How to calculate percentages: three formulas and the mental shortcuts

What does "percent" mean?

The word percent means "per hundred", so 1% is one hundredth of something and 100% is all of it. Writing 15% is a short way of writing 15 ÷ 100, which is the fraction fifteen hundredths or the decimal 0.15.

That single idea carries every calculation in this guide. To turn a percent into a decimal, divide by 100 by moving the decimal point two places left: 15% is 0.15, 8% is 0.08, 150% is 1.5. To turn a decimal back into a percent, multiply by 100: 0.75 is 75%.

The Common Core mathematics standards put it the same way for sixth graders (6.RP.A.3c): "30% of a quantity means 30/100 times the quantity". In seventh grade (7.RP.A.3) the same standards add tax, markups and markdowns, tips and percent increase and decrease, which is the full list this guide covers.

How do you find a percentage of a number?

To find a percentage of a number, change the percent to a decimal and multiply. That is the first percentage formula, and it answers "what is 15% of 80?"

1. Divide the percent by 100: 15% becomes 0.15.
2. Multiply by the number: 0.15 × 80 = 12.
3. Check the size: 15% is a bit less than a fifth, and a fifth of 80 is 16, so 12 is sensible.

Answer: 15% of 80 is 12.

Three everyday versions of the same step:

• Sale price. A 30% discount on 60 is 0.3 × 60 = 18 off, so you pay 60 − 18 = 42. Faster: you pay 70%, and 0.7 × 60 = 42.
• Sales tax. An 8% tax on 25 is 0.08 × 25 = 2, so the total is 27. Faster: 25 × 1.08 = 27.
• Tip. A 15% tip on 45 is 0.15 × 45 = 6.75.

The "faster" lines use one multiplier for the whole job: 1 minus the discount, or 1 plus the tax. That habit also prevents the most common sale-price error, which appears in the mistakes section.

How do you work out what percent one number is of another?

To work out what percent one number is of another, divide the part by the whole and multiply by 100. This form answers questions like "I got 18 out of 24 on the test; what percent is that?"

1. Put the part over the whole: 18 ÷ 24.
2. Divide: 18 ÷ 24 = 0.75.
3. Multiply by 100: 0.75 × 100 = 75%.

Answer: 18 out of 24 is 75%.

The hard part is deciding which number is the whole. The whole follows the word "of": in "18 is what percent of 24", 24 is the whole. The same rule runs backward when the whole is the unknown, a case the Common Core standard names directly. If 12 students are 30% of a class, the class has 12 ÷ 0.30 = 40 students. Check: 30% of 40 is 12.

Percentages sit next to averages in most sixth-grade units, and the find the average game drills the same divide-and-check habit.

How do you calculate percentage increase and decrease?

Percentage increase and decrease both use one formula: (new − old) ÷ old × 100. The old value always goes on the bottom, because a percent change is measured against where you started.

A price goes from 40 to 50.

1. Change: 50 − 40 = 10.
2. Divide by the old value: 10 ÷ 40 = 0.25.
3. Multiply by 100: a 25% increase.

A price goes from 50 back to 40.

1. Change: 40 − 50 = −10.
2. Divide by the old value: −10 ÷ 50 = −0.2.
3. Multiply by 100: a 20% decrease.

The two moves cover the same gap of 10, but the starting points differ. Ten is a quarter of 40 and a fifth of 50. Statistics offices use the same method: Eurostat's guide to percentage change writes it as [(later ÷ earlier) − 1] × 100 and works an employment rise from 4.8 to 5.2 million into +8.3%. Both versions give the same answer: 5.2 ÷ 4.8 = 1.0833, minus 1 is 0.0833, or 8.3%.

Play free in your browserPercentagesGrade 5+

The three percentage formulas side by side

The three percentage formulas are the same relation, part = percent × whole, solved for a different unknown each time.

A quick self-check before moving on. Try each, then compare:

1. What is 35% of 240? (84)
2. 45 is what percent of 60? (75%)
3. A price rises from 30 to 36. What is the percent increase? (20%)
4. A price falls from 120 to 90. What is the percent decrease? (25%)

How do you calculate a percentage in your head?

The fastest way to calculate a percentage in your head is to start from 10%, which is the number with its decimal point moved one place left. Every other common percent is built from that one move.

Combine the pieces for anything else. For 35% of 240, take three tens (72) plus a five (12) to get 84. For 3% of 350, take 1% (3.5) three times to get 10.5.

The swap trick. X% of Y always equals Y% of X, because both are X × Y ÷ 100. When one direction is awkward, flip it:

• 8% of 50 = 50% of 8 = 4
• 16% of 25 = 25% of 16 = 4
• 12% of 50 = 50% of 12 = 6

Mental percentages run on quick halving, doubling and dividing by 10, and the mental math tricks that work cover that layer in more depth. The percentages game turns the 10% trick into timed rounds, and the printable mixed worksheet for sixth graders practices the multiplication and division underneath, with an answer key.

Free printable worksheetMixed Operations — 6th GradersWorksheet · PDF

What are the most common percentage mistakes?

The most common percentage mistakes come from applying a percent to the wrong base, the number it is taken "of".

1. Adding percentages of different bases. A 20% discount followed by an extra 10% off is not 30% off. On 100, the first cut leaves 80 and the second takes 10% of 80, leaving 72. The total discount is 28%.
2. Expecting a fall and an equal rise to cancel. A 50% drop takes 100 to 50, and a 50% rise takes 50 to 75. The second 50% is taken of a smaller base, so you end up 25% below the start.
3. Reversing a discount by adding the percent back. A sale price of 45 after 25% off does not come from 45 + 25% of 45 = 56.25. You paid 75% of the original, so the original was 45 ÷ 0.75 = 60.
4. Confusing percent with percentage points. A change between two percentages is counted in points. NCES reports that the share of US adults at the lowest numeracy level in PIAAC rose "from 29 to 34 percent" between 2017 and 2023. That is a rise of 5 percentage points, and a relative rise of about 17%, since 5 ÷ 29 ≈ 0.17. Eurostat's guide makes the same distinction.

The same NCES figure is a reminder that about a third of US adults sit at the lowest numeracy level, so struggling with a tip or a discount is common and fixable. For a structured way back into arithmetic, getting better at math as an adult lays out a plan, and the math games for adults page collects practice at that level.

Twenty-two of MathIt's roughly 90 game types play free in a browser with no sign-up, and the free iOS and Android app adds adaptive difficulty, so the percentages get harder only once the easy ones are right.