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How to Calculate Percentages (With Examples)
Percentage means “per hundred.” Every percentage calculation comes down to one of three formulas. Here they are, with worked examples for each.
Formula 1: what is X% of Y?
The formula is:
Result = (X / 100) x Y
This is the most common percentage calculation. You use it for tips, discounts, taxes, and splits.
Example: What is 18% of 240?
(18 / 100) x 240 = 0.18 x 240 = 43.2
Example: What is 7.5% of $85?
(7.5 / 100) x 85 = 0.075 x 85 = $6.375, or $6.38 rounded.
Formula 2: what percent is X of Y?
The formula is:
Percentage = (X / Y) x 100
You use this when you have two numbers and want to know the ratio as a percentage.
Example: 36 is what percent of 150?
(36 / 150) x 100 = 0.24 x 100 = 24%
Example: You scored 42 out of 50 on a test. What percentage is that?
(42 / 50) x 100 = 0.84 x 100 = 84%
Formula 3: percent change
The formula is:
Percent change = ((New - Old) / Old) x 100
A positive result means an increase. A negative result means a decrease.
Example: A product’s price went from $80 to $92. What is the percent change?
((92 - 80) / 80) x 100 = (12 / 80) x 100 = 15% increase
Example: Your electric bill dropped from $145 to $118. What is the percent change?
((118 - 145) / 145) x 100 = (-27 / 145) x 100 = -18.62%, or about an 18.6% decrease.
Quick reference table
Here are common percentages of common numbers, pre-calculated.
| Base number | 10% | 15% | 20% | 25% | 50% |
|---|---|---|---|---|---|
| 50 | 5 | 7.5 | 10 | 12.5 | 25 |
| 100 | 10 | 15 | 20 | 25 | 50 |
| 150 | 15 | 22.5 | 30 | 37.5 | 75 |
| 200 | 20 | 30 | 40 | 50 | 100 |
| 500 | 50 | 75 | 100 | 125 | 250 |
| 1,000 | 100 | 150 | 200 | 250 | 500 |
Shortcut for 10%: move the decimal point one place to the left. 10% of 350 is 35. From there, 5% is half of that (17.5), and 20% is double (70).
Common mistakes to avoid
Mixing up the base number. “25 is what percent of 200?” and “200 is what percent of 25?” give very different answers. 25/200 = 12.5%. 200/25 = 800%. Always put the “part” on top and the “whole” on the bottom.
Percent change direction. With percent change, you always divide by the old (original) value, not the new one. Going from 50 to 75 is a 50% increase. Going from 75 to 50 is a 33.3% decrease. The same $25 difference produces different percentages because the base is different.
Forgetting to multiply by 100. The formula (X / Y) gives you a decimal like 0.36. You need to multiply by 100 to convert it to 36%.
Key takeaways
- What is X% of Y? Multiply: (X / 100) x Y
- What percent is X of Y? Divide: (X / Y) x 100
- Percent change: ((New - Old) / Old) x 100
- For 10%, just move the decimal one place left, then scale up or down for other percentages
- Percent change always uses the original value as the denominator
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