Percentage Formulas
Keep this sheet nearby when you need the exact expression rather than a story problem. Each formula maps to one calculator on this site. Spreadsheet versions use the same arithmetic with cell references.
Core arithmetic
These four cover most school and everyday questions. Change has a direction. Difference does not.
- Percent of a number: (X / 100) × Y
- What percent: (X / Y) × 100
- Percentage change: ((new − original) / original) × 100
- Percentage difference: |A − B| / ((A + B) / 2) × 100
Forward and reverse
Applying a percent and undoing a percent are not the same formula. After an increase, divide by 1 plus the rate. After a decrease, divide by 1 minus the rate.
- Increase a number by X%: Y × (1 + X / 100)
- Decrease a number by X%: Y × (1 − X / 100)
- Original after an X% increase: final / (1 + X / 100)
- Original after an X% decrease: final / (1 − X / 100)
Money, error, and slope
Markup divides by cost. Margin divides by selling price. Percentage error divides by the accepted value, not the average of the two measurements.
- Discount sale price: original × (1 − discount / 100)
- Markup percent: ((price − cost) / cost) × 100
- Margin percent: ((price − cost) / price) × 100
- Percentage error: |experimental − accepted| / |accepted| × 100
- Slope percent: (rise / run) × 100
Excel and Google Sheets
If A1 holds the first input and B1 holds the second, these three cover percent of, what percent, and change. Format the result cell as a number or as a percent depending on whether you already multiplied by 100.
- Percent of a number: =A1*B1/100
- What percent X is of Y: =(A1/B1)*100
- Percentage change from A1 to B1: =(B1-A1)/A1
Formula table
Use the table when you only need to glance at the expression and the matching tool.
| Question | Formula | Tool |
|---|---|---|
| What is X% of Y? | (X / 100) × Y | Percent of a number |
| X is what % of Y? | (X / Y) × 100 | What percent |
| Change from A to B | ((B − A) / A) × 100 | Percentage change |
| Difference between A and B | |A − B| / ((A + B) / 2) × 100 | Percentage difference |
| Original after ±% | final / (1 ± p / 100) | Reverse percentage |
| Apply ±% to a number | Y × (1 ± X / 100) | Increase or decrease by a percent |
| Sale price after % off | original × (1 − d / 100) | Discount |
| Markup on cost | ((price − cost) / cost) × 100 | Markup |
| Margin on price | ((price − cost) / price) × 100 | Margin |
| Percentage error | |E − A| / |A| × 100 | Percentage error |
| Slope percent | (rise / run) × 100 | Slope percentage |
Related reading
Formula questions
If you write =(A1/B1)*100, leave the cell as a number and type the percent sign in the label. If you write =A1/B1 and format the cell as a percent, Excel already multiplies by 100 for display.
They answer different questions. Markup is the extra amount relative to what you paid. Margin is the extra amount relative to what the customer paid. Cost 100 and price 150 is a 50% markup and a 33.333% margin.
Divide by 1 plus the rate. Subtracting the same percent from the new amount does not return the original. 100 increased by 10% is 110; 110 decreased by 10% is 99, not 100.
No. Error divides by the accepted value. Difference divides by the average of the two numbers.
Multiply the two percents and divide by 100. 20% of 50% is 10%. Apply that combined rate to an amount if you also have a starting number.