How to Calculate a Percentage
What's 18% of $65? What percent is 45 out of 60? If 15% of a number is 12, what's the number?
These look like three different problems, and many people learn three different methods. In fact, every basic percentage question uses the same single equation. Once you see it, you can solve any of them, and a surprising trick makes some of them easy to do in your head.
x% of y Always Equals y% of x
Here's a shortcut that sounds too good to be true:
8% of 50 = 50% of 8 = 4
It works every time, because both equal (8 × 50) / 100. So if one version is hard, flip it. What's 4% of 75? That's the same as 75% of 4, which is 3. Percentages are just multiplication, and multiplication doesn't care about order.
What a Percentage Means
Percent comes from the Latin per centum: "per hundred." A percentage is a fraction with a denominator of 100:
25% = 25/100 = 0.25
To convert a percentage to a decimal, divide by 100 (move the decimal point two places left). To convert a decimal to a percentage, multiply by 100.
The One Formula
Part = Percent × Whole
With the percent written as a decimal. Every basic percentage problem gives you two of these three values and asks for the third.
Type 1: Find the Part
"What is 18% of $65?"
Part = 0.18 × 65 = 11.70
Answer: $11.70. This is the calculation for tips, discounts and sales tax.
Type 2: Find the Percent
"45 is what percent of 60?"
Rearrange the formula:
Percent = Part ÷ Whole = 45 ÷ 60 = 0.75 → 75%
Answer: 75%. Use this for test scores, completion rates and survey results.
Type 3: Find the Whole
"12 is 15% of what number?"
Rearrange again:
Whole = Part ÷ Percent = 12 ÷ 0.15 = 80
Answer: 80. This is how you work backward, for example, to find an original price from a discount amount.
You can check any answer with the basic calculator.
Increasing and Decreasing by a Percentage
To increase a number by p%, multiply by (1 + p/100):
$80 increased by 15% = 80 × 1.15 = $92
To decrease a number by p%, multiply by (1 − p/100):
$250 decreased by 15% = 250 × 0.85 = $212.50
This one-step method avoids calculating the change separately and adding or subtracting it.
Mental Math Shortcuts
| To find | Do this | Example: 340 |
|---|---|---|
| 10% | Move the decimal one place left | 34 |
| 5% | Half of 10% | 17 |
| 1% | Move the decimal two places left | 3.4 |
| 20% | Double 10% | 68 |
| 25% | Divide by 4 | 85 |
| 50% | Divide by 2 | 170 |
| 15% | 10% + 5% | 51 |
A tip of 18% on a $65 meal? 10% is 6.50, 5% is 3.25, and about 3% is roughly 1.95. Total: about $11.70. Practice fast division with the division tables.
An Insider Reference: Where the % Sign Came From
In his classic 1928 work A History of Mathematical Notations, mathematics historian Florian Cajori traced how the % symbol developed. Italian merchants in the 15th century wrote "per cento" in account books, often abbreviated as "p cento."
Over time, scribes shortened the "cento" part into a small circle-like mark. A manuscript from around 1425 shows a form resembling "p" followed by a looped symbol. By the 1600s, the "p" was dropping away, and the looped mark evolved into a fraction-like o/o, which eventually became the modern %.
Common Mistakes
1. Forgetting to convert. 15% is 0.15, not 15. Multiplying by 15 gives an answer 100 times too big.
2. Using the wrong whole. "What percent of the class passed?" Divide by the total class size, not by the number who failed.
3. Reversing a percentage change. A price that dropped 20% to $80 wasn't $96 originally. It was 80 ÷ 0.80 = $100.
4. Adding successive percentages. 20% off, then another 10% off, is 28% off, not 30%. See The Mathematics of Discounts, Markups, and Sales Tax.
Two Concepts Worth Knowing
Ratio
A ratio compares two quantities, like 45 to 60. A percentage is a ratio scaled so the second quantity is 100: 45/60 = 75/100.
Proportion
A proportion states that two ratios are equal. "45 is to 60 as x is to 100" is a proportion you can solve by cross multiplication. See Why Does Cross Multiplication Work?
Quick Answer: How Do You Calculate a Percentage?
To find a percentage of a number, convert the percent to a decimal and multiply: 18% of 65 = 0.18 × 65 = 11.7. To find what percent one number is of another, divide the part by the whole and multiply by 100: 45 ÷ 60 × 100 = 75%. To find the whole, divide the part by the percent as a decimal: 12 ÷ 0.15 = 80.
Try Them Yourself
- Basic Calculator: check any percentage calculation
- Division Tables: build fluency for "part ÷ whole"
- Multiplication Tables: speed up "percent × whole"
- Multiplication Flash Cards: practice the core skill
- Why Percentages Are So Easy to Get Wrong: the traps to avoid
- How to Calculate Percent Change: the next step
Next time you're at a restaurant, calculate an 18% tip in your head using 10% + 5% + a little more. Then check it with the formula.