How to use this calculator
- Enter or choose total seats (intake).
- Enter or choose categories and quotas (one per line: name, %).
- Enter or choose fractional seats.
- The seats by category updates as you type. Use Copy result or Share to keep it.
Method
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)
- Share
- a category’s percentage; the remainder up to 100% is the open category
- Quota
- the exact, usually fractional, seat entitlement
Worked example
- 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.
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.