How To Calculate Percentages, Step By Step
The short version
- To find a percent of a number, turn the percent into a decimal and multiply. 15% of 80 is 0.15 × 80 = 12.
- To find what percent one number is of another, divide the part by the whole and multiply by 100. 14 out of 40 is 14 ÷ 40 = 0.35, or 35%.
- To find the whole from a part, divide. If 18 is 30% of a number, that number is 18 ÷ 0.30 = 60.
- Percent change uses the original number on the bottom. Going from 25 to 32 is 7 ÷ 25 = 28% up.
- For mental math, start at 10%. Move the decimal one place left, then build from there. 10% of 64 is 6.4, so 20% is 12.8 and 5% is 3.2.
Learning how to calculate percentages comes down to three moves, and which one you use depends on which number is missing. Percent means “out of 100,” so 15% is just another way of writing 15/100, or 0.15. Once that clicks, every percent problem is a multiplication or a division.
The confusing part is that textbooks present these as separate formulas to memorize. They’re not. They’re the same relationship rearranged, and the fastest way to get good at this is to learn the relationship once instead of memorizing three rules.
The one relationship behind every percent problem
Every percentage question fits this sentence: the part is some percent of the whole. Written as math, part ÷ whole = percent ÷ 100. Teachers often call this the “is over of” method, because in a word problem the number right after “is” goes on top and the number after “of” goes on the bottom.
“What is 20% of 60?” The 60 is the whole. “14 is what percent of 40?” The 14 is the part. Once you’ve labeled the numbers, only one spot is empty, and you either multiply or divide to fill it.
| What’s missing | What you do | Example |
|---|---|---|
| The part | Multiply whole by the decimal | 25% of 60 = 0.25 × 60 = 15 |
| The percent | Divide part by whole, then × 100 | 14 of 40 = 0.35 = 35% |
| The whole | Divide part by the decimal | 18 is 30% of what? 18 ÷ 0.3 = 60 |
How to calculate percentages of a number
This is the most common version. Drop the percent sign, move the decimal two places left, and multiply.
Find 15% of 80.
15% becomes 0.15
0.15 × 80 = 12
Find 68% of 50.
68% becomes 0.68
0.68 × 50 = 34
Moving the decimal two places is the whole conversion. 15% is 0.15, 7% is 0.07, 120% is 1.20. That last one matters: percents above 100 are real and they just mean more than the whole thing.
The 10% trick for doing it in your head
Ten percent of any number is that number with the decimal moved one place left. From there you can build almost anything.
| Percent | How to get it from 10% | For 64 |
|---|---|---|
| 10% | Move the decimal one left | 6.4 |
| 5% | Half of 10% | 3.2 |
| 20% | Double 10% | 12.8 |
| 15% | 10% plus 5% | 9.6 |
| 25% | Quarter of the number | 16 |
This is how people actually tip. For 18% on a $46.50 dinner: 10% is $4.65, so 20% is $9.30, and 2% is another $0.93 to take back off. That leaves $8.37, which is exactly what 0.18 × 46.50 gives. Same math, no calculator.
Finding what percent one number is of another
Divide the part by the whole, then multiply by 100.
A player makes 34 of 50 free throws. What percent?
34 ÷ 50 = 0.68
0.68 × 100 = 68%
A test has 40 questions and a student gets 14 wrong. What percent were wrong?
14 ÷ 40 = 0.35
0.35 × 100 = 35%
The order matters here and kids flip it constantly. The smaller piece goes on top when you’re asking what fraction of the total it represents. If your answer comes out above 100% and the part clearly isn’t bigger than the whole, you divided backwards.
Finding the whole when you know a percent of it
This one shows up in sale problems and it’s the one most students find hardest, because the missing number is the one you’d normally start with.
A student saved $45, which is 75% of the price of a game. What does the game cost?
45 ÷ 0.75 = $60
Check it: 0.75 × 60 = 45. That matches, so it’s right. Always run that check, because dividing instead of multiplying is an easy slip and the check catches it in five seconds.
Percent increase and percent decrease
Percent change compares the size of a change to where you started. The original number always goes on the bottom.
Percent change = (new – original) ÷ original × 100
A price goes from $25 to $32.
32 – 25 = 7
7 ÷ 25 = 0.28
28% increase
A price goes from $50 to $40.
50 – 40 = 10
10 ÷ 50 = 0.20
20% decrease
Notice that a $10 change is 25% when you start at 40 and 20% when you start at 50. Same dollars, different percent, because the starting point changed. That’s the piece students skip.
Discounts, tax, and tips
These are the percent problems adults actually use, and there’s a shortcut that saves a step.
A $75 pair of shoes is 20% off. The long way finds the discount and subtracts: 0.20 × 75 = 15, and 75 – 15 = 60. The short way: if 20% is off, you’re paying 80%, so 0.80 × 75 = $60 in one multiplication.
A $56 order with 7% sales tax. You’re paying 107% of the price, so 1.07 × 56 = $59.92.
One warning about stacking percents. A $100 item that drops 20% and then rises 20% does not return to $100. It goes to $80, and 20% of 80 is only 16, so it lands at $96. Percents always apply to whatever number is in front of them at that moment.
Common mistakes when calculating percentages
Using the percent as a whole number. Writing 15 × 80 instead of 0.15 × 80 gives 1,200 instead of 12. If an answer is wildly too big, check the decimal.
Dividing by the wrong number in percent change. The original value goes on the bottom, not the new one. Using the new value gives a different answer that looks plausible.
Assuming percent off and percent on cancel. They don’t, as the $100 example shows.
Mixing up percent and percentage points. A rate moving from 4% to 6% went up 2 percentage points, but that’s a 50% increase. News stories blur these two.
Flipping the part and the whole. 14 out of 40 is 35%, not 286%. Label which number is the total before dividing.
Rounding money too early. Carry the full decimal through, then round the final answer to the cent.
Practice problems
1. Find 25% of 60.
2. Find 10% of 47.
3. Find 15% of 80.
4. What percent of 40 is 14?
5. 18 is 30% of what number?
6. A $75 pair of shoes is marked 20% off. What’s the sale price?
7. A price rises from $25 to $32. What’s the percent increase?
8. A restaurant bill is $52 and you leave an 18% tip. Find the tip and the total.
Answers
1. 0.25 × 60 = 15
2. Move the decimal one place left: 4.7
3. 0.15 × 80 = 12
4. 14 ÷ 40 = 0.35, so 35%
5. 18 ÷ 0.30 = 60. Check: 0.30 × 60 = 18
6. 0.80 × 75 = $60
7. 32 – 25 = 7, and 7 ÷ 25 = 0.28, so 28% increase
8. 0.18 × 52 = $9.36 tip, and 52 + 9.36 = $61.36 total
What it means if your kid is stuck on percentages
Percent problems almost never fail because of percent. They fail because of what’s underneath. The first thing to check is fractions and decimals, since a percent is both at once. A kid who can’t confidently turn 3/4 into 0.75 will not be able to turn 75% into 0.75 either, and every percent problem starts with that conversion.
The second is decimal multiplication and division. 0.15 × 80 has a decimal point that has to land in the right place, and a student who guesses will be off by a factor of ten while doing everything else correctly. If your child’s percent answers are consistently 10 times too big or too small, that’s the gap.
The third is proportional reasoning, the sense that 20% of 60 should be a bit more than a tenth of it. Kids with that instinct catch their own errors. Kids without it write 1,200 and move on. Percent lands in sixth and seventh grade, and it’s a direct on ramp to ratios, rates, and the linear equations that follow, which is why gaps here get expensive fast. See struggling with algebra for how that plays out, math skills by grade level for where the fraction and decimal work is supposed to be solid, and 12 signs your child is behind in math if you’re trying to gauge how far back it goes.
Frequently asked questions
How do you calculate a percentage of a number quickly?
Move the decimal two places left and multiply. For 30% of 90, use 0.30 × 90 = 27. In your head, find 10% first and multiply that by 3.
How do you find what percent one number is of another?
Divide the part by the whole and multiply by 100. For 9 out of 12, that’s 9 ÷ 12 = 0.75, or 75%.
How do you calculate percentage increase?
Subtract the original from the new number, divide by the original, then multiply by 100. From 80 to 100 is 20 ÷ 80 = 0.25, a 25% increase.
What is the is over of method?
It’s a way to set up percent word problems as a proportion. The number after “is” goes over the number after “of,” and that equals the percent over 100. Then you cross multiply to find whatever is missing.
How do you find the original price after a discount?
Divide by what you paid as a decimal. If $60 was the price after 25% off, you paid 75%, so 60 ÷ 0.75 = $80 was the original.
What grade do students learn percentages?
Percent usually appears in sixth grade and gets heavy use in seventh, building on fourth and fifth grade fraction and decimal work. Students who still find fractions shaky tend to struggle here even when the percent lesson made sense.
Find the actual gap
If percentages are the current battle, the useful question is what’s sitting underneath them. Math Anon begins with a short adaptive assessment that works back through decimals, fractions, and division until it finds the skill that’s actually missing, then hands you a written report that names it. No grade level guessing.
Practice after that runs about 20 minutes a day and targets only those specific gaps, and you get a weekly report showing what closed. The assessment is $49 and the full amount comes back as credit on your first month. Start the assessment, or check pricing first.
