How to work out any percentage in seconds
Percentages turn up everywhere: the tip at the bottom of a restaurant bill, the red discount sticker in a shop window, the sales tax added at the till, the pay rise your boss just promised, the grade on a test. The word looks technical, but a percentage is only a fraction with the bottom number fixed at 100. Once you know which of four simple questions you are asking, every percentage problem becomes a single line of arithmetic. This page walks through those four questions with real, everyday examples, and the calculator above does the maths for you instantly.
What is X% of Y?
This is the question you ask when you already know the rate and want the amount. The formula is straightforward: turn the percent into a decimal by dividing by 100, then multiply by the whole number.
X% of Y = (X ÷ 100) × Y
Real example (a tip): your dinner came to $60 and you want to leave an 18% tip. That is (18 ÷ 100) × 60 = 0.18 × 60 = $10.80. Add it to the bill and you pay $70.80. The same shape of sum answers "what is 8% sales tax on a $45 jacket?" — 0.08 × 45 = $3.60, so the jacket costs $48.60 at the register.
X is what percent of Y?
Here you have two amounts and want to know how they compare as a percentage. Divide the part by the whole and multiply by 100.
Percent = (X ÷ Y) × 100
Real example (a grade): you scored 42 marks out of a possible 50 on a test. That is (42 ÷ 50) × 100 = 0.84 × 100 = 84%. The same method tells you that if you have saved $1,500 toward a $6,000 holiday, you are (1500 ÷ 6000) × 100 = 25% of the way there.
Percentage increase
When a number grows and you want to express the growth as a percent, work out the difference first, then divide by the original value. The starting number always goes on the bottom — that is the single most common mistake people make.
Increase % = ((New − Old) ÷ Old) × 100
Real example (a price rise): a monthly transit pass went from $80 to $92. The difference is $12, so ((92 − 80) ÷ 80) × 100 = (12 ÷ 80) × 100 = 15%. Your commute just got 15% more expensive. The same formula handles a pay rise: a salary moving from $50,000 to $54,000 is a (4000 ÷ 50000) × 100 = 8% raise.
Percentage decrease
A drop uses exactly the same logic — the difference comes out negative, which simply signals a fall.
Decrease % = ((Old − New) ÷ Old) × 100
Real example (a discount): a $120 pair of shoes is marked down to $90. The drop is $30, so (30 ÷ 120) × 100 = 25% off. Going the other way, if you see a "30% off $120" sign, the saving is 0.30 × 120 = $36 and you pay $84.
Percentage difference (when there is no "original")
Sometimes neither number is the starting point — you just want to know how far apart two values are. Divide the difference by the average of the two numbers.
Difference % = (|A − B| ÷ ((A + B) ÷ 2)) × 100
Real example: one shop sells a kettle for $40 and another for $50. The gap is $10 and the average is $45, so (10 ÷ 45) × 100 ≈ 22%. Notice this is symmetric: it does not matter which price you call A and which you call B.
Two quick mental-math shortcuts
Swap the numbers. X% of Y always equals Y% of X. Working out 16% of 25 looks awkward, but 25% of 16 is just a quarter of 16 — which is 4. Same answer, far less effort.
Build it from 10% and 1%. To find 10% of any number, slide the decimal point one place left: 10% of 240 is 24. To find 1%, slide it two places: 1% of 240 is 2.40. From those two building blocks you can assemble almost anything — 15% is 10% plus half of it (24 + 12 = 36), and 17% is 10% + 5% + 2% (24 + 12 + 4.80 = 40.80). This is exactly how to size a tip in your head while the waiter waits.
For longer-term growth where each year builds on the last, percentages stack rather than simply add — try our compound interest calculator. You can also browse the full set of free calculators for splitting bills, converting units and more.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percent by 100 to get a decimal, then multiply by the number. For 20% of 150, work out 0.20 times 150, which equals 30.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. If 42 out of 50 questions are correct, that is 42 divided by 50 times 100, which equals 84 percent.
What is the percentage change formula?
Subtract the old value from the new value, divide by the old value, then multiply by 100. A rise from 80 to 92 is 12 divided by 80 times 100, which equals a 15 percent increase. A negative result means a decrease.
Why do I divide by the original number for percentage change?
Because the change is measured relative to where you started. Dividing by the new value instead gives a different and misleading figure, so the original (starting) value always goes on the bottom.
What is the difference between percentage change and percentage difference?
Percentage change has a clear before and after, so it divides by the original value. Percentage difference compares two values with no starting point, so it divides by their average and is the same whichever way round you put them.
Is X percent of Y the same as Y percent of X?
Yes, they are always equal. 8 percent of 50 and 50 percent of 8 both equal 4. Swapping the numbers often makes the sum much easier to do in your head.