Start by identifying what the question is asking
Percentage questions can contain the same numbers and still require different formulas. The words around the values determine which number is the part, which is the whole and which is the original baseline.
Write the question in plain language before calculating. This prevents a common error: using the formula for a percentage of a number when the task actually asks what percentage one number represents of another.
- What is X% of Y? Multiply Y by X ÷ 100.
- X is what percent of Y? Divide X by Y, then multiply by 100.
- What is the percentage change from X to Y? Divide the change by the magnitude of X, then multiply by 100.
- What is Y after an X% increase or decrease? Multiply Y by 1 plus or minus X ÷ 100.
Percentage of a number and percentage of a whole
To find 15% of 240, turn 15% into the decimal 0.15 and multiply: 0.15 × 240 = 36. This is useful for a discount amount, tax, commission, allocation or any stated share of a base value.
To find what percentage 36 is of 240, reverse the relationship: 36 ÷ 240 × 100 = 15%. The whole belongs in the denominator. If you exchange the part and whole, the answer describes a different relationship.
Percentage change depends on the original value
Percentage change compares the difference with the starting value: (new − original) ÷ |original| × 100. Moving from 80 to 100 is an increase of 20, and 20 is 25% of the original 80, so the percentage increase is 25%.
Reversing the direction produces a different percentage. Moving from 100 back to 80 is a decrease of 20%, because the decrease is measured against the new starting value of 100. Percentage changes are directional, not symmetric.
- Find the absolute change
Subtract the original value from the new value.
- Divide by the original magnitude
The starting value is the baseline that gives the change its context.
- Multiply by 100
Convert the decimal ratio into a percentage.
- Interpret the sign
A positive result is an increase and a negative result is a decrease.
Percentage points and repeated changes are different ideas
When a rate moves from 20% to 25%, it has increased by 5 percentage points. Relative to the original 20%, however, the increase is 25%. State which measure you mean, especially when discussing survey results, interest rates or conversion rates.
Repeated percentage changes multiply rather than add. A 20% increase changes 100 to 120. A subsequent 20% decrease is calculated from 120 and removes 24, leaving 96. Equal percentage increases and decreases do not cancel unless they use the same base.
- Use percentage points for the direct difference between two rates.
- Use relative percentage change to describe the difference compared with the original rate.
- Apply successive changes one at a time to the updated value.
- Keep more precision during intermediate calculations and round the final answer appropriately.
Questions about this task
How do I add 10% to a number?
Multiply the number by 1.10. The 1 keeps the original value and 0.10 adds ten percent of it.
Why do a 20% increase and 20% decrease not cancel?
The decrease is applied to the larger, already-increased value. Starting from 100 gives 120 and then 96, not 100.
What is the difference between percent and percentage points?
Percentage points measure the direct difference between rates. Percent change compares that difference with the original rate.