{
    "name": "University Seat Allocation Calculator",
    "url": "https://calculators.geekmidst.com/calculators/university-seat-allocation-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/university-seat-allocation-calculator.md",
    "category": "Education",
    "description": "Divide a programme’s seats among categories by percentage quota using the largest-remainder method or round-down, with leftover seats shown as open.",
    "summary": "Quotas rarely divide into whole seats. This applies your category percentages and settles the fractions transparently, by largest remainder or by rounding every category down.",
    "also_called": [
        "Seat matrix calculator",
        "Quota seat calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "total_seats",
            "label": "Total seats (intake)",
            "type": "number",
            "default": "50"
        },
        {
            "name": "categories",
            "label": "Categories and quotas (one per line: name, %)",
            "type": "textarea",
            "default": "Category A 27\nCategory B 15\nCategory C 7.5"
        },
        {
            "name": "method",
            "label": "Fractional seats",
            "type": "select",
            "default": "largest_remainder",
            "options": {
                "largest_remainder": "Largest remainder (Hamilton)",
                "floor": "Round each category down, rest open"
            }
        }
    ],
    "outputs": [
        {
            "key": "allocation",
            "label": "Seats by category",
            "format": "text"
        },
        {
            "key": "reserved_seats",
            "label": "Seats in listed categories",
            "format": "integer"
        },
        {
            "key": "open_seats",
            "label": "Open / unreserved seats",
            "format": "integer"
        },
        {
            "key": "open_share",
            "label": "Open share",
            "format": "percent"
        }
    ],
    "formula": {
        "text": "Quota = Seats × Share ÷ 100;  each category first gets ⌊Quota⌋;  remaining seats go one each to the largest fractional parts (ties: larger quota first, then list order)",
        "variables": {
            "Share": "a category’s percentage; the remainder up to 100% is the open category",
            "Quota": "the exact, usually fractional, seat entitlement"
        }
    },
    "worked_example": {
        "inputs": {
            "total_seats": "50",
            "categories": "Category A 27\nCategory B 15\nCategory C 7.5",
            "method": "largest_remainder"
        },
        "steps": [
            "Quotas: A 13.5, B 7.5, C 3.75, open (50.5%) 25.25.",
            "Round down: 13 + 7 + 3 + 25 = 48, leaving 2 seats.",
            "Largest remainders: C (0.75), then A and B tie at 0.5 and A’s larger quota wins: A 14, B 7, C 4, open 25."
        ],
        "result": "Of 50 seats, categories A, B and C get 14, 7 and 4, and 25 seats stay open."
    },
    "interpretation": "Many admission rules specify their own rounding (for example rounding each category down, or carrying fractions across years). Use the method your rules require; the table shows exact quotas so you can audit either.",
    "assumptions": [
        "Quotas are percentages of the total intake, applied at the same time."
    ],
    "limitations": [
        "Horizontal (within-category) reservations, supernumerary seats and carry-forward rules are not modelled."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "What is the largest remainder method?",
            "answer": "Give each category its whole-number quota, then hand the leftover seats one by one to the categories with the biggest fractions. It keeps every category within one seat of its exact quota."
        },
        {
            "question": "Why do the two methods give different answers?",
            "answer": "Round-down moves every fraction into the open category, so listed categories can get slightly fewer seats than their exact quota."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Percentage Calculator",
            "url": "https://calculators.geekmidst.com/calculators/percentage-calculator"
        },
        {
            "name": "Classroom Capacity Calculator",
            "url": "https://calculators.geekmidst.com/calculators/classroom-capacity-calculator"
        },
        {
            "name": "Ratio Calculator",
            "url": "https://calculators.geekmidst.com/calculators/ratio-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}