Spanish Vocabulary Retention Estimator

ANA›Life Services Authority›National Calculator Authority›Spanish Vocabulary Retention Estimator

.calc-container { max-width: 640px; margin: 2rem 0; padding: 1.5rem; background: #fff; border: 1px solid #ddd; border-radius: 8px; box-shadow: 0 1px 3px rgba(0,0,0,0.06); font-family: system-ui, -apple-system, sans-serif; } .calc-container h3 { font-family: Georgia, serif; font-size: 1.15rem; color: #1a1a1a; margin-bottom: 1rem; padding-bottom: 0.5rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-row { display: flex; align-items: center; gap: 0.75rem; margin-bottom: 0.75rem; flex-wrap: wrap; } .calc-row label { min-width: 160px; font-size: 0.9rem; color: #333; font-weight: 500; } .calc-row input[type="number"], .calc-row select { flex: 1; min-width: 120px; max-width: 200px; padding: 0.5rem 0.6rem; border: 1px solid #ccc; border-radius: 4px; font-size: 0.9rem; font-family: system-ui, sans-serif; color: #1a1a1a; background: #fafaf8; } .calc-row input:focus, .calc-row select:focus { outline: none; border-color: var(--ac, #3d5a80); box-shadow: 0 0 0 2px rgba(26,74,138,0.12); } .calc-row .unit { font-size: 0.82rem; color: #888; min-width: 30px; } .calc-btn { display: inline-block; margin-top: 0.5rem; padding: 0.55rem 1.5rem; background: var(--ac, #3d5a80); color: #fff; border: none; border-radius: 4px; font-size: 0.9rem; font-weight: 600; cursor: pointer; font-family: system-ui, sans-serif; } .calc-btn:hover { opacity: 0.9; } .calc-result { margin-top: 1.25rem; padding: 1rem 1.25rem; background: #f0f6fc; border-left: 3px solid var(--ac, #3d5a80); border-radius: 0 6px 6px 0; display: none; } .calc-result.visible { display: block; } .calc-result-label { font-size: 0.78rem; text-transform: uppercase; letter-spacing: 0.06em; color: #666; margin-bottom: 0.25rem; } .calc-result-value { font-size: 1.6rem; font-weight: 700; color: var(--ac, #3d5a80); } .calc-result-detail { font-size: 0.85rem; color: #555; margin-top: 0.5rem; line-height: 1.5; } .calc-note { margin-top: 1rem; font-size: 0.8rem; color: #888; font-style: italic; } .calc-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 0.75rem; margin-top: 0.75rem; } .calc-grid-item { padding: 0.6rem 0.8rem; background: #f8f9fa; border-radius: 4px; border: 1px solid #eee; } .calc-grid-item .label { font-size: 0.75rem; color: #888; text-transform: uppercase; letter-spacing: 0.04em; } .calc-grid-item .value { font-size: 1.1rem; font-weight: 600; color: #1a1a1a; } @media (max-width: 720px) { .calc-row { flex-direction: column; align-items: flex-start; gap: 0.3rem; } .calc-row label { min-width: auto; } .calc-row input[type="number"], .calc-row select { max-width: 100%; width: 100%; } .calc-grid { grid-template-columns: 1fr; } } .calc-chart { margin: 1rem 0; text-align: center; } .calc-chart svg { max-width: 100%; height: auto; } .calc-chart-legend { display: flex; flex-wrap: wrap; justify-content: center; gap: 0.6rem 1.2rem; margin-top: 0.6rem; font-size: 0.8rem; color: #555; } .calc-chart-legend span { display: inline-flex; align-items: center; gap: 0.3rem; } .calc-chart-legend i { display: inline-block; width: 10px; height: 10px; border-radius: 2px; font-style: normal; } .calc-related { max-width: 640px; margin: 2rem 0 1rem; padding: 1.25rem 1.5rem; background: #f8f9fa; border: 1px solid #e8e8e8; border-radius: 8px; } .calc-related h3 { font-family: Georgia, serif; font-size: 1rem; color: #1a1a1a; margin: 0 0 0.75rem; padding-bottom: 0.4rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-related-list { list-style: none; padding: 0; margin: 0 0 0.75rem; display: grid; grid-template-columns: 1fr 1fr; gap: 0.4rem 1.5rem; } .calc-related-list li a { font-size: 0.88rem; color: var(--ac, #3d5a80); text-decoration: none; } .calc-related-list li a:hover { text-decoration: underline; } .calc-browse-all { margin: 0.5rem 0 0; font-size: 0.9rem; font-weight: 600; } .calc-browse-all a { color: var(--ac, #3d5a80); text-decoration: none; } .calc-browse-all a:hover { text-decoration: underline; } @media (max-width: 720px) { .calc-related-list { grid-template-columns: 1fr; } }

Spanish Vocabulary Retention Estimator

Estimate long-term Spanish vocabulary retention using the Ebbinghaus Forgetting Curve combined with spaced repetition and active recall factors.

Total Words Studied

Number of Spanish words you have actively studied.

Days Since Last Review

How many days ago you last reviewed the vocabulary.

Number of Past Review Sessions

Total number of times you have reviewed this vocabulary set.

Active Recall Accuracy (%)

Your average correct recall rate during practice sessions (1–100%).

Primary Study Method

Passive Reading / Listening Flashcards (no spaced repetition) Spaced Repetition System (SRS) SRS + Active Writing Practice SRS + Immersion (speaking/writing daily)

Your primary method of studying Spanish vocabulary.

Average Sleep per Night (hours)

Sleep strongly affects memory consolidation.

Estimate Retention

Your results will appear here.

function spaCalc() { const resultDiv = document.getElementById('spa-result');

// --- Gather inputs --- const wordsLearned = parseFloat(document.getElementById('spa-words-learned').value); const daysSince = parseFloat(document.getElementById('spa-days-since').value); const reviews = parseFloat(document.getElementById('spa-reviews').value); const recallRate = parseFloat(document.getElementById('spa-recall-rate').value); const methodFactor = parseFloat(document.getElementById('spa-method').value); const sleep = parseFloat(document.getElementById('spa-sleep').value);

// --- Validation --- const errors = []; if (isNaN(wordsLearned) || wordsLearned 100) errors.push("Active Recall Accuracy must be between 1 and 100."); if (isNaN(sleep) || sleep 12) errors.push("Average Sleep must be between 1 and 12 hours.");

if (errors.length > 0) { resultDiv.innerHTML = 'Please fix the following:' + errors.map(e => '').join('') + ''; return; }

// --------------------------------------------------------------- // CORE FORMULA // // Step 1 — Ebbinghaus Forgetting Curve (base retention after t days): // R_base(t) = e^(-t / S) // where S = memory stability (days), starting at 1 and growing with reviews. // // Step 2 — Memory Stability grows with each successful review: // S = 1 * (1 + 0.5 * reviews)^0.6 // (Simplified SuperMemo-style stability increase; each review multiplies stability.) // // Step 3 — Recall quality modifier (higher accuracy → slower forgetting): // recallMod = recallRate / 100 // S_adjusted = S * (0.5 + recallMod) [scales S between 0.5× and 1.5×] // // Step 4 — Study method multiplier applied to stability: // S_final = S_adjusted * methodFactor // // Step 5 — Sleep consolidation factor: // sleepFactor = 0.7 + 0.3 * (sleep / 8) [optimal at 8 h; capped at 1.0 above 8 h] // sleepFactor = min(sleepFactor, 1.0) // // Step 6 — Adjusted retention rate: // R = e^(-daysSince / S_final) * sleepFactor // R = clamp(R, 0, 1) // // Step 7 — Estimated words retained: // wordsRetained = wordsLearned * R // // Step 8 — Next optimal review interval (SuperMemo approximation): // nextReview = S_final * ln(0.9) / (-1) → day when retention drops to 90% // nextReview = S_final * 0.10536 // ---------------------------------------------------------------

// Step 2: Base stability const S_base = Math.pow(1 + 0.5 * reviews, 0.6);

// Step 3: Recall modifier const recallMod = recallRate / 100; const S_adjusted = S_base * (0.5 + recallMod);

// Step 4: Method multiplier const S_final = S_adjusted * methodFactor;

// Step 5: Sleep factor const sleepFactor = Math.min(0.7 + 0.3 * (sleep / 8), 1.0);

// Step 6: Retention rate let R = Math.exp(-daysSince / S_final) * sleepFactor; R = Math.max(0, Math.min(1, R));

// Step 7: Words retained const wordsRetained = Math.round(wordsLearned * R);

// Step 8: Next optimal review (retention drops to 90%) const nextReview = Math.max(1, Math.round(S_final * 0.10536));

// Retention category let category = '', catColor = ''; if (R >= 0.85) { category = 'Excellent'; catColor = '#27ae60'; } else if (R >= 0.65) { category = 'Good'; catColor = '#2980b9'; } else if (R >= 0.45) { category = 'Fair'; catColor = '#f39c12'; } else if (R >= 0.25) { category = 'Poor'; catColor = '#e67e22'; } else { category = 'Critical'; catColor = '#c0392b'; }

const retentionPct = (R * 100).toFixed(1);

resultDiv.innerHTML = ` ### Retention Estimate

Estimated Retention Rate ${retentionPct}% (${category}) Words Likely Retained ${wordsRetained.toLocaleString()} of ${wordsLearned.toLocaleString()} Words at Risk of Forgetting ${(wordsLearned - wordsRetained).toLocaleString()} Memory Stability (S) ${S_final.toFixed(2)} days Next Optimal Review In ${nextReview} day${nextReview !== 1 ? 's' : ''} (to stay above 90% retention) Sleep Consolidation Factor ${(sleepFactor * 100).toFixed(1)}%

Tip: ${R

`; }

#### Formula

1. Memory Stability (S): S_base = (1 + 0.5 × reviews)^0.6 S_adjusted = S_base × (0.5 + recallAccuracy) S_final = S_adjusted × methodFactor

2. Sleep Consolidation Factor: sleepFactor = min(0.7 + 0.3 × (sleep / 8), 1.0)

3. Ebbinghaus Retention Rate (R): R = e^(−daysSinceReview / S_final) × sleepFactor

4. Words Retained: wordsRetained = totalWords × R

5. Next Optimal Review Interval (90% threshold): nextReview = S_final × ln(1/0.9) ≈ S_final × 0.10536

#### Assumptions & References

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References

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