Ebbinghaus Forgetting Curve Calculator
The Ebbinghaus forgetting curve (1885) shows that memory decays exponentially: retention R = e^(−t/S), where S is the memory strength (in days). Enter the strength and elapsed time to see the current retention, predicted values at common intervals (20 minutes, 1 hour, 1 day, 6 days, 31 days — Ebbinghaus's original retest points) and the optimal review window where retention is between 80 % and 90 % — handy for revision schedules, Anki/SuperMemo users, language learners and exam prep.
Invalid input — memory strength S must be > 0 and elapsed time t must be ≥ 0.
Retention R
36.8 %
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Recommended review timing
- Retention drops to 90%
- —
- Retention drops to 80%
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- Retention drops to 50%
- —
Retention at common intervals
| Interval | Retention |
|---|
Formula
R(t) = e^(−t ÷ S) t(R) = −S × ln(R)
- · R is the retention probability (0–1, i.e. 0–100 %); t is elapsed time; S is the memory strength, defined as the time at which retention drops to 1/e ≈ 36.8 %.
- · Typical S values: a first encounter with no review sits around 0.5–2 days; after several spaced reviews 5–20 days; deeply over-learnt material (mother-tongue vocabulary, well-rehearsed exam answers) can reach 30+ days or more.
- · The optimal review window is 80–90 % retention (t ≈ 0.1–0.2 × S) — the "desirable difficulty" sweet spot used by Anki, SuperMemo and other spaced-repetition systems (Bjork & Bjork 2011).
- · Original study: Ebbinghaus (1885) "Über das Gedächtnis", English translation "Memory: A Contribution to Experimental Psychology" (1913). Murre & Dros (2015, PLOS ONE) replicated the original and confirmed the exponential form for nonsense-syllable material.
- · Limitations: large individual variation; meaningful material (stories, lecture content) is retained noticeably better than the original nonsense syllables; emotional and procedural memories (cycling, instruments) follow quite different decay models.
- · Practical takeaway: reviewing too early (R ≥ 95 %) wastes effort; reviewing too late (R < 50 %) is essentially relearning. Aim for the 80–90 % window and stretch the next interval each time (the spacing effect).
Frequently asked
What value should I use for "memory strength S"?
S depends on two things: how deeply you encoded the material the first time, and how many spaced reviews you have done since. Rule of thumb: (1) wholly new, unconnected facts (phone numbers, unfamiliar vocabulary, raw formulas) — about 0.5–1 day after first study; (2) meaningful material or a concept someone explained well — 1–3 days; (3) after one successful spaced review — 3–7 days; (4) after 4–5 progressively stretched reviews, S is typically ≥ 30 days and the memory is approaching long-term storage. Start at 1 day if unsure and adjust upwards based on what you actually still remember after a few days.
What retention level is optimal for the next review?
Research consensus is the 80–90 % band. Below 80 % you are on the edge of relearning and each review is hard; above 90 % the marginal benefit drops sharply because the memory is already stable. Anki defaults to 90 % retention and SuperMemo SM-2 was designed around the same window. This tool lists the time at which retention drops to 90 %, 80 % and 50 % so you can pick whichever fits your workflow.
Does the forgetting curve apply to every type of memory?
No. The exponential Ebbinghaus model fits "declarative / semantic memory" best — facts, vocabulary, definitions. But: (1) procedural memory (cycling, playing an instrument, typing) barely decays once mastered; (2) emotional memory (events with strong affect) has its own consolidation pathway and can stay stable for decades; (3) connected material (a finished novel, a project you completed) is retained much better than isolated facts; (4) sleep is critical for consolidation — the same calendar interval that includes a night of sleep yields markedly higher retention than fully-awake hours. So this tool is most useful for material you deliberately memorise: vocabulary, formulas, legal clauses, historical dates and the like.
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