Calculate a Percentage: The Formula With Worked Examples

The three core questions, each with a real example

Write the relationship as part equals rate times whole, with the rate as a decimal (15 percent is 0.15). Then solve for whatever is missing:

• What is 20 percent of 150? Multiply: 0.20 times 150 equals 30. That is your discount on a $150 jacket.
• 30 is what percent of 120? Divide the part by the whole: 30 divided by 120 is 0.25, so 25 percent. That could be your savings rate on a $120 weekly budget.
• 18 is 15 percent of what? Divide the part by the rate: 18 divided by 0.15 equals 120. Useful when you know the tip you left and the percentage you meant to leave.
• Grade check: 42 out of 50 is 42 divided by 50 times 100, or 84 percent, a B on most US scales.

A fast mental shortcut: 10 percent is the number with the decimal moved one place left. 10 percent of 86 is 8.6, so 5 percent is 4.3 and 15 percent is 12.9. Half of any number is 50 percent, a quarter is 25 percent and a fifth is 20 percent, which covers most sale signs you will ever see without reaching for a phone.

Percent change for raises, prices and growth

When a value moves from an old number to a new one, subtract, divide by the old number and multiply by 100. A raise from $52,000 to $55,120 is a change of 3,120, and 3,120 divided by 52,000 is 0.06, so a 6 percent raise.

The direction matters because the base changes. Going from 80 to 100 is a 25 percent increase, but going from 100 back to 80 is a 20 percent decrease. That is why a stock that falls 50 percent must then rise 100 percent just to get back to even, and why a store can mark something up 25 percent and later advertise 20 percent off without losing a cent.

To apply a change, multiply by one plus or minus the rate. A $50 item after a 15 percent increase is 50 times 1.15, or $57.50; after a 15 percent decrease it is 50 times 0.85, or $42.50.

Work backward to find the original number

Many everyday questions give you the result and hide the starting point. The fix is to divide instead of subtracting:

• A sale price of $60 after 25 percent off: the $60 is 75 percent of the original, so 60 divided by 0.75 equals $80. Subtracting 25 percent of 60 would wrongly give $75.
• A take-home bonus of $3,900 after 22 percent federal withholding: 3,900 divided by 0.78 is $5,000 gross.
• A population of 10,500 after 5 percent growth: 10,500 divided by 1.05 gives 10,000 the year before.
• A receipt total that already includes a sales levy works the same way, divided by one plus the rate.

Whenever a question says after, including or already, reach for division by the multiplier rather than taking a percentage of the final number.

Traps that make a percentage look wrong

These four catch people most often:

• Stacked discounts do not add. 20 percent off, then an extra 10 percent off, is 0.80 times 0.90, or 0.72 of the price, a 28 percent total discount rather than 30.
• Percent versus percentage points. A mortgage rate moving from 4 percent to 5 percent rose one point, which is a 25 percent increase in the rate itself.
• The wrong base. A 50 percent margin and a 50 percent markup are different: a $100 cost marked up 50 percent sells for $150, a 33 percent margin.
• Tiny bases exaggerate. Sales going from 2 units to 6 is a 200 percent jump, which sounds dramatic and means very little.

A quick sanity check catches most slips: a part smaller than the whole must be under 100 percent, and a decrease can never exceed 100 percent. When a headline or a colleague quotes a dramatic figure, ask for the two raw numbers behind it; the story usually changes once you see the base.

Stacked percentages are a classic trap, as this explanation of why 40% plus 15% is not 55% shows with real numbers.

Step-by-step

Common mistakes to avoid

Pro tips

Frequently asked questions