Every percent problem has three pieces
Percent means "per hundred". So 20% is 20 out of every 100, or 0.20 as a decimal. Every everyday percent question involves three things: a whole, a part of that whole, and the rate linking them. You'll always know two and need the third.
"What is 20% of 150?" gives you the whole and the rate. "30 is what percent of 150?" gives you the part and the whole. "30 is 20% of what?" gives you the part and the rate. Same three numbers, three different questions. Name the pieces first and the formula picks itself.
Formula notes
Part = whole x rateRate = part / wholeWhole = part / rate
Finding the base is the real skill
The base is whatever counts as 100%. Get it right and the rest is arithmetic. Get it wrong and the answer can look reasonable while being far off.
Watch the small words. "Of" usually points at the base: in "20% of 150", 150 is the base. "From" marks the base in a change question: in "from 80 to 100", 80 is the base. The bigger number isn't automatically the base, and neither is the newer one.
Percent change, step by step
Subtract old from new, divide by old, multiply by 100. Sales that grew from 80 to 100 rose by 20, and 20 / 80 is 0.25, so the growth is 25%. A negative answer means a decrease.
This is the method the U.S. Bureau of Labor Statistics lays out for price index changes, and it's the one to use any time there's a clear before and after. Only use the old value as the divisor. Dividing the change of 20 by 100 instead would report 20% and understate the growth.
Reverse percentages trip up almost everyone
A jacket costs $96 after a 20% discount. What was the original price? The tempting move is to add 20% of 96 back on, which gives $115.20. That's wrong, because the discount was 20% of the original price, not of $96.
The sale price is 80% of the original, so divide: 96 / 0.80 = $120. Check it forward: 20% of 120 is 24, and 120 - 24 = 96. The same idea works for tax, tips and markups. Divide by the multiplier, never subtract the percent from the final number.
Shortcuts for doing it in your head
10% is the number with the decimal point moved one place left. From there you can build most common rates. 5% is half of 10%, 20% is double it, and 15% is 10% plus 5%. For 15% of 80: 10% is 8, 5% is 4, so the answer is 12.
Percentages also flip. 8% of 25 is the same as 25% of 8, which is 2. When one of the two numbers is awkward, swapping them often makes it easy.
- 1%: move the decimal two places left
- 10%: move it one place left
- 25%: divide by 4
- 50%: divide by 2
- 75%: take 25% and multiply by 3
When to let a calculator do it
Mental shortcuts work for single steps with tidy numbers. Chained changes, reverse problems and anything with decimals are where slips creep in. Our percentage calculator has a separate mode for each question type and prints the base it used, so you can see straight away if it divided by the number you meant.
Whatever you use, finish with a sanity check. A part should be smaller than its whole unless the rate is over 100%. An increase should give a bigger number. If the answer fails a quick check like that, the base is usually the culprit.
Frequently asked questions
What does percent actually mean?
It means per hundred. 35% is 35 out of 100, which is 0.35 as a decimal or 35/100 as a fraction.
How do you turn a fraction into a percentage?
Divide the top by the bottom and multiply by 100. 3/8 is 0.375, so it's 37.5%.
Is x% of y the same as y% of x?
Yes, always. Both equal x times y divided by 100, so 8% of 50 and 50% of 8 are both 4.
How do I find 1% of a number?
Divide it by 100. 1% of 2,450 is 24.5. Multiply that by any whole rate to get other percentages quickly.
Why does a 50% loss need a 100% gain to recover?
The base shrinks. Losing half of 100 leaves 50, and getting back to 100 means adding another 50, which is 100% of the new base.
References
These sources support the method or guidance used for Percentage Calculator. Verify time-sensitive rules at the source.
Try the calculator
Open Percentage Calculator, enter your scenario, and compare its supporting rows with this guide's method and checks.