Roller Rink: Split A Skate Order Across A Size Curve

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Order 260 pairs of rental skates split across five size runs and you hit the oldest problem in allocation: the rounded parts do not add up to the whole. Here they come to 259. The fix is not to fudge the shares — it is to let the largest line absorb the difference, which is both defensible and one formula.


Quick formula: Round each share, then make one line the plug so the column ties to the order:
=ROUND($B$11*B5,0) and on the largest line =$B$11-SUM(others)

Five size runs against 260 pairs round to 259. The Adult 7–9 line takes the extra pair and the order ties exactly.

Functions used (tap for the full reference guide):

The example

A 260-pair order split across the size curve a rink actually sees on a Saturday.

ABCDE
1Size runShareRaw pairsRoundedFinal order
2Youth 1-312%31.23131
3Youth 4-617%44.24444
4Adult 7-935%91.09192
5Adult 10-1227%70.27070
6Adult 13-159%23.42323
7TOTAL100%260.0259260

The formula

Two columns and one exception, and the exception is the whole point:

=ROUND($B$11*B5,0) then on the plug line =$B$11-SUM(D5:D6)-SUM(D8:D9) // round every line, then make one line the remainder

How it works

Why the plug line is the right answer rather than a hack:

  1. $B$11*B5 is the raw allocation — the order total times that size's share of the curve. Keep the total in one absolute cell so a change to the order re-splits everything at once.
  2. ROUND(...,0) gives whole pairs, because you cannot buy 31.2 skates. Each line rounds independently, and independent rounding is exactly why the column no longer sums to 260.
  3. The plug line takes the remainder: the order total less every other rounded line. Choose the largest share for it — a one-pair adjustment on a 91-pair line is noise, the same adjustment on a 23-pair line is a 4% distortion.
  4. Confirm the total row equals the order. If it does not, either a share is wrong or the plug formula is not excluding itself, which is the classic circular-reference version of this mistake.

Check the shares sum to exactly 100% before anything else. A curve that sums to 99% will look like a rounding problem and is actually a data problem.

Try it: interactive demo

Interactive

Enter an order total and a size share to see the raw, rounded and drift figures.

Variations

Spread the drift instead of plugging one line

When the drift is larger than a pair or two, add one to each of the largest remainders in turn rather than dumping it all on a single size.

=ROUND(Total*Share,0)+IF(RANK(Remainder,Remainders)<=Drift,1,0)

Rebuild the curve from last season

Derive shares from actual rentals rather than a guess: each size's rentals over total rentals is the curve you should be ordering to.

=SizeRentals/SUM(AllRentals)

Pitfalls & errors

Do not point the plug formula at a range that includes itself — =Total-SUM(D5:D9) on row 7 is a circular reference. Sum the two ranges either side of the plug line instead.

Rounding each line independently can drift by more than one unit when there are many lines. With a dozen size runs the drift can reach three or four pairs, at which point spreading it across the largest remainders is fairer than plugging.

Rental fleets skew smaller than retail size curves because children rent and adults often own. Build the curve from your own rental log, not from a manufacturer's retail distribution.

Practice workbook

📊
Download the free Roller Rink: Split A Skate Order Across A Size Curve practice workbook
Edit the yellow share cells and the order total at the bottom; the allocation and the drift fix recalculate.

Frequently asked questions

Which line should be the plug?
The one with the largest share, because a one-unit adjustment there is the smallest proportional distortion. Some finance teams instead plug the line with the largest fractional remainder, which is mathematically tidier; for a skate order the largest-line rule is easier to explain to whoever signs the purchase order.
Can I just round the shares so they add up?
You can, but it moves the problem rather than solving it. Shares are estimates from history; pairs are things you buy. It is cleaner to keep the shares honest and reconcile in the whole-unit column, which is where the constraint actually lives.

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Function references: ROUNDSUM