Percentages turn up everywhere: sale tags, tax receipts, exam marks, pay rises, interest rates and news headlines. The word simply means "per hundred", so 25% is 25 out of every 100, or one quarter. Once you see a percentage as a fraction with 100 on the bottom, almost every percentage question becomes a short multiplication or division.
In practice you only need three formulas. This guide explains each one with worked examples, covers reverse percentages and the classic traps, and shows how they apply to discounts and sales tax. If you just want the answer, our percentage calculator handles all three question types instantly.
How do you find a percentage of a number?
To find X% of a number, convert the percentage to a decimal by dividing by 100, then multiply. For example, 15% of 80 is 0.15 × 80 = 12. The same method works for any value: 7.5% of 2,000 is 0.075 × 2,000 = 150.
For mental math, it helps to build from easy pieces. 10% of a number is found by moving the decimal point one place left, 5% is half of that, and 1% is moving it two places. So 15% of 80 is 8 (10%) plus 4 (5%), which gives 12. Tipping, quick discounts and rough tax estimates all become easy this way.
How do you work out what percentage one number is of another?
To express a part as a percentage of a whole, divide the part by the whole and multiply by 100. If you scored 18 out of 24 on a test, your mark is 18 ÷ 24 × 100 = 75%.
This is really a fraction-to-percentage conversion. 18/24 simplifies to 3/4, and 3/4 as a decimal is 0.75, or 75%. If you are working with awkward fractions such as 3/8, our fraction calculator gives the decimal (0.375), which you then multiply by 100 to get 37.5%.
How to calculate percentage increase and decrease
Percentage change compares a new value with an original value: (new − old) ÷ old × 100. A positive result is an increase and a negative result is a decrease. If a price rises from 50 to 65, the change is (65 − 50) ÷ 50 × 100 = 30%.
The starting value always goes on the bottom, which is why changes are not symmetrical. If the same price falls back from 65 to 50, the change is (50 − 65) ÷ 65 × 100 ≈ −23.08%, not −30%. The difference is 15 in both cases, but it is measured against a different base.
- Increase: a salary going from 40,000 to 42,000 is a 5% rise.
- Decrease: a weight going from 80 kg to 76 kg is a 5% drop.
- Doubling is a 100% increase; halving is a 50% decrease.
Reverse percentages: finding the original number
Sometimes you know the result and the percentage but not the starting value. If 45 is 60% of a number, divide by the percentage as a decimal: 45 ÷ 0.60 = 75. Check it by going forward: 60% of 75 is 45.
Reverse percentages are essential for prices that already include tax. If a receipt shows 107 including 7% sales tax, the pre-tax price is 107 ÷ 1.07 = 100, not 107 minus 7% of 107 (which would give 99.51). Our sales tax and VAT calculator adds or removes tax this way, so you can see the net amount, the tax and the gross amount side by side.
Percentages in shopping: discounts and stacked offers
A discount is a percentage decrease. To find a sale price directly, multiply by what is left: 25% off 80 means paying 75%, so 0.75 × 80 = 60. This one-step method is faster than working out the discount and subtracting it.
Stacked discounts are applied one after another, so they do not simply add up. "20% off, then an extra 10% off" on a 200 item gives 200 × 0.80 × 0.90 = 144, which is a total discount of 28%, not 30%. The discount calculator handles stacked offers and optional tax for you.
Common percentage mistakes to avoid
Most percentage errors come from using the wrong base or treating different kinds of change as if they were the same. Watch out for these frequent slips:
- Undoing a change with the same percentage: a 20% rise followed by a 20% fall leaves you at 96% of the start, not 100%.
- Confusing percent with percentage points: a rate moving from 4% to 5% is a rise of 1 percentage point, but a 25% increase in the rate itself.
- Adding stacked discounts: 20% plus 10% off is 28% off, because the second discount applies to a smaller price.
- Removing tax by subtracting the rate: divide by (1 + rate) instead of subtracting the rate from the total.
- Averaging percentages from groups of different sizes without weighting them by the group size.
Where else percentages matter
Interest rates are percentages too, and the same ideas carry over. An annual rate of 12% becomes a monthly rate of 1% when it is divided by 12, which is exactly how loan payments are worked out in our guide on how loan EMI is calculated. Understanding the base also helps you read statistics in the news, where a "50% increase" in a rare event can still mean a very small number.
Percentages are just one of several everyday calculations that are easier with a tool to check your working. Explore our other math calculators for averages, fractions and random numbers.
Key takeaways
- X% of a number: divide X by 100 and multiply by the number.
- Part as a percentage of a whole: part ÷ whole × 100.
- Percentage change: (new − old) ÷ old × 100, always using the original value as the base.
- To remove a percentage that was added, divide by (1 + rate) rather than subtracting.
- Successive percentage changes multiply; they do not add.