Knowledge Retention Curve Simulator Calculator

The simulation uses the exponential form of the forgetting curve, R equals e raised to minus t over S, where R is retained proportion, t is days since the last encounter, and S is a stability constant in days. Everything interesting sits in S. Here it is derived from the ratio of engagement to material difficulty, capturing the two variables a learner can actually manipulate: how deeply the material was processed at encoding, and how much element interactivity it carries. Because decay is exponential, two summary statistics describe the whole curve. The half-life is S multiplied by the natural log of 2, about 0.693 S, and the point at which 90 percent is gone is S multiplied by ln 10, about 2.30 S. A stability of 2.0 days therefore means half the material is gone in about 1.4 days and 90 percent within 4.6 days, which is the ordinary experience of cramming. Reviews are modelled as partial restoration of R combined with a multiplicative increase in S, so each successful retrieval both raises the curve and flattens it. This is why expanding intervals outperform fixed ones: if S grows by roughly half at each review, the interval that lands just before substantial decay must lengthen too, producing schedules along the lines of 1, 3, 7, 18 and 44 days. Two limits deserve emphasis. First, the retrieval must be effortful and successful; re-reading restores far less stability than recall does. Second, the exponential form is a convenient approximation. Ebbinghaus himself fitted a logarithmic function, and subsequent modelling work has favoured power-law and other decelerating forms for aggregate data, so the numbers here are for comparing schedules against each other rather than predicting an individual's exact recall.

Hermann Ebbinghaus, working largely alone in Berlin in the late 1870s and early 1880s, made memory experimentally tractable by inventing the nonsense syllable, roughly 2,300 consonant-vowel-consonant items designed to strip away prior association. Using himself as the sole subject, he learned lists to criterion and measured the savings in relearning time after intervals ranging from about twenty minutes to thirty-one days. The results were published as Uber das Gedachtnis in 1885, translated into English as Memory: A Contribution to Experimental Psychology in 1913. In the same work he reported the spacing effect, noting that repetitions distributed over several days were markedly more efficient than the same number massed into one session. The findings proved durable. Jaap Murre and Joeri Dros published a careful replication in PLOS ONE in 2015 that reproduced the original curve closely, and the spacing effect has been confirmed across hundreds of studies, with Nicholas Cepeda and colleagues reporting a large synthesis of distributed-practice research in Psychological Bulletin in 2006. The engineering side came from Piotr Wozniak in Poland, who began systematically recording his own review intervals in 1985, wrote the first SuperMemo program for DOS in 1987, and published the SM-2 algorithm in 1990. SM-2 assigned each item an ease factor updated by the learner's self-rated recall quality, and it remains the basis of the scheduler in Anki, the open-source flashcard application released by Damien Elmes in 2006. Later systems, including the FSRS scheduler, replaced the fixed heuristics with fitted memory models estimating stability and retrievability per item.