How to Calculate Percentages: The 3 Formulas You Actually Need
Every percentage problem comes down to one of three questions: what is X% of Y, what percent is X of Y, or what’s the percentage change from X to Y. Once you know which one you’re facing, the math takes ten seconds.
The three formulas
1. Finding a percentage of a number (a discount, a tip, a tax)
Result = (X / 100) × Y2. Finding what percent one number is of another (a tip you left, a score you got)
Result = (X / Y) × 1003. Finding the percentage change between two numbers (a raise, a price hike, a drop in sales)
Result = ((New − Original) / |Original|) × 100A positive result is an increase, a negative one is a decrease. The absolute value on the original matters: it keeps the sign of the answer tied to whether the number went up or down, not to whether the original was already negative.
Worked example: a jacket, a tip, and a rent hike
Here’s each formula with real numbers.
| Scenario | Formula | Numbers | Result |
|---|---|---|---|
| 25% off an $80 jacket | Mode 1 | 25% of 80 | $20 off, pay $60 |
| You tipped $15 on a $75 bill | Mode 2 | 15 is what % of 75 | 20% |
| Rent went from $1,200 to $1,350 | Mode 3 | change from 1,200 to 1,350 | +12.5% |
Calculate with your own numbers
The reverse percentage trap
This is the one that trips up most people: you know the price after a discount and need the original price. Adding the percentage back onto the discounted price does not work.
Take the jacket from the table above. You paid $60 after 25% off. The wrong move is to add 25% of $60 ($15) back on, which lands on $75, not $80. The correct formula is:
Original = Final / (1 − discount% / 100)$60 / (1 − 0.25) = $60 / 0.75 = $80, which checks out. The shortcut fails because 25% off $80 and 25% “added back” onto $60 are percentages of two different numbers. Always divide by what’s left, never multiply by what was taken away.
Percentage points are not percent
A savings rate moving from 4% to 5% is a 1 percentage point increase, but it’s a 25% relative increase, since 1 is 25% of 4. News headlines blur this distinction constantly (“rates up 1%” usually means up 1 percentage point), and the gap gets wider the smaller the starting number is. A rate going from 2% to 3% is still 1 percentage point, but it’s a 50% relative jump. When the base number actually matters to you, on a loan, a tax bracket, or an investment yield, check which one is being quoted before you act on it.
Common mistakes
- Forgetting to convert to a decimal. 15% is 0.15 when you multiply, not 15. Plugging 15 straight into the formula inflates the result 100x.
- Chaining percentage changes as if they add up. A 20% drop followed by a 20% rise doesn’t get you back to the start. $100 drops 20% to $80, then rises 20% to $96, not $100, because each percentage applies to a different base.
- Using the wrong base in mode 2. “15 is what % of 75” and “75 is what % of 15” give very different answers (20% vs. 500%). Confirm which number is the whole and which is the part before you calculate.
- Skipping the reverse formula. Adding a percentage back the same way you subtracted it, instead of dividing, is the single most common percentage mistake people make with discounts.
FAQ
How do I calculate X% of a number?
Divide the percentage by 100, then multiply by the number: (X / 100) × Y. For 25% of 80, that’s (25 / 100) × 80 = 20.
How do I find the original price before a discount?
Divide the final price by (1 − discount / 100), not by the discount itself. A $60 price after 25% off means the original was 60 / 0.75 = $80.
What’s the difference between percentage points and percent change? A percentage point is the raw gap between two percentages (4% to 5% is 1 point). Percent change measures that gap relative to the starting value (1 point on a base of 4% is a 25% relative increase). Both are correct, they just answer different questions.
Can I calculate a percentage decrease the same way as an increase?
Yes. The formula ((New − Original) / |Original|) × 100 returns a negative number automatically when the value dropped, so no separate formula is needed.