The simplest way to find a percentage

To find a percentage, divide the part by the whole, then multiply by 100. That is the entire formula. If you have 25 items out of 100 total, you divide 25 by 100 to get 0.25, then multiply by 100 to get 25 percent.

The formula written out is: (Part ÷ Whole) × 100 = Percentage. You can use this same three-step process whether you are calculating a test score, a discount at a store, or how much of your paycheck goes to taxes.

The reason you multiply by 100 is because a percentage literally means "per hundred." When you divide the part by the whole, you get a decimal — a number between 0 and 1. Multiplying by 100 converts that decimal into the percentage form you see written with the % symbol.

Key Takeaways

  • Divide the part by the whole, then multiply the result by 100 to get the percentage.
  • If you scored 18 out of 20 on a test, divide 18 by 20 to get 0.9, then multiply by 100 to get 90 percent.
  • A percentage can never be more than 100 unless the part is larger than the whole, which means you have more than one full set.
  • You can rearrange the formula to find the part or the whole if you already know the percentage and one other number.

Working through a real example step by step

Say you answered 42 questions correctly on a 50-question test. To find your percentage score, start by dividing 42 by 50. On a calculator, this gives you 0.84. Now multiply 0.84 by 100, which gives you 84. Your score is 84 percent.

Here is another example: a shirt costs $60, and it is on sale for 20 percent off. To find how much money you save, multiply 60 by 0.20 (which is 20 percent written as a decimal). That gives you $12. The shirt now costs $60 minus $12, or $48.

Notice that in the second example, you converted the percentage to a decimal first by dividing 20 by 100. This is the reverse of what you do when you are finding a percentage — you go from percentage to decimal instead of decimal to percentage. Both directions use the same relationship between decimals and percentages.

When the part is larger than the whole

Percentages can be larger than 100. This happens when the part you are measuring is bigger than the whole you started with. If a store had 80 items in stock and received a shipment of 120 more items, the shipment is 150 percent of the original stock (120 ÷ 80 × 100 = 150).

This is not a mistake or a sign that you did the math wrong. It straightforward means you have more than one full set. A percentage over 100 is perfectly valid and shows up often in real life — in population growth, salary increases, or inventory changes.

Finding the part or the whole when you know the percentage

Sometimes you know the percentage and need to work backwards to find either the part or the whole. If you know that 30 percent of your $2,000 monthly income goes to rent, you can find the rent amount by multiplying 2,000 by 0.30, which equals $600.

If you know that 15 items represent 25 percent of a total, you can find the total by dividing 15 by 0.25, which equals 60. The formula rearranged is: Part ÷ Percentage (as a decimal) = Whole. Learning to flip the formula this way makes it much easier to solve different types of percentage problems.

Common mistakes to avoid

The most frequent error is forgetting to multiply by 100 at the end. If you divide 25 by 100 and stop there, you get 0.25 — which is correct as a decimal, but it is not the percentage. You must multiply by 100 to get 25 percent. Without that step, your answer will be 100 times too small.

Another mistake is mixing up which number is the part and which is the whole. The part always goes on top (in the numerator) and the whole always goes on the bottom (in the denominator). If you reverse them, your answer will be completely wrong. Read the problem carefully to figure out which number represents the full amount and which represents the portion of it.

Using a calculator versus doing it by hand

A calculator makes percentage problems faster, but understanding the steps matters more than speed. If you use a calculator, enter the part first, press the division button, enter the whole, press equals, then multiply by 100. Writing down each step helps you catch errors and understand what the answer means.

If you do the math by hand, you may need to round your decimal to a reasonable number of places. For example, if dividing gives you 0.333333 repeating, you might round to 0.33 and then multiply by 100 to get 33 percent. Rounding to two decimal places is standard for most everyday situations.

Percentages in everyday situations

You use percentages constantly without always thinking about it. A restaurant tip of 20 percent, a sales tax rate of 8 percent, a test score of 92 percent, a discount of 15 percent off — all of these follow the same formula. Once you understand the basic method, you can handle any percentage problem that comes up.

The key is recognizing what the "part" and "whole" are in each situation. In a tip, the whole is your bill and the part is the amount you add. In a discount, the whole is the original price and the part is the amount you save. In a test score, the whole is the total number of questions and the part is the number you got right. Identify those two numbers, plug them into the formula, and you have your answer.

Frequently Asked Questions

What is the difference between a decimal and a percentage?

A decimal and a percentage represent the same value in different forms. The decimal 0.5 is the same as 50 percent. To convert a decimal to a percentage, multiply by 100. To convert a percentage to a decimal, divide by 100. They are just two ways of writing the same thing.

Can a percentage be negative?

Yes. A negative percentage shows a decrease. If a company's profit was $100,000 last year and $80,000 this year, the change is negative 20 percent. You calculate it the same way — (80,000 − 100,000) ÷ 100,000 × 100 = −20 percent. The negative sign tells you the value went down, not up.

How do I find what percentage one number is of another?

Divide the first number by the second number, then multiply by 100. If you want to know what percentage 18 is of 45, divide 18 by 45 to get 0.4, then multiply by 100 to get 40 percent. This is the basic formula applied to any two numbers you want to compare.

What if my percentage comes out to a decimal like 33.33 percent?

That is normal and correct. Some divisions do not result in a whole number. You can round to the nearest whole number (33 percent) or keep the decimal places depending on how precise you need to be. For most everyday situations, rounding to the nearest whole number or to one decimal place is fine.