Vocabulary Growth Rate Calculator
ANA›Life Services Authority›National Calculator Authority›Vocabulary Growth Rate Calculator
.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; } }
Vocabulary Growth Rate Calculator
Calculate your vocabulary growth rate — how many new words you're learning per day, week, or month — and project future vocabulary size.
Initial Vocabulary Size (words)
Current / Final Vocabulary Size (words)
Time Elapsed
Time Unit
Days Weeks Months Years
Projection Period (days, optional)
Calculate
function vocCalc() { var resultDiv = document.getElementById('voc-result'); resultDiv.style.display = 'block';
var V0 = parseFloat(document.getElementById('voc-initial').value); var Vt = parseFloat(document.getElementById('voc-final').value); var t = parseFloat(document.getElementById('voc-time').value); var unit = parseFloat(document.getElementById('voc-unit').value); var proj = parseFloat(document.getElementById('voc-project').value);
// --- Validation --- if (isNaN(V0) || V0 ⚠ Initial vocabulary size must be a non-negative number.'; return; } if (isNaN(Vt) || Vt ⚠ Final vocabulary size must be a non-negative number.'; return; } if (isNaN(t) || t ⚠ Time elapsed must be a positive number.'; return; } if (V0 === 0) { resultDiv.innerHTML = '⚠ Initial vocabulary size cannot be zero (division by zero in growth rate formula).'; return; } if (Vt ⚠ Final vocabulary size is less than initial — this calculator models growth, not decline.'; return; }
// Convert elapsed time to days var tDays = t * unit;
// --- Core Formulas --- // 1. Absolute new words learned var newWords = Vt - V0;
// 2. Linear growth rate (words per day) var linearRatePerDay = newWords / tDays;
// 3. Compound Annual Growth Rate (CAGR) style — continuous growth rate // r = ln(Vt / V0) / t_years var tYears = tDays / 365.25; var continuousRate = Math.log(Vt / V0) / tYears; // per year
// 4. Percentage growth rate over the period var pctGrowth = ((Vt - V0) / V0) * 100;
// 5. Annualised percentage growth rate // CAGR% = (Vt/V0)^(1/tYears) - 1 var cagrPct = (Math.pow(Vt / V0, 1 / tYears) - 1) * 100;
// 6. Words per week / month var ratePerWeek = linearRatePerDay * 7; var ratePerMonth = linearRatePerDay * 30.4375;
// --- Projection --- var projHTML = ''; if (!isNaN(proj) && proj > 0) { // Using compound model: V_proj = Vt * e^(r_daily * proj) var rDaily = Math.log(Vt / V0) / tDays; var Vproj = Vt * Math.exp(rDaily * proj); projHTML = 'Projected Vocabulary in ' + proj + ' days' + Math.round(Vproj).toLocaleString() + ' words'; }
resultDiv.innerHTML = '### Results ' + '' + 'MetricValue' + 'New Words Learned' + newWords.toLocaleString() + ' words' + 'Growth Rate (per day)' + linearRatePerDay.toFixed(2) + ' words/day' + 'Growth Rate (per week)' + ratePerWeek.toFixed(1) + ' words/week' + 'Growth Rate (per month)' + ratePerMonth.toFixed(1) + ' words/month' + 'Total Growth Over Period' + pctGrowth.toFixed(2) + '%' + 'Annualised Growth Rate (CAGR)' + cagrPct.toFixed(2) + '% / year' + 'Continuous Growth Rate' + (continuousRate * 100).toFixed(2) + '% / year' + projHTML + ''; }
#### Formulas Used
1. Absolute Growth: New Words = Vt − V0
2. Linear Growth Rate: Rate = (Vt − V0) / t (words per day)
3. Percentage Growth Over Period: Growth% = ((Vt − V0) / V0) × 100
4. Compound Annual Growth Rate (CAGR): CAGR = (Vt / V0)1/tyears − 1
5. Continuous Growth Rate: r = ln(Vt / V0) / tyears
6. Projection (Compound Model): Vproj = Vt × erdaily × d where rdaily = ln(Vt / V0) / tdays
#### Assumptions & References
- The continuous growth rate uses the natural logarithm model: r = ln(Vt/V0) / t, standard in population and learning growth models.
- Reference: Nation, I.S.P. & Waring, R. (1997). Vocabulary size, text coverage and word lists. In N. Schmitt & M. McCarthy (Eds.), Vocabulary: Description, Acquisition and Pedagogy. Cambridge University Press.
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