What is a percentage?

What a percentage is

A percentage is a way of expressing a part of a whole in hundredths. The % symbol means "per hundred", that is, "out of every hundred". When we say 20%, we mean 20 out of every 100, i.e. the fraction 20/100 = 0.20¹. So any percentage becomes a decimal once you divide it by 100, and that decimal is what we use in the sums.

Percentages are behind almost everything involving money: the interest rate on a deposit or a loan, the VAT rate on a purchase, the income tax rate on a salary, a discount in a shop or a pay rise. Knowing how to do these sums is the foundation of financial literacy.

What is a percentage of a value

The most common sum is finding how much X% of a value is. Divide the percentage by 100 and multiply by the value:

X% of a value = X ÷ 100 × value

So 20% of 100 is 0.20 × 100 = 20; and 23% of €1,500 (Portugal’s mainland standard VAT rate) is 0.23 × 1,500 = €345. It is the same sum for a commission, a tip or tax withholding.

What percentage one value is of another

The other way round, to find what percentage the part is of the total, divide the part by the total and multiply by 100:

percentage = part ÷ total × 100

If you spend €300 on rent out of a €1,200 income, the rent is 300 ÷ 1,200 × 100 = 25% of your income. This is how you see the weight of each cost in your budget, a central idea in the 50/30/20 rule.

The percentage change between two values

The percentage change measures how much a value rose or fell, relative to the starting point:

change = (ending value − starting value) ÷ starting value × 100

From €100 to €125 there is a +25% rise; from €200 to €150, a −25% fall. This is how you read inflation, a pay rise or an investment’s return. Note the important detail: the change is always measured on the starting value, not the ending one.

Increase or decrease a value by a percentage

To apply an increase or a discount, add or subtract the percentage of the value itself:

increase: value × (1 + X ÷ 100) · decrease: value × (1 − X ÷ 100)

A 30% discount on €80 leaves 80 × 0.70 = €56; a 23% rise on €1,000 gives 1,000 × 1.23 = €1,230. You can run any of these sums in the percentage calculator.

The most common mistakes

Three traps catch a lot of people:

1. Adding percentages from different bases. Two successive discounts of 20% and 10% are not 30%. The second applies to the already-reduced value, so the total discount is 28%.
2. Confusing percentage points with percentage. Raising a rate from 4% to 5% is a rise of 1 percentage point, but 25% in relative terms.
3. Assuming a discount and the equivalent rise cancel out. Taking off 30% and adding it back does not return the original value, because the base changed: €80 with -30% is €56, and €56 with +30% is only €72.80. To get from €56 back to €80 you would need a rise of about +42.9%.

Where percentages are used

Once you master these four sums, every other calculator becomes clearer: VAT is a percentage of the price, compound interest is a percentage applied repeatedly, the profit margin is a percentage of the selling price and inflation is the percentage change in prices. To do any of these percentage sums quickly, use the percentage calculator.