Percentage calculator
Work out a percentage of a number, express one number as a percentage of another, or find the percentage increase or decrease between two values.
Answer
30
15% of 200
Working: (15 ÷ 100) × 200
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The three questions
Almost every percentage problem is one of three shapes, and this calculator handles each separately so you can pick the one matching how you would say it out loud.
“What is 15% of 200?” Convert the percentage to a decimal and multiply.
result = (percentage ÷ 100) × number
15% of 200 → (15 ÷ 100) × 200 = 30“30 is what percent of 200?” Divide the part by the whole, then scale to 100.
result = (part ÷ whole) × 100
(30 ÷ 200) × 100 = 15%“What is the change from 200 to 260?” Take the difference, divide by the starting value.
result = ((new − old) ÷ |old|) × 100
((260 − 200) ÷ 200) × 100 = +30%The third is where mistakes cluster, because it matters enormously which number you divide by. Dividing by the new value instead gives 23%, which is a different - and wrong - answer to the question asked.
Everyday applications
A discount. A $80 jacket at 25% off: 25% of 80 is $20, so you pay $60. Faster: multiply by 0.75 directly.
A tip. For 18% on a $64 bill, take 10% ($6.40), halve it for 5% ($3.20), then take a fifth of the 10% for 2% ($1.28). Total $10.88. Mental percentage arithmetic is almost always easier in pieces.
Sales tax added. $250 plus 8.25% tax: multiply by 1.0825 to get $270.63.
Removing tax. A $270.63 total including 8.25% tax: divide by 1.0825 to get $250. This is the operation people most often get wrong.
Interest and growth. A salary rising from $58,000 to $61,500 is a 6.03% increase. A price falling from $1.85 to $1.42 is a 23.2% decrease.
A caution about averaging percentages
You cannot average percentages unless the bases are identical. If a shop converts 10% of 1,000 visitors on Monday and 20% of 100 visitors on Tuesday, the combined rate is not 15%. It is (100 + 20) ÷ 1,100 = 10.9%. Always return to the raw counts before combining.
Percentage points versus percent
This distinction carries real money. If a fund’s fee rises from 0.5% to 0.75%, that is 0.25 percentage points - and a 50% increase in what you pay. Whichever framing a seller chooses usually tells you which direction they want you to look.
Common questions
Why does a 50% fall need a 100% rise to recover?
Because each percentage is measured against a different base. A stock falling from $100 to $50 loses 50% of $100. Climbing back to $100 means gaining $50 on a base of $50, which is 100%. Percentage changes are not symmetric, and this asymmetry is why a portfolio that drops 50% needs to double just to break even.
What is the difference between percentage points and percent?
If a rate moves from 4% to 6%, that is a rise of 2 percentage points but a 50% increase. Both are correct and they describe different things. News reports mixing them up is one of the most common sources of misleading statistics.
How do I remove a percentage that has already been added?
Divide, do not subtract. To strip 20% VAT from a $120 total, divide by 1.2 to get $100 - subtracting 20% of $120 would wrongly give $96. The general rule is to divide by (1 + rate ÷ 100).
How do I apply two discounts in a row?
Multiply the remaining fractions rather than adding the discounts. 20% off then 10% off leaves 0.8 × 0.9 = 0.72, so 28% off in total - not 30%. Stacked discounts are always worth less than their sum.
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