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Malti🎓 Learning Curves
Model Ebbinghaus forgetting curves and spaced repetition scheduling. See how memory retention decays exponentially between reviews, and how optimally timed repetitions build long-term memory.
About the Learning Curves Simulator
This simulator models how memory fades over time and how well-timed reviews rebuild it. It plots the Ebbinghaus forgetting curve, where retention follows R(t) = e−t/S: the chance of recall decays exponentially with time t, governed by a stability parameter S (in days). Each review resets recall to 100% and lengthens S, so the curve flattens and memories last longer between sessions.
You choose an algorithm — Ebbinghaus, SM-2, or Leitner — set the initial stability S₀ (0.2–5 days), and pick a review quality (2–5). Pressing "Add Review Now" schedules the next review at the algorithm's optimal interval, building a chain of segments across 30 days. Spaced repetition like this underpins flashcard apps such as Anki and is central to efficient long-term learning.
Frequently Asked Questions
What is the Ebbinghaus forgetting curve?
It is a model, first described by Hermann Ebbinghaus in 1885, of how newly learned information is lost over time. Retention drops sharply at first and then more slowly, following an approximately exponential decay. This simulator uses R(t) = e to the power −t/S, where S is the memory stability in days.
What does the stability parameter S do?
Stability S sets how slowly you forget: it is the time constant of the exponential decay. A larger S means a flatter curve and slower forgetting. After roughly S days the chance of recall falls to about 37 percent. The initial value S₀ is set with the slider between 0.2 and 5 days.
How does a review change the curve?
Each review resets recall to 100 percent, starting a fresh forgetting segment, and increases stability so the next decay is slower. In the Ebbinghaus mode the new stability is S multiplied by (1 + (q − 3) × 0.3), where q is the review quality, so good reviews stretch the interval and poor ones shrink it.
What is the difference between the Ebbinghaus, SM-2 and Leitner modes?
Ebbinghaus schedules the next review when predicted retention falls to 90 percent, using the interval S × ln(1/0.9). SM-2, the algorithm behind Anki, multiplies the previous interval by an ease factor near 2.5. Leitner uses fixed box intervals of 1, 3, 7, 14 and 30 days, promoting a card one box per successful review.
What does the review quality setting mean?
Quality grades how well you recalled the item on a scale where 5 is perfect, 4 is good, 3 is hard, and 2 is a near miss that you still remembered. In SM-2 it feeds the ease factor, and in Ebbinghaus mode it scales the stability growth, so higher quality lengthens the gap before the next review.
Why is the optimal review interval based on 90 percent retention?
Reviewing too early wastes effort on material you still know well, while reviewing too late means the item is already forgotten and must be relearned. Targeting around 90 percent retention is a common compromise that keeps recall high while spacing reviews as far apart as practical. The interval is computed as S × ln(1/0.9), about 0.105 × S days.
What is the "time savings vs massed" statistic?
It compares day-30 retention under your spaced schedule against cramming everything at day 0 with no further review. Massed practice retention is e to the power −30/S₀, which is usually very low. The difference, shown in percentage points, illustrates the spacing effect: distributed reviews produce far stronger long-term memory than a single intense session.
What do the preset buttons represent?
The presets set the initial stability S₀ to match different material. Vocabulary uses a low S₀ of 0.5 days because isolated words are forgotten quickly, Math Facts uses 1.5 days, and Concepts uses 3.0 days because meaningful, well-understood ideas are retained longer from the outset.
Is this simulation scientifically accurate?
It captures the qualitative behaviour of memory well: exponential decay, the spacing effect, and how reviews extend retention. The exact numbers are simplified for clarity rather than fitted to any individual. Real memory depends on sleep, prior knowledge, interference and difficulty, so treat the curves as an illustrative model, not a precise prediction.
How is spaced repetition used in the real world?
Flashcard tools such as Anki, SuperMemo, Memrise and Duolingo schedule reviews using SM-2 style algorithms to maximise retention with minimal study time. The same principle is applied in medical and language training, professional certification revision, and any setting where large amounts of material must be retained durably.
Why does forgetting follow an exponential rather than a straight line?
An exponential decay arises when the rate of forgetting is proportional to how much you still remember, which fits experimental recall data better than a linear drop. It produces the characteristic shape of rapid early loss followed by a long, slow tail, meaning the items most at risk are those reviewed only once.
Ebbinghaus forgetting curve, spaced repetition SM-2 algorithm and memory retention visualised interactively.
3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install