Percentage Calculator

Three tools in one: percent of a number, percentage ratio, and percentage change.

The three percentage formulas

Percent of a number: multiply the number by the percentage and divide by 100. So 15% of 200 = 200 × 15 ÷ 100 = 30. Use this for discounts, tips, tax and commission.

Percentage ratio: divide the part by the whole and multiply by 100. Scoring 30 out of 120 means 30 ÷ 120 × 100 = 25%. Use this for exam marks, market share and progress tracking.

Percentage change: subtract the old value from the new, divide by the old value, and multiply by 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = a 25% increase. Use this for price changes, salary raises and growth rates.

Percentages in everyday life

Percentages appear everywhere: exam scores, shop discounts, bank interest, sales tax and VAT, tips, commission and statistics in the news. Mastering the three core operations — a percentage of a number, one number as a percentage of another, and percentage change — covers almost every real situation you will meet.

Common percentage mistakes to avoid

Two traps catch most people. First, a percentage increase and decrease of the same size don't cancel: +50% then −50% leaves you below where you started. Second, "percentage points" and "percent" are different — moving from 10% to 15% is a rise of 5 percentage points but a 50% increase. Reading these carefully prevents costly errors in finance and grades.

Percentage increase and decrease, step by step

This is the calculation people get wrong most often, because the answer depends entirely on which number you treat as the starting point. The formula is ((new − old) ÷ old) × 100. The old value always goes on the bottom.

Say a salary rises from 40,000 to 46,000. The change is 6,000, and 6,000 ÷ 40,000 = 0.15, so that is a 15% increase. Now run it backwards: if it falls from 46,000 to 40,000, the change is still 6,000, but you divide by 46,000 this time, giving 13.04%. Same two numbers, different answers — because the base changed. This is why a 50% loss needs a 100% gain to recover: losing half of 100 leaves 50, and getting back to 100 means doubling.

Working backwards to the original number

If you know the final figure and the percentage applied, you can recover the starting value — useful for stripping tax out of a total or finding a pre-sale price. Divide rather than multiply: original = final ÷ (1 + rate) for an increase, or final ÷ (1 − rate) for a decrease.

A bill of 1,180 that includes 18% tax started at 1,180 ÷ 1.18 = 1,000. The common error is taking 18% off 1,180, which gives 967.60 — wrong, because that 18% was calculated on 1,000, not on the total. The same logic recovers a pre-discount price: an item at 340 after 15% off was 340 ÷ 0.85 = 400.

Percentage points vs percentages

These are different things and mixing them up changes the meaning entirely. If an interest rate moves from 4% to 6%, that is a rise of 2 percentage points — but a 50% increase in the rate itself. Both statements are true, and they sound very different. News reports and lenders often use the more flattering one, so it is worth checking which measure you are being shown.

Mental shortcuts worth knowing

Most everyday percentages can be done without a calculator once you know a few tricks. 10% is just moving the decimal one place left, and every other round figure builds from there: 5% is half of 10%, 20% is 10% doubled, 15% is 10% plus half of it again. For a 15% tip on 60: 10% is 6, half of that is 3, so 9.

The reversal trick is the most useful one and almost nobody knows it: x% of y equals y% of x. Finding 4% of 75 sounds awkward, but 75% of 4 is obviously 3 — and it is the same answer. Similarly 16% of 25 becomes 25% of 16, which is 4.

Frequently asked questions