How to Calculate a Percentage: The Four Everyday Cases
A percentage is just a fraction with a fixed denominator of 100. "45%" means 45 out of 100, or 0.45. Almost every percentage question you meet in daily life is one of four shapes, and all four come down to that same conversion between a percent and a decimal.
1. Finding a percentage of a number
This is the most common one: a tip, a discount, a tax, a commission, an interest amount. Convert the percent to a decimal and multiply.
value × (percent ÷ 100)
Worked example. A restaurant bill is $62 and you want to leave an 18% tip. That is 62 × 0.18 = $11.16. The total is $73.16. The tip calculator does exactly this, plus splitting the total between people.
Worked example. A $1,250 laptop is 15% off. The discount is 1250 × 0.15 = $187.50, so you pay $1,062.50. Note that taking 15% off and then adding it back does not return you to $1,250 — see case 3.
2. Expressing one number as a percentage of another
You have two numbers and want to know the proportion: a test score, a completion rate, a market share, "how much of my budget did I spend."
(part ÷ whole) × 100
Worked example. You got 45 questions right out of 60. That is 45 ÷ 60 = 0.75, or 75%.
Worked example. You spent $340 of a $400 allowance. That is 340 ÷ 400 = 0.85, or 85% of the budget used, 15% left.
The one trap here is division by zero. If the "whole" is 0, the percentage is undefined — there is no meaningful answer, and a calculator should say so rather than show Infinity or crash.
3. Increasing a number by a percentage
Markups, rate rises, inflation, "price plus tax." You are not looking for the increase on its own — you want the new total.
value × (1 + percent ÷ 100)
Worked example. A $1,250 item with 15% sales tax added: 1250 × 1.15 = $1,437.50. The sales tax calculator works this both ways — adding tax to a pre-tax price, or pulling the tax back out of a tax-inclusive total.
Why "off then on" doesn't cancel. Take 15% off $1,250 and you get $1,062.50. Add 15% back and you get 1062.50 × 1.15 = $1,221.88 — not $1,250. The second percentage is calculated on a smaller base, so it is a smaller amount. This is the same reason a 50% loss needs a 100% gain to recover.
4. Decreasing a number by a percentage
Discounts expressed as a final price, depreciation, a pay cut, "how much is left after a drop."
value × (1 − percent ÷ 100)
Worked example. A $1,250 asset depreciates 15% in a year: 1250 × 0.85 = $1,062.50 at year end.
Percentage points vs. percent
These are different and the difference matters. If an interest rate goes from 4% to 6%, that is a rise of 2 percentage points, but a 50% increase in the rate (2 ÷ 4 = 0.5). News headlines routinely blur the two. When you see "up 2%," check whether they mean two points or two percent of the current value.
Reversing a percentage change
If you know a total after a percentage was applied and want the original, divide rather than multiply. A price of $1,437.50 that already includes 15% tax started at 1437.50 ÷ 1.15 = $1,250. A common mistake is to take 15% off the $1,437.50 instead, which gives $1,221.88 — wrong, for the same "smaller base" reason as above.
Quick mental-maths checks
- 10% — move the decimal one place left. 10% of 84 is 8.4.
- 5% — half of 10%. 5% of 84 is 4.2.
- 1% — move the decimal two places left. 1% of 84 is 0.84.
- 20% — double 10%. Useful for a quick tip.
- x% of y equals y% of x — 18% of 50 is awkward; 50% of 18 is obviously 9.
The percentage calculator has a mode for each of the four cases and updates as you type, so you can check any of the examples above.