Card Sorting Category Optimization Calculator

ANA›Life Services Authority›National Calculator Authority›Card Sorting Category Optimization 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; } }

Card Sorting Category Optimization Calculator

Optimize the number of categories, cards per category, and participant count for card sorting UX research studies. Calculates agreement scores, optimal category ranges, and study reliability metrics.

Total Number of Cards

Recommended: 20–100 cards per study

Number of Participants

Minimum 15 recommended for reliable results

Number of Categories Created (avg per participant)

Average number of groups participants created

Number of Agreed Card Pairs

Card pairs placed together by majority of participants

Card Sorting Study Type

Open Card Sort Closed Card Sort Hybrid Card Sort

Calculate

function carCalc() { var totalCards = parseFloat(document.getElementById('car-total-cards').value); var participants = parseFloat(document.getElementById('car-num-participants').value); var numCategories = parseFloat(document.getElementById('car-num-categories').value); var agreedPairs = parseFloat(document.getElementById('car-agreement-pairs').value); var studyType = document.getElementById('car-study-type').value; var resultDiv = document.getElementById('car-result');

// Validation if (isNaN(totalCards) || isNaN(participants) || isNaN(numCategories) || isNaN(agreedPairs)) { resultDiv.style.display = 'block'; resultDiv.innerHTML = 'Please fill in all fields with valid numbers.'; return; } if (totalCards 200) { resultDiv.style.display = 'block'; resultDiv.innerHTML = 'Total cards must be between 5 and 200.'; return; } if (participants Minimum 5 participants required. 15+ recommended.'; return; } if (numCategories Number of categories must be at least 2.'; return; } if (numCategories >= totalCards) { resultDiv.style.display = 'block'; resultDiv.innerHTML = 'Number of categories must be less than total cards.'; return; }

// Total possible card pairs: C(n, 2) = n*(n-1)/2 var totalPossiblePairs = (totalCards * (totalCards - 1)) / 2;

if (agreedPairs > totalPossiblePairs) { resultDiv.style.display = 'block'; resultDiv.innerHTML = 'Agreed pairs cannot exceed total possible pairs (' + totalPossiblePairs + ').'; return; }

// 1. Agreement Score (AS) = agreed pairs / total possible pairs var agreementScore = agreedPairs / totalPossiblePairs;

// 2. Optimal category range using square root rule: sqrt(n/2) to sqrt(n) var optimalCatMin = Math.round(Math.sqrt(totalCards / 2)); var optimalCatMax = Math.round(Math.sqrt(totalCards)); // Ensure at least 2 categories optimalCatMin = Math.max(2, optimalCatMin); optimalCatMax = Math.max(optimalCatMin + 1, optimalCatMax);

// 3. Average cards per category var avgCardsPerCategory = totalCards / numCategories;

// 4. Category Consistency Index (CCI): how close participant categories are to optimal // CCI = 1 - |numCategories - optimalMid| / optimalMid var optimalMid = (optimalCatMin + optimalCatMax) / 2; var cci = Math.max(0, 1 - Math.abs(numCategories - optimalMid) / optimalMid);

// 5. Study Reliability Score based on participants // Based on Nielsen's formula: reliability = 1 - (1 - p)^n // where p = probability single participant finds issue (approx 0.31 for usability) // For card sorting, use p = 0.20 (more conservative) var p = 0.20; var reliability = 1 - Math.pow(1 - p, participants);

// 6. Standardized Agreement Score (SAS) — normalized 0-100 var sas = agreementScore * 100;

// 7. Recommended additional participants to reach 95% reliability // n = log(1 - 0.95) / log(1 - p) var targetReliability = 0.95; var requiredParticipants = Math.ceil(Math.log(1 - targetReliability) / Math.log(1 - p)); var additionalNeeded = Math.max(0, requiredParticipants - participants);

// 8. Category Overload Index: ratio of actual to optimal max var categoryOverloadIndex = numCategories / optimalCatMax;

// 9. Cognitive Load Score (CLS): based on Miller's Law (7 ± 2 items per category) // Ideal: 5-9 items per category var millerMin = 5, millerMax = 9; var cls; if (avgCardsPerCategory >= millerMin && avgCardsPerCategory = 0.70) return 'Strong Agreement'; if (score >= 0.40) return 'Moderate Agreement'; return 'Weak Agreement'; } function getCCILabel(val) { if (val >= 0.80) return 'Excellent'; if (val >= 0.50) return 'Acceptable'; return 'Poor — consider restructuring categories'; } function getReliabilityLabel(val) { if (val >= 0.95) return 'High Reliability'; if (val >= 0.80) return 'Moderate Reliability'; return 'Low Reliability — add more participants'; } function getCLSLabel(val) { if (val === 100) return 'Optimal (Miller's Law)'; if (val >= 60) return 'Acceptable'; return 'High Cognitive Load'; }

resultDiv.style.display = 'block';
resultDiv.innerHTML =
'### Card Sorting Optimization Results
' +
'' +
'MetricValueInterpretation' +
'Study Type' + studyTypeLabel + '' + studyTypeNote + '' +
'Total Possible Card Pairs' + totalPossiblePairs.toLocaleString() + 'C(' + totalCards + ', 2) = n(n-1)/2' +
'Agreement Score (AS)' + (agreementScore * 100).toFixed(1) + '%' + getAgreementLabel(agreementScore) + '' +
'Standardized Agreement Score' + sas.toFixed(1) + ' / 100Normalized 0–100 scale' +
'Optimal Category Range' + optimalCatMin + ' – ' + optimalCatMax + '√(n/2) to √(n) rule' +
'Actual Avg Categories' + numCategories + '' + (numCategories optimalCatMax ? 'Too many — split risk' : 'Within optimal range') + '' +
'Category Consistency Index (CCI)' + (cci * 100).toFixed(1) + '%' + getCCILabel(cci) + '' +
'Avg Cards per Category' + avgCardsPerCategory.toFixed(1) + 'Ideal: 5–9 (Miller's Law)' +
'Cognitive Load Score (CLS)' + cls.toFixed(1) + ' / 100' + getCLSLabel(cls) + '' +
'Category Overload Index' + categoryOverloadIndex.toFixed(2) + 'x' + (categoryOverloadIndex > 1.5 ? 'Overloaded — reduce categories' : categoryOverloadIndex ' +
'Study Reliability' + (reliability * 100).toFixed(1) + '%' + getReliabilityLabel(reliability) + '' +
'Participants for 95% Reliability' + requiredParticipants + '' + (additionalNeeded > 0 ? 'Add ' + additionalNeeded + ' more participant(s)' : 'Sufficient participants') + '' +
'' +
'' +
'Recommendation: ' +
(agreementScore >= 0.70 && cci >= 0.80 && cls >= 80
? 'Your card sort shows strong agreement and well-structured categories. Proceed to information architecture design.'
agreementScore optimalCatMax
? 'Too many categories created. Consider merging related groups or reducing card count.'
numCategories '; }

#### Formulas Used

Total Possible Card Pairs: C(n, 2) = n × (n − 1) / 2

Agreement Score (AS): AS = Agreed Pairs / Total Possible Pairs

Optimal Category Range: Min = √(n/2), Max = √(n)  (square root rule)

Category Consistency Index (CCI): CCI = 1 − |actual_categories − optimal_midpoint| / optimal_midpoint

Cognitive Load Score (CLS): Based on Miller's Law — ideal 5–9 items per category (7 ± 2)

Study Reliability: R = 1 − (1 − p)ⁿ  where p = 0.20 (discovery probability), n = participants

Category Overload Index: COI = actual_categories / optimal_max_categories

#### Assumptions & References

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References

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