The Four Percentage Calculations People Get Wrong

Percentages are the arithmetic of daily life — discounts, raises, VAT, statistics — and four specific cases account for nearly every mistake.

1. Percentage of a number

value = base × pct ÷ 100. 18% of 4,500 is 810. Simple, and rarely wrong.

2. Increase and decrease

Increase: base × (1 + pct/100). Decrease: base × (1 − pct/100). The trap is chaining them. A price falls 20% from 100 to 80; a 20% rise on 80 gives 96, not 100. To recover a 20% fall you need a 25% rise, because the base changed. The general rule: to undo a drop of p, you need p / (1 − p).

3. Percentage difference between two numbers

(new − old) ÷ old × 100. The denominator is always the original value. Reversing it is how a report ends up claiming a 50% growth that was really 33%.

4. Reverse percentage

You paid 12,700 including 27% VAT, or bought at 30% off for 210. Divide, do not subtract: original = paid ÷ (1 − 0.30) = 300. The percentage calculator handles all four directions, and the VAT calculator applies the same logic specifically to tax.

Percentage points vs percent

An interest rate moving from 4% to 6% has risen by two percentage points — and by 50%. Both are true; only one is usually meant. In writing, always say which.

A sanity habit

Before accepting any percentage result, estimate it. Ten percent is a decimal shift; half of that is 5%; a quarter of the number is 25%. If the calculated answer is far from the estimate, you have used the wrong base.

FAQ

How do I calculate a margin from a markup? Margin = markup ÷ (1 + markup). A 50% markup is a 33.3% margin.

What is a percentage point? The arithmetic difference between two percentages.

Can percentages exceed 100%? Yes, for increases. A decrease cannot exceed 100% without going negative.