# University Seat Allocation Calculator

> Divide a programme’s seats among categories by percentage quota using the largest-remainder method or round-down, with leftover seats shown as open.

Category: Education · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/university-seat-allocation-calculator

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.

## Inputs
- Total seats (intake) (default 50)
- Categories and quotas (one per line: name, %) (default Category A 27
Category B 15
Category C 7.5)
- Fractional seats (options: Largest remainder (Hamilton), Round each category down, rest open; default largest_remainder)

## Results
- Seats by category
- Seats in listed categories
- Open / unreserved seats
- Open share

## Formula

```
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)
```

Where:
- Share: a category’s percentage; the remainder up to 100% is the open category
- Quota: the exact, usually fractional, seat entitlement

## Worked example
1. Quotas: A 13.5, B 7.5, C 3.75, open (50.5%) 25.25.
2. Round down: 13 + 7 + 3 + 25 = 48, leaving 2 seats.
3. 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.

## What the result means

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 and limits
- Quotas are percentages of the total intake, applied at the same time.
- Horizontal (within-category) reservations, supernumerary seats and carry-forward rules are not modelled.

## Questions

### What is the largest remainder method?

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.

### Why do the two methods give different answers?

Round-down moves every fraction into the open category, so listed categories can get slightly fewer seats than their exact quota.

## Related calculators
- [Percentage Calculator](https://calculators.geekmidst.com/calculators/percentage-calculator)
- [Classroom Capacity Calculator](https://calculators.geekmidst.com/calculators/classroom-capacity-calculator)
- [Ratio Calculator](https://calculators.geekmidst.com/calculators/ratio-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/university-seat-allocation-calculator