How to Calculate a Percentage (Increase, Decrease, and Percent Of)
Percentages show up constantly in everyday life - discounts, statistics, grades, growth rates - yet the three most common percentage calculations each use a slightly different formula, and mixing them up is one of the most frequent sources of math mistakes. Here is exactly how each one works.
1. Finding "X% of Y"
This is the most basic percentage calculation - finding a percentage of a given number.
Result = (Percentage / 100) x Number
Worked Example
What is 20% of 1,500?
Result = (20 / 100) x 1,500 = 0.20 x 1,500 = 300
2. Finding What Percentage X Is of Y
This flips the question around - instead of finding a percentage of a number, you are finding what percentage one number represents of another.
Percentage = (X / Y) x 100
Worked Example
What percentage is 45 of 300?
Percentage = (45 / 300) x 100 = 0.15 x 100 = 15%
3. Percentage Increase or Decrease
This calculates how much a value has changed, expressed as a percentage of the original value.
Percentage Change = ((New Value - Original Value) / Original Value) x 100
A positive result indicates an increase; a negative result indicates a decrease.
Worked Example: Increase
A value goes from 60 to 80. What is the percentage increase?
Percentage Change = ((80 - 60) / 60) x 100 = (20 / 60) x 100 = 33.3% increase
Worked Example: Decrease
A value goes from 200 to 150. What is the percentage decrease?
Percentage Change = ((150 - 200) / 200) x 100 = (-50 / 200) x 100 = -25%, or a 25% decrease
The Most Common Mistake: Reversing the Base
A frequent error is using the wrong number as the "original value" (the denominator) in a percentage change calculation. Going from 60 to 80 is a 33.3% increase - but going from 80 back down to 60 is not also a 33.3% decrease. It is actually a 25% decrease, because the base number being measured against is different in each direction (60 in the first case, 80 in the second).
A Related Trap: Percentage Points vs Percentages
If a rate goes from 10% to 15%, that is a change of 5 percentage points - but it is a 50% percentage increase relative to the original 10% (since (15-10)/10 x 100 = 50%). These two descriptions of the same change sound similar but mean very different things, and mixing them up is a common source of confusion in news reporting and statistics.
Reversing "X% of Y" to Solve for Y
Sometimes you know the result and the percentage, but need to find the original number. Rearranging the first formula:
Y = Result / (Percentage / 100)
Worked Example
If 20% of a number is 300, what is the number?
Y = 300 / 0.20 = 1,500
Step-by-Step: Choosing the Right Formula
- Identify what you actually know and what you are solving for - a percentage and a number, two numbers, or a before/after pair.
- If finding a percentage of a number, multiply the number by (percentage / 100).
- If finding what percentage one number is of another, divide the first by the second and multiply by 100.
- If finding percentage change, always divide by the original value, not the new one.
- Double-check your base number - this is where most percentage mistakes actually happen.
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Our free Percentage Calculator handles all of these calculation types instantly - just select what you are trying to find and enter your numbers.
Final Thoughts
Percentage calculations are simple individually, but easy to mix up when switching between the three main types - finding a percentage of a number, finding what percentage one number is of another, and calculating percentage change. The formulas never change; the key is correctly identifying which one your specific question actually calls for, and always being careful about which number is the "original" base.