How to Calculate a Percentage: 3 Formulas Everyone Should Know
Percentage calculations come up constantly. Discounts, tips, pay raises, exam scores, interest rates, statistics, sale prices. Most of us can handle simple cases but get fuzzy when the question is phrased differently. These three formulas cover almost every percentage problem you will encounter in daily life.
Formula 1: What Is X% of Y?
This is the most common percentage question. You know the percentage and the base number. You want the actual amount.
The formula is: Answer = (X / 100) multiplied by Y
Example: What is 18% of $240? (18 / 100) x 240 = 0.18 x 240 = 43.20. The 18% tip on a $240 restaurant bill is $43.20.
Another example: A jacket is priced at $150 and is 30% off. The discount is (30 / 100) x 150 = $45. You pay $150 minus $45 = $105.
Mental shortcut: To find 10% of any number, simply move the decimal point one place to the left. 10% of 340 = 34. From there, 20% is double (68), 5% is half of 10% (17), and 15% is the 10% figure plus the 5% figure (34 + 17 = 51).
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Formula 2: What Is the Percentage Change?
This formula tells you how much something has increased or decreased in percentage terms, relative to the original value.
The formula is: Percentage change = ((New value - Old value) / Old value) x 100
Example 1, increase: A salary was $52,000 and rises to $55,000. Change = ((55,000 - 52,000) / 52,000) x 100 = (3,000 / 52,000) x 100 = 5.77% increase.
Example 2, decrease: A house sold for $480,000 then resold for $440,000. Change = ((440,000 - 480,000) / 480,000) x 100 = (-40,000 / 480,000) x 100 = -8.33%. The price dropped 8.33%.
Important note: a 50% increase followed by a 50% decrease does not bring you back to where you started. If you start at 100, a 50% increase takes you to 150. A 50% decrease on 150 takes you to 75. Percentage changes are always calculated relative to the current value, not the original.
Formula 3: X Is What Percent of Y?
This formula gives you a proportion expressed as a percentage. You know both a part and a whole, and you want to express the part as a percentage of the whole.
The formula is: Percentage = (X / Y) x 100
Example: You answered 34 questions correctly out of 40 total. 34 is what percent of 40? (34 / 40) x 100 = 0.85 x 100 = 85%. You scored 85%.
Another example: 750 out of 3,200 employees voted in favour of a policy change. What percentage voted in favour? (750 / 3,200) x 100 = 23.44%.
A Common Source of Confusion
Percentage and percentage points are not the same thing and mixing them up leads to real misunderstandings, particularly in financial and political reporting.
If a mortgage rate rises from 3% to 5%, it has increased by 2 percentage points. But as a percentage change, it has increased by ((5 - 3) / 3) x 100 = 66.7%. Both statements are technically correct but they describe completely different things. Percentage points describe the arithmetic difference. Percentage change describes the proportional increase relative to the starting value.
Frequently Asked Questions
What is 15% of 80?
15% of 80 is 12. Calculate it as (15 / 100) x 80 = 0.15 x 80 = 12. Alternatively use the mental shortcut: 10% of 80 is 8, and 5% of 80 is 4. Add them together to get 15% = 12.
How do I calculate a percentage increase?
Subtract the original number from the new number, divide by the original number, then multiply by 100. If sales went from 200 to 250 units, the increase is ((250 - 200) / 200) x 100 = 25%. Make sure you always divide by the original starting value, not the final value.
How do I work out the original price before a percentage increase?
Divide the final price by (1 plus the decimal rate). If a product is now priced at $120 after a 20% increase, the original price was 120 / 1.20 = $100. For a decrease, divide by (1 minus the decimal rate). If a price dropped 15% to reach $85, the original was 85 / 0.85 = $100.
What is the fastest way to calculate 20% in your head?
Find 10% by moving the decimal point one place left, then double it. 20% of 360: 10% = 36, double to get 20% = 72. This takes two seconds once the habit is established and is accurate for any number.