Percentage Calculator

The three questions a percentage answers

Almost every percentage question on a receipt, a pay stub or a news story is one of three shapes, and they are all rearrangements of the same ratio.

• Percent of a number: what is 15 percent of 80? Multiply 80 by 0.15 and you get 12.
• One number as a percent of another: 45 is what percent of 180? Divide 45 by 180 and multiply by 100, which gives 25 percent.
• Percent change: a price moves from 80 to 92. The change is 12, and 12 divided by the starting value 80 is 15 percent.

The calculator above runs all three, plus the reverse case where you know the final number and the percentage and need the starting value. That fourth case is the one people get wrong most often, because the base is not the number in front of them.

One habit makes all of this easier: name the base before you touch the calculator. In "15 percent off", the base is the list price. In "7 percent tax", the base is the discounted price. Two percentages with different bases never add.

Worked example: the three shapes on real numbers

Take a dinner bill of $64.50 and a tip of 18 percent. The tip is 0.18 times 64.50, which is $11.61, so the card total is $76.11. That is the first shape.

Now a gym that sold 45 of its 180 day passes. 45 divided by 180 is 0.25, so 25 percent of the passes sold, and 135 remain. That is the second shape.

Then a subscription that goes from $80 a year to $92. The dollar change is $12, and 12 divided by 80 is 0.15, so the price rose 15 percent. Notice that dividing 12 by 92 gives 13.04 percent, which is the wrong base: the increase is measured against what you paid before, not what you pay now.

The last row is the reverse case. If a $63 price already includes a 25 percent discount, the original is 63 divided by 0.75, which is $84. Adding 25 percent to 63 gives $78.75, and that is the classic wrong answer.

Percent change versus percentage points

These two sound alike and mean different things, and the confusion shows up in every inflation report.

The Consumer Price Index rose 3.7 percent in the 12 months ending September 2026, after a 3.4 percent rise in the 12 months ending August 2026, according to the Bureau of Labor Statistics. The move from 3.4 to 3.7 is 0.3 percentage points. It is also an 8.82 percent increase in the inflation rate itself, because 0.3 divided by 3.4 is 0.0882.

Reporters use percentage points when they compare two rates and percent when they compare two quantities. If a bank raises a savings rate from 4 percent to 5 percent, that is one percentage point, and it is a 25 percent increase in the interest you earn. Both statements are true and they describe different things.

The calculator keeps them apart: the change mode returns a percent, and the difference between the two inputs is the number of percentage points.

Worked example: percent change from index levels

Index numbers are built so that percent changes are easy to compute without knowing the dollar values behind them. The CPI-U stood at 321.435 in June 2025 and 332.568 in June 2026, both from the BLS Real Earnings release.

• Change in index points: 332.568 minus 321.435 = 11.133.
• Divide by the starting index: 11.133 divided by 321.435 = 0.03464.
• As a percent: 3.46 percent over the 12 months.

That is the whole method for any index, whether it is the CPI, a house price index or a stock index. The index level itself means nothing on its own; only the ratio between two levels carries information.

Wages are compared the same way. Median weekly earnings of full-time workers were $1,251 in the second quarter of 2026, up from $1,196 a year earlier, a gain of 4.6 percent, per the BLS weekly earnings release. Against 3.9 percent CPI inflation over the same period, the real gain was small but positive.

Discounts, sales tax and why percentages do not add

A $120 jacket is marked 25 percent off, and your state charges 7 percent sales tax at the register. The tempting sum is 32 percent, and it is wrong in both directions at once.

• Discount: 120 times 0.25 = $30 off, so the price is $90.
• Tax: 90 times 0.07 = $6.30, charged on the discounted price, not the list price.
• Total: $96.30, which is 19.75 percent below the $120 list price.

Adding 25 and 7 would suggest a price of $81.60, which is $14.70 less than the register will ask for. The reason is that the second percentage applies to a base that the first one already changed. Percentages with different bases multiply: 0.75 times 1.07 is 0.8025, so you pay 80.25 percent of list.

The order does not matter for the final total in this case, 120 times 1.07 times 0.75 is also $96.30, but it does matter for what the tax authority sees, and some states tax the pre-discount price on rebates and coupons. That is a rule to check locally, not something a calculator can decide for you.

Working backwards to the original number

Reverse percentage questions show up at sale racks, on invoices and in any conversation about a raise. The rule is to divide, not to subtract the percentage from the final number.

A laptop costs $63 after a 25 percent discount. The $63 is 75 percent of the original, so the original is 63 divided by 0.75, which is $84. The discount was $21.

Same shape, different sign: a salary of $52,000 after a 4 percent raise means the old salary was 52,000 divided by 1.04, which is $50,000. And a price of $46 after 8 percent sales tax means the shelf price was 46 divided by 1.08, which is $42.59.

The calculator's reverse mode takes the final value and the percentage, and it asks whether the change was an increase or a decrease, because that decides whether it divides by 1 plus the rate or 1 minus the rate.

Percentages of income: the 30 percent housing rule

One percentage that shapes real budgets is the affordability standard used by the Department of Housing and Urban Development. A household spending more than 30 percent of its income on housing is counted as cost burdened, and above 50 percent as severely burdened, as described in HUD's own explanation of the measure.

On a gross monthly income of $4,500, 30 percent is $1,350. Rent plus utilities above that line puts the household in the burdened group, and at $2,250 it is severely burdened. For an $83,730 household income, the 2024 median reported by the Census Bureau, 30 percent works out to $2,093 a month.

Percent-of-income math is also where rounding gets dangerous. A landlord who asks for 30 percent of income and a lender who caps housing at 28 percent of gross pay are using two different bases if one means pretax and the other take-home pay. Always ask which income figure the percentage refers to before you compare offers.

Mistakes and edge cases worth knowing

Most percentage errors come from picking the wrong base, and the rest come from treating a percent as a number you can add freely.

• A 20 percent drop needs a 25 percent rise to recover. 100 falls to 80, and 80 needs 20 points back, which is 25 percent of 80. The two percentages are not symmetric.
• Percent of a percent multiplies. 50 percent of 50 percent is 25 percent, because 0.5 times 0.5 is 0.25.
• A 100 percent increase doubles, a 200 percent increase triples. The base is always included once.
• Percentages above 100 are legal. Revenue up 150 percent means it is 2.5 times the old figure.

For comparisons across groups, percentages need a denominator you trust. The Census Bureau reports that among full-time, year-round workers the female-to-male earnings ratio was 80.9 percent in 2024, down from 82.7 percent in 2023. That is a percent of a median, not an average of individual ratios, and the difference matters when the underlying distributions differ.

One boundary worth stating: this page is percentage arithmetic, not grade conversion. Turning an 88 percent course score into grade points is a different job with credit weights, which the percentage to GPA converter handles. And when the only question is a single rise or fall, the percent increase calculator walks through that one formula step by step.