Discount, tip, increase and tax.
Discount, tip, increase and tax.
This calculator handles the three most common percentage questions in one tool. Use What is X% of Y? for calculating discounts, tips, and tax amounts. Use X is what percent of Y? to find a rate or ratio. Use Percentage change to calculate growth rates, price changes, and comparing two values over time. All results update instantly as you type.
Finding a percentage of a number: Multiply the number by the percentage expressed as a decimal. 15% of $240 = 240 ร 0.15 = $36. This handles tips, discounts, commissions, tax calculations, and investment returns.
Finding what percentage one number is of another: Divide the part by the whole, then multiply by 100. If 35 out of 200 students passed, the pass rate is (35 รท 200) ร 100 = 17.5%.
Percentage change: Subtract the old value from the new value, divide by the old value, multiply by 100. A stock that went from $48 to $63 increased by (63 โ 48) รท 48 ร 100 = 31.25%.
Percentages don't add symmetrically. A 50% drop followed by a 50% gain does NOT return you to the original value. Starting at $100, a 50% drop takes you to $50. A 50% gain on $50 only brings you back to $75 โ you're still down 25%. This asymmetry is why investment losses are harder to recover from than people expect.
Percentage of a percentage. An interest rate that rises from 2% to 3% has increased by 1 percentage point, but by 50% in relative terms. Financial reporting uses both forms โ make sure you know which one is being cited.
Almost every percentage problem is one of three forms, and knowing which you are solving prevents most errors.
What is X% of Y? Multiply: 15% of 80 is 0.15 × 80 = 12.
X is what percent of Y? Divide and multiply by 100: 12 is 12 ÷ 80 = 15% of 80.
X is P% of what? Divide: if 12 is 15% of something, that something is 12 ÷ 0.15 = 80.
The third form is the one people get wrong most often, because the instinct is to multiply rather than divide.
To find the change between two values:
Change % = (New − Old) ÷ Old × 100
The denominator must be the original value. This is the source of the most common percentage error there is: a rise from 40 to 50 is a 25% increase, but a fall from 50 to 40 is a 20% decrease. Same absolute change, different base, different percentage.
It follows that a 50% loss requires a 100% gain to recover. A stock falling from $100 to $50 has lost half; returning to $100 requires doubling. This asymmetry is why large losses are so much more damaging than equivalent-sized gains are helpful.
These are different and are frequently conflated, sometimes deliberately.
If an interest rate rises from 4% to 6%, that is an increase of 2 percentage points, or a 50% increase in the rate. Both statements are true and they sound very different, which is why the choice of framing matters in reporting.
The same applies to stacked percentages. Two consecutive 10% increases are not a 20% increase — they are 21%, because the second applies to the already-increased figure. And a 20% increase followed by a 20% decrease leaves you at 96% of where you started, not back to even.
Move the decimal one place left to get 10%, then double it for 20%. On a $73 bill: 10% = $7.30, doubled = $14.60. For 15%, find 10% ($7.30), take half of that ($3.65), and add them: $10.95.
A percentage point is an absolute difference between two percentages. If unemployment rises from 4% to 6%, it rose by 2 percentage points โ but by 50% in relative terms (2 รท 4 = 0.5). The distinction matters enormously in finance, economics, and politics where small changes in rates are reported both ways.
If an item is marked down 25% and now costs $90, the original price was $90 รท (1 โ 0.25) = $90 รท 0.75 = $120. Don't make the mistake of adding 25% back to $90 โ that gives you $112.50, which is wrong.