How it works
“Percent” means “per hundred,” so 15% is 15/100 = 0.15. All three modes come from that idea:
1. What is X% of Y?
Result = X ÷ 100 × Y
15% of 80 = 0.15 × 80 = 12.
2. X is what percent of Y?
Percent = X ÷ Y × 100
30 is 25% of 120.
3. Percentage change from X to Y
% change = (Y − X) ÷ |X| × 100
A positive result is an increase and a negative result is a decrease. From 50 to 65 is a 30% increase. The calculator rounds results to four decimal places.
Worked examples
What is 15% of 80?
0.15 × 80 = 12.
45 is what percent of 180?
45 ÷ 180 × 100 = 25%.
Rent goes from $1,850 to $1,980. What is the percentage increase?
(1,980 − 1,850) ÷ 1,850 × 100 = 7.027%.
A stock falls from $64 to $48
(48 − 64) ÷ 64 × 100 = -25%, a 25% decrease. Getting back to $64 requires a 33.3333% gain.
Percentages in personal finance
- Discounts: 25% off a $120 jacket saves $30.00, so you pay $90.00.
- Sales tax: 7% tax on $45 is $3.15, for a total of $48.15.
- Tips: 18% on an $85 restaurant bill is $15.30.
- Raises: going from $62,000 to $65,100 is a 5% raise. Compare it with inflation using the inflation calculator to see whether your real pay went up.
- Savings rate: saving $900 of a $4,500 monthly take-home pay is a 20% savings rate, right on the 50/30/20 target. See the budget calculator.
- Investment returns: a portfolio that grows from $20,000 to $23,400 gained 17%.
Common percentage mistakes
Percentage changes don't cancel out. If a stock falls 50% and then rises 50%, you are not back to even. $100 becomes $50, then $75. To recover from a loss of L%, you need a gain of L ÷ (100 − L) × 100%. A 20% loss needs a 25% gain, and a 50% loss needs a 100% gain.
Percent vs. percentage points. If a mortgage rate rises from 6% to 7%, it rose by 1 percentage point, but by 16.6667% in relative terms. News reports and loan documents use both, so check which one is meant.
Reverse percentages. If a price after a 20% discount is $80, the original price was $80 ÷ 0.80 = $100, not $80 × 1.20 = $96. Divide by (1 − discount), don't multiply by (1 + discount).
Choosing the base. Percentage change always uses the original value as the base. Going from 50 to 65 is +30%, but going from 65 back to 50 is -23.0769%.
Quick mental math tricks
- 10%: move the decimal point one place left. 10% of 340 is 34.
- 5%: half of 10%. 5% of 340 is 17.
- 1%: move the decimal two places left. 1% of 340 is 3.4.
- Swap trick: X% of Y equals Y% of X. 8% of 50 is the same as 50% of 8, which is 4.
- Compounding percentages: two successive 10% increases make 21%, not 20% (1.1 × 1.1 = 1.21). For growth over many periods, use the compound interest calculator.
Percentages vs. fractions and decimals
Every percentage can be written as a decimal (divide by 100) or a fraction: 25% = 0.25 = 1/4, 12.5% = 0.125 = 1/8, 33⅓% ≈ 0.333 = 1/3. Converting to a decimal first makes any percentage calculation a simple multiplication or division.
Percentage change vs. percentage difference
Percentage change has a direction: it measures how much a value moved from an original starting point. Percentage difference compares two values without treating either as the original. It is usually calculated as the absolute difference divided by their average, × 100. Comparing 50 and 65 gives a percentage difference of 26.09%, while the change from 50 to 65 is 30%. Use percentage change for before-and-after comparisons such as prices, salaries and account balances. Use percentage difference when comparing two things side by side, such as two stores' prices.
Annualizing a percentage change
If an investment grew 50% over 5 years, it did not grow 10% a year. The compound annual growth rate (CAGR) is (1.50)1/5 − 1 = 8.45% a year. Dividing a multi-year change by the number of years overstates the annual rate whenever growth compounds. The same logic applies to inflation. Prices rising 34% over 10 years means about 3% a year, not 3.4%.
Percentages of percentages
Stacking discounts is another trap. A 20% discount followed by an extra 10% off the sale price is a total discount of 28%, not 30%: 0.80 × 0.90 = 0.72. Likewise, a 25% employer match on the first 6% of salary is worth 1.5% of salary (0.25 × 6%). When percentages apply one after another, multiply the factors rather than adding the percentages.
Rounding and precision
This calculator shows up to four decimal places. For money, round to the cent at the end of a calculation, not in the middle, to avoid small rounding errors building up. For reporting, one or two decimal places is usually enough.
Converting between percentages and multipliers
An increase of p% is the same as multiplying by (1 + p/100), and a decrease of p% is the same as multiplying by (1 − p/100). A 7% raise multiplies salary by 1.07, and a 15% drop multiplies a price by 0.85. Thinking in multipliers makes chains of changes easy: multiply the factors together, then subtract 1 to get the total percentage change.
Whatever the problem, start by identifying the whole (the base) and the part. Most percentage mistakes come from dividing by the wrong number.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 20% of 150 = 0.20 × 150 = 30.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 30 out of 120 = 30 ÷ 120 × 100 = 25%.
How do I calculate percentage increase?
Subtract the original value from the new value, divide by the original value and multiply by 100. From 50 to 65: (65 − 50) ÷ 50 × 100 = 30%.
How do I calculate percentage decrease?
Use the same formula. The result will be negative. From 80 to 60: (60 − 80) ÷ 80 × 100 = −25%, a 25% decrease.
What is the difference between percent and percentage points?
Percentage points measure the simple difference between two percentages (6% to 7% is +1 point). Percent change measures the relative change (6% to 7% is a 16.67% increase).
Why doesn't a 50% loss followed by a 50% gain break even?
Because the gain is calculated on a smaller base. $100 − 50% = $50, and $50 + 50% = $75. You would need a 100% gain to recover a 50% loss.
How do I reverse a percentage discount?
Divide the sale price by (1 − discount rate). An $80 price after 20% off came from $80 ÷ 0.80 = $100.