How to Calculate a Percentage

Percentages show up everywhere: sale prices, tips, exam marks, interest, tax, and progress bars. The word itself gives the method away. Per cent means per hundred, so a percentage is simply a number expressed as a fraction of one hundred. Once you see that, most percentage problems become one short calculation, not a puzzle to dread.

This guide covers the four calculations people actually need: a percent of a number, one number as a percentage of another, a percentage increase, and a percentage decrease. Each one comes with a formula and a worked example you can check by hand.

The basic formula: a percent of a number

To find a percentage of a number, multiply the number by the percentage and divide by one hundred:

Percentage value = number × percentage ÷ 100

For example, what is 20 percent of 150? Multiply 150 by 20 to get 3,000, then divide by 100 to get 30. So 20 percent of 150 is 30. The same method works for any size of number. To find 15 percent of 80, multiply 80 by 15 to get 1,200, then divide by 100 to get 12.

A useful shortcut is to find 10 percent first, because 10 percent of any number is just that number with the decimal point moved one place to the left. Ten percent of 240 is 24. From there, 20 percent is double that (48), and 5 percent is half of it (12). Combining those pieces lets you estimate many percentages in your head: 25 percent is a quarter, 50 percent is a half, and 75 percent is three quarters.

One number as a percentage of another

Sometimes the question runs the other way. You scored 45 out of 60 on a test, or you spent 30 out of a 200 budget, and you want the percentage. The formula is:

Percentage = part ÷ whole × 100

For the test example, divide 45 by 60 to get 0.75, then multiply by 100 to get 75 percent. For the budget example, 30 divided by 200 is 0.15, which is 15 percent. The key point is to be clear about which number is the whole. In a test, the whole is the total marks available. In a budget, the whole is the total budget, not the amount left over.

This same formula answers questions such as what share of a day you spent on a task, what fraction of a class passed, or how much of a goal you have completed. Whenever the phrase is something out of something, the something out of is usually the whole.

Percentage increase: how much has something grown?

A percentage increase compares a new value with an old value. First find the change, then express that change as a percentage of the old value:

Percentage increase = (new value − old value) ÷ old value × 100

Suppose a price rises from 200 to 250. The change is 50. Divide 50 by the old value, 200, to get 0.25, and multiply by 100 to get 25 percent. So the price increased by 25 percent. Note that the denominator is always the starting value, not the new one. That is the most common mistake in percentage problems, and it changes the answer completely.

The same method works for salaries, rents, scores, and follower counts. If a monthly bill goes from 80 to 100, the increase is 20 divided by 80, which is 25 percent. Saying it rose by 20 may sound small, but as a percentage of the original bill it is a quarter more.

Percentage decrease: how much has something fallen?

A percentage decrease uses the same idea, but the change runs downwards:

Percentage decrease = (old value − new value) ÷ old value × 100

If a price falls from 200 to 150, the drop is 50. Divide 50 by the old value, 200, to get 0.25, which is 25 percent. So the price fell by 25 percent. Again, the old value is the base. This matters for discounts: a jacket reduced from 120 to 90 has fallen by 30, and 30 divided by 120 is 25 percent off, not 33 percent. Dividing by the sale price instead of the original price is a classic error that makes a discount look bigger than it is.

Discounts, weight loss, and falling costs all use this formula. The result tells you the size of the change relative to where you started, which is usually the comparison people actually want.

Note on percentage points: a rise from 10 percent to 15 percent is 5 percentage points, but a 50 percent relative increase — the two measure different things, so check which one is meant before acting on a number.

Everyday percentage problems, solved

Notice how the tip and discount examples use the basic formula, the test example uses part divided by whole, and the salary and price examples use the increase and decrease formulas. Sorting a problem into one of those four types is most of the work. Once you know the type, the arithmetic is short.

Common mistakes to avoid

• Using the wrong base. For increases and decreases, always divide by the original value, not the new one.
• Adding percentages that have different bases. A 20 percent rise followed by a 20 percent fall does not return you to the start, because the fall is calculated on the larger, increased value.
• Confusing percent off with the amount to pay. If an item is 30 percent off, you pay 70 percent of the price, not 30 percent of it.
• Forgetting to convert. A decimal such as 0.35 is 35 percent; multiply by 100 to move from a decimal to a percentage.
• Rounding too early. Keep full numbers through the calculation and round only the final answer, so small errors do not grow.

Checking your answer

A fast sanity check catches most slips: a percentage below 100 of a number must be smaller than the number itself, and a discount should leave you paying most of the original price. For anything that matters, such as a payslip or a bill, run the numbers twice — once by hand and once with a calculator — and check which value you used as the base if they disagree.

Bottom line: most percentage problems are one of four types — a percent of a number, a part as a percent of a whole, a percent increase, or a percent decrease. Identify the type, use the original value as the base for changes, and check that the answer looks plausible before you trust it.