Forgetting Curve Calculator
Estimate how much of what you studied you still remember with the Ebbinghaus forgetting curve (R = e^−t/S), how reviews slow forgetting, and when to review before you drop below a target.
How it works
Retention R = e^(−t ÷ S) × 100% · stability S = initial stability × gain^reviews · time to fall to a target r: t = −S × ln(r)
Hermann Ebbinghaus (1885) measured how fast he forgot nonsense syllables and found memory drops steeply in the first day and more slowly afterwards; a 2015 replication by Murre and Dros confirmed the shape. The simple exponential model used here, R = e^(−t/S), treats memory “stability” S as the time for retention to fall to 37%, and each spaced review multiplies stability — the principle behind spaced-repetition apps such as Anki and SuperMemo. The numbers are illustrative: real forgetting depends on the material, sleep, prior knowledge and how actively you review.
Worked example
New material with 2 days of stability, reviewed twice with a 2× gain each time, has a stability of 2 × 2² = 8 days. After 7 days, R = e^(−7 ÷ 8) = 41.69% retained. To stay above 80% you should review within −8 × ln 0.8 = 1.8 days of the last review.
Sources: Murre & Dros (2015), Replication and Analysis of Ebbinghaus’ Forgetting Curve, PLOS ONE · Ebbinghaus (1885), Memory: A Contribution to Experimental Psychology (Classics in the History of Psychology)
Frequently asked questions
What is the Ebbinghaus forgetting curve?
It is the pattern Hermann Ebbinghaus found in 1885: we forget much of new information within hours or days unless we review it, and the rate of forgetting slows over time. It is usually modeled as R = e^(−t/S).
How much do we forget after one day?
In Ebbinghaus’s experiments with nonsense syllables, savings fell to about a third after one day. Meaningful, well-understood material is forgotten much more slowly.
How do you beat the forgetting curve?
Review at growing intervals (spaced repetition), test yourself instead of rereading (retrieval practice), and sleep well. Each successful review makes the memory more stable.
When should I review?
Just before retention would fall below your target. With this model, a stability of 8 days and an 80% target means reviewing within about 1.8 days; the next interval will then be longer.
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This calculator is for educational purposes. Double-check important results before acting on them.