Learning Retention Rate Calculator

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Learning Retention Rate Calculator

Estimate memory retention over time using the Ebbinghaus Forgetting Curve formula. Understand how much information is retained after initial learning and how spaced repetition improves long-term memory.

Time Elapsed Since Learning (days)

How many days since the material was first learned

Memory Stability / Strength (days)

Stability constant S — average is ~1.84 days for new material; increases with repetitions

Number of Spaced Repetitions Completed

Each repetition multiplies stability by ~2.5 (SuperMemo model)

Initial Test Score After Learning (%)

Score immediately after learning session (baseline retention)

Calculate Retention

function leaCalc() { const resultDiv = document.getElementById('lea-result');

const t = parseFloat(document.getElementById('lea-time-elapsed').value); const S0 = parseFloat(document.getElementById('lea-stability').value); const n = parseInt(document.getElementById('lea-repetitions').value); const R0 = parseFloat(document.getElementById('lea-initial-score').value);

// --- Validation --- if (isNaN(t) || t ⚠ Please enter a valid time elapsed greater than 0.'; return; } if (isNaN(S0) || S0 ⚠ Please enter a valid memory stability value greater than 0.'; return; } if (isNaN(n) || n 20) { resultDiv.style.display = 'block'; resultDiv.innerHTML = '⚠ Please enter a valid number of repetitions (0–20).'; return; } if (isNaN(R0) || R0 100) { resultDiv.style.display = 'block'; resultDiv.innerHTML = '⚠ Please enter a valid initial score between 1 and 100.'; return; }

// --- Core Formula --- // Ebbinghaus Forgetting Curve: R(t) = e^(-t / S) // Effective stability after n repetitions: S_eff = S0 * (2.5 ^ n) // Actual retention: R_actual = R0 * e^(-t / S_eff)

const S_eff = S0 * Math.pow(2.5, n); const rawRetention = Math.exp(-t / S_eff); // 0–1 scale const retentionRate = Math.min(rawRetention * R0, 100); // scaled by initial score

// --- Derived Metrics --- // Half-life: time at which retention drops to 50% of initial // 0.5 = e^(-t_half / S_eff) => t_half = S_eff * ln(2) const halfLife = S_eff * Math.LN2;

// Forgetting percentage const forgotten = 100 - retentionRate;

// Next optimal review (when retention drops to 90% of current) // 0.9 = e^(-t_review / S_eff) => t_review = S_eff * ln(1/0.9) const nextReview = S_eff * Math.log(1 / 0.9);

// Retention category let category, categoryColor, advice; if (retentionRate >= 80) { category = "Strong Retention"; categoryColor = "#27ae60"; advice = "Excellent! Schedule your next review in " + nextReview.toFixed(1) + " days to maintain this level."; } else if (retentionRate >= 60) { category = "Moderate Retention"; categoryColor = "#f39c12"; advice = "Good retention. Consider reviewing soon — ideally within " + nextReview.toFixed(1) + " days."; } else if (retentionRate >= 40) { category = "Weak Retention"; categoryColor = "#e67e22"; advice = "Significant forgetting has occurred. Review immediately and increase repetition frequency."; } else { category = "Critical — Mostly Forgotten"; categoryColor = "#c0392b"; advice = "Most material has been forgotten. A full re-learning session is recommended."; }

// --- Output --- resultDiv.style.display = 'block'; resultDiv.innerHTML = '### Retention Results ' +

'' + '' + 'Effective Memory Stability (S_eff)' + '' + S_eff.toFixed(2) + ' days' + '' + '' + 'Raw Forgetting Curve Value e^(−t/S_eff)' + '' + (rawRetention * 100).toFixed(2) + '%' + '' + '' + 'Estimated Retention Rate' + '' + retentionRate.toFixed(2) + '%' + '' + '' + 'Estimated Forgotten' + '' + forgotten.toFixed(2) + '%' + '' + '' + 'Memory Half-Life' + '' + halfLife.toFixed(2) + ' days' + '' + '' + 'Next Optimal Review (at 90% of current)' + '' + nextReview.toFixed(2) + ' days from now' + '' + '' +

'' + 'Status: ' + category + '' + '' + advice + '' + '' +

'' + 'Interpretation: After ' + t + ' day(s) with ' + n + ' repetition(s), ' + 'you retain approximately ' + retentionRate.toFixed(1) + '% of the originally learned material. ' + 'Your memory stability has grown from ' + S0.toFixed(2) + ' to ' + S_eff.toFixed(2) + ' days through spaced repetition.' + ''; }

#### Formulas Used

Ebbinghaus Forgetting Curve:

R(t) = e−t / S_eff

Where:

Effective Stability with Spaced Repetition (SuperMemo SM-2 model):

S_eff = S₀ × 2.5n

Actual Retention Rate:

Retention (%) = R₀ × e−t / S_eff

Memory Half-Life:

t½ = S_eff × ln(2)

Next Optimal Review (at 90% retention threshold):

treview = S_eff × ln(1 / 0.9)

#### Assumptions & References

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