enter the time elapsed t. How long since you last studied or reviewed, in the same units as S — here t = 2 days.
- 3 Divide the exponent. −t ÷ S = −2 ÷ 2 = −1.
- 4 Read the retention. R = e^(−1) = 0.368, so you retain about 36.8% of the material.
- 5 Find the half-life. Retention hits 50% at t = S·ln2 = 2 × 0.6931 ≈ 1.39 days — review before then to stay ahead of the drop.
Retention at multiples of S
Because R depends only on t ÷ S, the same fractions apply whatever your memory strength is.
| Time elapsed (t) | Retention (R) |
|---|---|
| 0 | 100% |
| 0.5 · S | 60.7% |
| S | 36.8% |
| 2 · S | 13.5% |
Why review beats cramming
Each time you successfully recall something, the curve resets higher and, crucially, gets flatter — the next decline is slower, so the memory lasts longer before it needs another review. Reviewing at widening intervals as the curve falls is the core idea behind spaced repetition: a handful of well-timed reviews holds material far better than one long cramming session.
Treat the numbers as a guide, not a guarantee. The exponential curve is a model, not an exact law — actual forgetting depends on how deeply you understood the material, how it connects to what you already know, and how much you slept between study and recall. Meaningful, well-organised material and good sleep both stretch S, flattening the curve on their own.