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📊 Math & Statistics

Why Your Percentages Add Up to 100.1, and How to Make Them Not

Three equal parts are 33.3% each, which sums to 99.9. Rounding each value correctly does not fix it. Largest-remainder allocation does.

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How the calculation works

Three equal parts of one whole rounded independently 33.3% 33.3% 33.3% 99.9% largest remainder 33.4% 33.3% 33.3% 100.0% Each individual rounding on the left is correct. The total still is not.

How to Use This Tool

Paste your values, one per line. You get percentages that sum to exactly 100, with the naive version shown alongside so you can see which entries were adjusted and by how much.

Why the total comes out wrong

Round each percentage on its own and you make a small error each time. Those errors are independent, so they do not cancel — sometimes they all point the same way. Three equal parts each round to 33.3%, and 33.3 × 3 is 99.9.

Nothing is wrong with any individual figure. The problem is that the rounded values are being asked to do something the unrounded ones did automatically: add up.

Largest remainder allocation

The fix is to treat it as an allocation problem rather than a rounding problem:

  1. Round every share down to the chosen precision.
  2. Count how many units are left over from the total.
  3. Hand those units, one at a time, to whichever entries had the largest fractional part discarded.

The result sums exactly, and every value is within one unit of its true share — which is the best any set of rounded numbers can do. This is the same method used to allocate parliamentary seats to parties from vote shares, where the requirement that the total be exact is not negotiable.

How the leftover gets allocated true share 33.33 33.33 33.33 rounded down 33.3 33.3 33.3 total 99.9, so 0.1 is unallocated remainder discarded 0.03 0.03 0.03 final 33.4 33.3 33.3 first entry takes the spare 0.1
With a genuine tie the choice is arbitrary, which is honest and unavoidable.

When the tie is genuinely arbitrary

If several entries have identical remainders, as in the example above, something has to break the tie and any rule is a convention. Order of appearance is used here. That means one entry gets a hundredth of a percent more than an identical one, which is a real if tiny unfairness — and it is unavoidable, because the total must be exact and the extra unit cannot be split.

This is why seat allocation methods are politically contested: with seats instead of hundredths, the same arbitrary choice decides who governs.

When not to force the total

Two cases where 99.9% is the honest answer:

  • The categories overlap or are incomplete. If someone can be counted in two rows, or an "other" bucket is missing, the parts genuinely do not make a whole and forcing them to sum to 100 asserts something false.
  • The figures are estimates with real uncertainty. Adjusting a hundredth to make a column tidy implies a precision that is not there.

Where the parts really are a partition of a whole — a budget, traffic sources, a vote — forcing the total is right, because the underlying quantity does sum exactly and only the display was losing it.

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Frequently Asked Questions

Why don't my percentages add up to 100?
Because each was rounded independently and the errors do not cancel. Three equal parts each round to 33.3%, which sums to 99.9. Every individual figure is correct; the rounded set is simply being asked to add up, which the unrounded values did automatically.
How do I make percentages sum to exactly 100?
Largest remainder allocation: round every share down, count the leftover units, then give them one at a time to whichever entries had the largest fractional part discarded. The total is then exact and every value is within one unit of its true share.
What is the largest remainder method?
An allocation rule that distributes a fixed total among parts without the rounding errors accumulating. It is best known from parliamentary seat allocation, where the number of seats is fixed and the shares must add up exactly — the same constraint a percentage breakdown has.
Is it dishonest to adjust a percentage so the total is 100?
Not when the parts genuinely make a whole, such as a budget or a vote — the underlying quantity does sum exactly and only the display was losing precision. It is misleading when the categories overlap or are incomplete, because then forcing 100 asserts a completeness that does not exist.
What happens when two entries have the same remainder?
Something has to break the tie and any rule is a convention; order of appearance is used here. That gives one entry a fraction more than an identical one, which is a genuine if tiny unfairness and cannot be avoided, because the total must be exact and the spare unit cannot be split.
Should I show percentages to more decimal places instead?
It shrinks the discrepancy without removing it — 33.333% three times is 99.999%. More decimals also imply a precision your data may not have. Allocating the remainder solves the problem at whatever precision you actually want to display.

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