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How to calculate percentages (with the formulas you actually need)

The four percentage calculations everyone uses — X% of Y, what percent, percentage change and reverse percentages — with worked examples and common traps.

· 5 min read

Almost every everyday percentage question is one of four calculations: a share of a total, a ratio expressed out of 100, a change between two values, or working backwards from a value that already includes a percentage. Once you can tell which of the four you are looking at, the arithmetic takes a few seconds.

The quickest route here: open the Percentage calculator, pick the phrasing that matches your question and read the result. Everything below explains what it is doing, so you can check the answer or do it on paper.

The four calculations at a glance

Question Formula Example
What is X% of Y? Y × X ÷ 100 15% of 64 = 9.60
X is what percent of Y? X ÷ Y × 100 42 out of 60 = 70%
By what percentage did it change? (new − old) ÷ old × 100 750 → 800 = +6.67%
What was it before the change? final ÷ (1 + p ÷ 100) 96 after +20% = 80

1. What is X% of Y?

Y × X ÷ 100. What is 15% of 64? → 64 × 15 ÷ 100 = 9.60. Per cent means "per hundred", so 15% is simply the fraction 15/100, and "of" means multiply.

2. X is what percent of Y?

X ÷ Y × 100. 42 correct answers out of 60? → 42 ÷ 60 × 100 = 70%. The number after "of" is the one you divide by. Get that backwards and 42 out of 60 becomes 143%, which is the usual sign that the two numbers have been swapped.

3. By what percentage did it change?

(new − old) ÷ old × 100. Rent went from 750 to 800? → 50 ÷ 750 × 100 = +6.67%. A negative result is a decrease. The Percentage increase and Percentage decrease calculators handle both directions and show the absolute difference alongside the percentage.

4. What was the price before the percentage?

final ÷ (1 + p ÷ 100). A price is 96 after a 20% increase — what was it before? → 96 ÷ 1.20 = 80. Not 96 − 20% = 76.80. The percentage was applied to the original value, not to the final one, so you divide rather than subtract. The same logic recovers a pre-discount price: an item sold at 1,170 after 10% off started at 1,170 ÷ 0.90 = 1,300.

Trap 1: percentages do not add up

A 30% discount followed by an extra 10% is not 40% off. The second discount applies to the already reduced price: 0.70 × 0.90 = 0.63, so the total reduction is 37%. Stack three reductions of 20%, 10% and 5% and you get 0.80 × 0.90 × 0.95 = 0.684, a 31.6% reduction rather than 35%. The Discount calculator applies reductions in sequence for you.

The same effect works against you in reverse: a price that rises 6% and then falls 6% does not return to where it started. 1,200 × 1.06 × 0.94 = 1,195.68, about 0.36% below the original.

Trap 2: up and down are not symmetrical

A share price falls 50% (100 → 50) and then rises 50% (50 → 75). You are still 25% down. To get back to 100 from 50 you need a 100% rise, because the base has changed. The bigger the fall, the larger the rise needed to undo it.

Trap 3: percent versus percentage points

An interest rate going from 2% to 3% rises by 1 percentage point, which is a 50% increase. Both statements are true and they describe the same event. News reports, and sometimes contracts, mix the two, so it is worth checking which one is meant before you react to a number.

Trap 4: choosing the base when there is no "original"

Percentage change assumes one value came first. When neither did — two quotes, two measurements, two suppliers — dividing by either one gives a different answer: 180 and 200 differ by 11.11% if you start from 180 and by 10% if you start from 200. The Percentage difference divides by the average of the two instead, which gives a single symmetrical figure of 10.53%.

Rounding: where the missing cent comes from

Percentages rarely land on whole cents. Three items at 12.42, 12.31 and 11.72 carry VAT at 20% of 2.48, 2.46 and 2.34 once each line is rounded — 7.28 in total. Apply the rate to the sum instead (36.45 × 0.20) and you get 7.29. Neither is wrong; they use different rounding points. Accounting systems pick one rule and apply it everywhere, which is why an invoice total can differ by a cent from your own check.

Keep full precision until the last step when you can, and round once at the end.

Two shortcuts worth knowing

Build from 10% and 1%. 10% of 86 is 8.6 and 1% is 0.86, so 15% is 8.6 + (5 × 0.86) = 12.90.

X% of Y equals Y% of X. 18% of 50 is awkward; 50% of 18 is 9, and it is the same number. 4% of 75 is the same as 75% of 4 = 3.

Where percentages show up

Situation What to calculate Tool
Sale price, stacked offers Successive reductions Discount
Net and gross prices Add or remove a tax rate VAT
Pay rise, price change Percentage change Percentage increase
Comparing two figures Percentage difference Percentage difference

Removing a tax from a price is calculation 4 above, applied to a rate: the guide VAT explained covers the formulas and the country rates. When a percentage is applied over and over — savings, inflation, investment returns — the result stops being linear, which is what How compound interest works is about.

Questions people ask

What does "percentage of a percentage" mean? Multiply the two fractions. 25% of 40% is 0.25 × 0.40 = 0.10, or 10%.

Can a percentage be over 100? Yes, whenever the part is larger than the base. A price going from 20 to 50 is a 150% increase. Percentages of a whole, such as a share of a budget, should not exceed 100.

How do I turn a fraction into a percentage? Divide, then multiply by 100. 2 ÷ 7 = 0.2857, so 28.57%.

Why does the calculator show 6.67% and not 6.7%? Results are computed at full precision and rounded only for display. The underlying value here is 6.666…%, which never terminates.

Next steps

Tools used in this guide

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