Ancestor Generation Calculator

ANA›Life Services Authority›National Calculator Authority›Ancestor Generation 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; } }

Ancestor Generation Calculator

Calculate the total number of ancestors at a specific generation, cumulative ancestors, or the relationship between two people based on generational distance.

### Mode

Calculation Type:

Ancestors at Generation N Cumulative Ancestors up to Generation N Relationship by Generational Distance Closest Common Ancestor

Generation Number (N):

Generation 0 = yourself, 1 = parents, 2 = grandparents, etc.

Average Number of Parents per Person:

Use 2 for standard biological ancestry.

Your Generation Distance to Common Ancestor:

Other Person's Generation Distance to Common Ancestor:

Example: You and a first cousin both have a grandparent (distance=2) as common ancestor.

Person A's Generation (from you):

Person B's Generation (from you):

Enter how many generations above/below you each person is (0 = same generation as you).

Calculate Results will appear here.

function ancUpdateMode() { var mode = document.getElementById('anc-mode').value; document.getElementById('anc-panel-gen').style.display = (mode === 'ancestors_at' || mode === 'cumulative') ? '' : 'none'; document.getElementById('anc-panel-rel').style.display = (mode === 'relationship') ? '' : 'none'; document.getElementById('anc-panel-common').style.display = (mode === 'common_ancestor') ? '' : 'none'; document.getElementById('anc-result').innerHTML = 'Results will appear here.'; }

function ancGetInt(id, label, min, max) { var val = document.getElementById(id).value.trim(); if (val === '' || isNaN(val)) throw label + ' must be a number.'; var n = parseInt(val, 10); if (n max) throw label + ' must be between ' + min + ' and ' + max + '.'; return n; }

function ancRelationshipLabel(a, b) { // a = distance from person A to common ancestor // b = distance from person B to common ancestor // cousin degree = min(a,b) - 1, removal = |a - b| if (a === 1 && b === 1) return 'Siblings'; if (a === 1 && b === 2) return 'Uncle/Aunt – Nephew/Niece'; if (a === 2 && b === 1) return 'Uncle/Aunt – Nephew/Niece'; if (a === 1 && b >= 3) return 'Great-' + 'Great-'.repeat(b-3) + (b===3?'':'') + 'Grand Uncle/Aunt – Grand Nephew/Niece'; if (b === 1 && a >= 3) return 'Great-' + 'Great-'.repeat(a-3) + (a===3?'':'') + 'Grand Uncle/Aunt – Grand Nephew/Niece';

var minD = Math.min(a, b); var removal = Math.abs(a - b); var degree = minD - 1;

if (degree N = ' + p + '' + n + ' = ' + count.toLocaleString() + '

' + (n >= 30 && p === 2 ? '⚠️ At generation 30+, ancestor counts exceed world population — pedigree collapse (shared ancestors) is certain.

' : '');

} else if (mode === 'cumulative') { var n = ancGetInt('anc-gen', 'Generation N', 0, 64); var p = ancGetInt('anc-parents', 'Parents per person', 1, 4); // Cumulative ancestors from gen 1 to gen N (excluding yourself at gen 0) // Sum = p^1 + p^2 + ... + p^N = p(p^N - 1)/(p - 1) for p != 1 // For p = 1: sum = N var total; if (p === 1) { total = n; } else { total = p * (Math.pow(p, n) - 1) / (p - 1); } var rows = ''; var running = 0; for (var i = 1; i ' + i + '' + atGen.toLocaleString() + '' + running.toLocaleString() + ''; } if (n > 15) rows += '... (showing first 15 generations)'; resultDiv.innerHTML = '### Cumulative Ancestors up to Generation ' + n + ' ' + 'Total Ancestors (Generations 1–' + n + '):* ' + total.toLocaleString() + '

' + 'Formula: Σ pi for i=1 to N = p(pN−1)/(p−1)

' + 'GenerationAncestors at GenCumulative Total' + rows + '' + (n >= 33 && p === 2 ? '⚠️ Theoretical count exceeds Earth's estimated total humans ever born (~108 billion). Real trees have pedigree collapse.

' : '');

} else if (mode === 'relationship') { var a = ancGetInt('anc-gen-a', 'Your distance to common ancestor', 1, 30); var b = ancGetInt('anc-gen-b', 'Other person's distance', 1, 30); var label = ancRelationshipLabel(a, b); var r = ancDNACoefficient(a, b); var pct = (r * 100).toFixed(4); var cM_approx = (r * 6800).toFixed(0); // ~6800 cM total genome resultDiv.innerHTML = '### Relationship Result ' + 'Relationship: ' + label + '

' + 'Coefficient of Relationship (r): (1/2)' + a + '+' + b + ' = (1/2)' + (a+b) + ' ≈ ' + r.toFixed(6) + ' (' + pct + '%)

' + 'Approximate Shared DNA: ~' + cM_approx + ' cM (centimorgans)

' + 'Your distance to common ancestor: ' + a + ' generation(s)

' + 'Other person's distance: ' + b + ' generation(s)

' + 'Note: r = (1/2)a+b assumes no inbreeding and standard diploid inheritance.

';

} else if (mode === 'common_ancestor') { var ga = ancGetInt('anc-person-a', 'Person A generation', 0, 30); var gb = ancGetInt('anc-person-b', 'Person B generation', 0, 30); // Generational distance between two people relative to you: // If both are at generation ga and gb from you, their distance from each other // depends on their relationship to you. // Simplest interpretation: both descend from you (or share you as ancestor). // Distance between them = ga + gb (if you are their common ancestor) // Closest common ancestor generation = max(ga, gb) from you var distFromYou = ga + gb; var closestCommonGen = Math.max(ga, gb); var r = Math.pow(0.5, distFromYou); var label2 = ancRelationshipLabel(ga === 0 ? 1 : ga, gb === 0 ? 1 : gb); resultDiv.innerHTML = '### Common Ancestor Analysis ' + 'Person A: ' + ga + ' generation(s) from you

' + 'Person B: ' + gb + ' generation(s) from you

' + 'Generational Distance Between A and B: ' + distFromYou + ' steps (through you as common ancestor)

' + 'Closest Common Ancestor: ' + closestCommonGen + ' generation(s) above the closer person

' + 'Approximate Relationship (A↔B): ' + label2 + '

' + 'Coefficient of Relationship (r): (1/2)' + distFromYou + ' ≈ ' + r.toFixed(6) + ' (' + (r*100).toFixed(4) + '%)

' + 'Assumes you are the most recent common ancestor of A and B.

'; }

} catch(e) { resultDiv.innerHTML = '⚠️ ' + e + '

'; } }

#### Formulas Used

• Ancestors at Generation N: A(N) = pN, where p = number of parents (typically 2)
• Cumulative Ancestors (Gen 1 to N): Σ pi = p(pN − 1) / (p − 1) for p ≠ 1
• Coefficient of Relationship: r = (1/2)a + b, where a and b are each person's generational distance to their closest common ancestor
• Cousin Degree: Degree = min(a, b) − 1; Removal = |a − b|
• Approximate Shared DNA: cM ≈ r × 6,800 cM (total human genome length)

#### Assumptions & References

• The coefficient of relationship formula r = (1/2)a+b assumes no inbreeding and autosomal (non-sex-linked) inheritance.
• References: Wright, S. (1922). "Coefficients of Inbreeding and Relationship." American Naturalist. | ISOGG Wiki: Coefficient of Relationship.

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