To calculate what percentage one number is of another, divide the part by the whole and multiply by 100. For example, 18 out of 60 is 18 ÷ 60 × 100 = 30%. The trick is identifying which number represents the whole before you reach for a calculator.
Different questions need slightly different formulas. Finding 30% of a number, working out a percentage increase, and recovering a price before a discount are related calculations, but they are not interchangeable. Here is how to choose the right one.
What does a percentage mean?
Percent means “per hundred.” So 25% means 25 out of every 100, which is the same proportion as 0.25 or one quarter. To convert a percentage to a decimal, divide by 100. To turn a decimal into a percentage, multiply by 100 and add the percent sign.
For example, 7.5% becomes 0.075, while 0.6 becomes 60%. Be especially careful with small percentages: 0.5% is 0.005 as a decimal, not 0.5. The latter would mean 50%.
How to find what percentage a part is of a whole
Percentage = (part ÷ whole) × 100
Suppose you answer 42 questions correctly on a 56-question test. The part is 42 and the whole is 56. Calculate 42 ÷ 56 = 0.75, then multiply by 100. Your score is 75%.
Use matching units. If you have completed 45 minutes of a two-hour task, first convert two hours to 120 minutes. Then 45 ÷ 120 × 100 = 37.5%. Dividing 45 by 2 would compare minutes with hours and give a meaningless answer.
The denominator should match the question. If 12 of 40 attendees are new members, new members make up 30% of attendees. Comparing those 12 with the 28 returning members answers a different question.
How to calculate a percentage of a number
Amount = whole × (percentage ÷ 100)
To find 18% of 250, convert 18% to 0.18 and calculate 250 × 0.18 = 45. You can check this mentally: 10% of 250 is 25, and 20% is 50, so an 18% result should fall between them.
For a $72 item discounted by 25%, the saving is 72 × 0.25 = $18. Subtract that saving from the original price: $72 − $18 = $54. Alternatively, multiply by the percentage you still pay: 72 × 0.75 = 54. Any additional fees or taxes would need their own calculation.
These relationships follow the basic percent equations explained in OpenStax’s guide to percent applications.
How to calculate percentage increase or decrease
Percentage change = ((new value − original value) ÷ original value) × 100
If weekly orders rise from 160 to 200, the increase is 40. Divide by the original 160: 40 ÷ 160 × 100 = 25%. Orders increased by 25%, not 20%; dividing by the new value would use the wrong starting point.
If orders instead fall from 200 to 160, calculate (160 − 200) ÷ 200 × 100 = −20%. The negative sign indicates a decrease. You can report this as “a 20% decrease,” without keeping the minus sign in that wording.
An increase and an equal percentage decrease do not cancel out. Starting at 100, a 20% increase gives 120. A subsequent 20% decrease removes 24, leaving 96. Each change applies to a different base.
How to work backward from a percentage
When the known amount is a percentage of an unknown whole, divide by the percentage expressed as a decimal. If 36 is 30% of a number, the whole is 36 ÷ 0.30 = 120.
For a discounted price, divide by the percentage remaining. A jacket costs $84 after a 30% discount, so $84 represents 70% of its original price. Calculate 84 ÷ 0.70 = $120. Adding 30% to $84 would give $109.20, which does not restore the original price.
For an increased amount, divide by one plus the increase rate. If a quantity becomes 324 after rising 8%, its original value was 324 ÷ 1.08 = 300. Check by multiplying 300 by 1.08.
Percentage points versus percent change
If a survey result rises from 40% to 50%, the difference is 10 percentage points. Its relative percentage increase is (50 − 40) ÷ 40 × 100 = 25%.
Use percentage points when subtracting two percentages directly. Use percent change when describing the difference relative to the starting value. Reed College’s quantitative skills primer explains why those two descriptions should not be confused.
How to calculate percentages in Excel
Enter the part in A2 and the whole in B2. Type =A2/B2 in another cell, then apply Percentage formatting. If A2 contains 42 and B2 contains 56, the underlying result is 0.75 and the formatted display is 75%.
To calculate 18% of an amount in A2, use =A2*18%. For percentage change, put the original amount in A2 and the new amount in B2, then use =(B2-A2)/A2 and format the result as a percentage.
Do not multiply the formula by 100 and also apply Percentage formatting: doing both turns 0.75 into a displayed 7500%. See Microsoft’s percentage calculation instructions for spreadsheet examples.
Common questions and quick checks
Can a percentage be more than 100%?
Yes. If you complete 150 units against a target of 120, you achieve 150 ÷ 120 × 100 = 125% of the target. That is 25% above the target, not a 125% increase.
What if the starting value is zero?
Ordinary percentage change is undefined when the original value is zero because the formula divides by zero. If orders go from zero to 15, report the increase as 15 orders rather than assigning a percentage. A zero part divided by a positive whole, however, is simply 0%.
When should I round?
Keep extra digits during calculations and round the final answer to the precision you need. For instance, 2 ÷ 7 × 100 is approximately 28.5714%, or 28.57% to two decimal places. Rounding the fraction to 0.29 first would produce 29%, losing useful accuracy.
Can I average several percentages?
Only use a simple average when the groups have equal weight. A score of 9 out of 10 is 90%, and 30 out of 50 is 60%. Combined, the score is 39 out of 60, or 65%, not the simple average of 75%.
Before accepting any answer, ask: What is the whole? Are the units consistent? Is the answer a percentage, an amount, or a change? Those three checks catch most percentage mistakes.
If you prefer a physical keypad for practice, browse basic desktop calculator options on Amazon. A standard calculator is enough for the arithmetic in this guide.
Leave a Reply