No piece of everyday maths causes more quiet workplace anxiety than percentages. Not because they’re hard — because three different calculations all answer to the same name, and mixing them up produces confident, wrong numbers. Untangle them once and the panic never comes back.

First, the foundation from the number-formats lesson: a percentage is just a decimal in costume. 25% is 0.25. Excel stores the decimal; the % format displays it. Which is why the formulas below never multiply or divide by 100 — the costume handles the 100, and formulas that do it themselves end up wrong by a factor of exactly that.

Calculation one: X% of something

The easy one — of means multiply:

=B2 * 20%          20% of the amount
=B2 * (1 + 20%)    the amount plus 20% (VAT-style)
=B2 / (1 + 20%)    the amount BEFORE 20% was added

That third line deserves a pause, because it’s the classic trap: to remove VAT from a gross price you divide by 1.2 — you do not multiply by 80%. A £120 gross price is £100 net; multiplying by 0.8 gives £96, confidently wrong by £4. The rule: undoing a percentage increase is a division, because the increase was applied to the smaller number, not the one you’re holding.

Calculation two: percent change

The one in every monthly report — how different is new from old?

=(new - old) / old

The mnemonic is “difference over original” — and the denominator is always the old value, because the question is “changed from what?”. Format the result as a percentage (Ctrl+1) and the costume shows +8.3% or −4.1% untouched.

£100 £125 £100 +25% −20% up 25%, then down only 20% — and you're exactly back where you began
Rises and falls aren't symmetric: +25% then −25% would leave you below the start. The denominator changed under you — that's the whole trick.

That asymmetry in the figure is worth internalising: a 50% loss needs a 100% gain to recover, because the recovery is measured from the smaller base. It explains everything from investment maths to why “we cut prices 30%, then raised them 30%” loses money.

Calculation three: percentage points

The subtle one, and the favourite of misleading headlines. When a rate moves from 4% to 6%, it has risen two percentage points — but 50 per cent ((6−4)/4). Both statements are true; they answer different questions. In a sheet this bites when someone computes percent-change on numbers that are already percentages: margin moving 30% → 33% is “+3 pts” (a subtraction) or “+10%” (difference over original). Label which one you mean — pts vs % in the header — and you’ll never watch a meeting argue about a number that both sides computed correctly.

The percent-of-total pattern

The other workhorse: each row as a share of the whole.

=B2 / SUM($B$2:$B$500)

The denominator wears full pins so it survives the copy-down — or, in a Table, =[@Amount]/SUM([Amount]), no pins needed. Sanity check: the shares must sum to 100%. If they show 99.9%, that’s display rounding, not an error — resist “fixing” a share by hand, which creates a real one.

And when the percentages themselves need averaging — careful. The average of 10% and 50% is not 30% if one was 10% of ten thousand and the other 50% of ten. Never average percentages with different bases; recompute from the underlying sums (one SUMIFS over each, then divide). The percentage is a view of two numbers; when in doubt, go back to the numbers.

Three calculations, one costume, one asymmetry. Percentages don’t get easier than that — they were never hard; they were just three things wearing one name.