Percentage Calculator Guide: Formula, Percent Change & Real Uses
Understand the three most common percentage calculations, when to use each one, and how to check your work before applying a discount, markup, rate change, or comparison.
A percentage is a way to express a value as a share of 100. That makes percentages useful whenever you need to compare values with different sizes: a sale discount, a tax rate, a grade, a margin, an investment return, or an increase from one period to the next.
The important part is choosing the right formula. “What is 20% of 80?” is different from “80 is what percent of 20?” and both are different from “what percent did 80 increase from 20?”
What Percentages Measure
Percentages convert a part-to-whole relationship into a standard scale. If 25 out of 100 people choose an option, that is 25%. If 5 out of 20 choose the same option, that is also 25%, because 5 ÷ 20 = 0.25.
This structure is why percentages are helpful for comparisons. They remove the scale of the original numbers and show the relationship between them.
The Core Percentage Formulas
1. Find a percentage of a number
Use this for discounts, tips, commissions, fees, taxes, and any situation where a rate is applied to a base number.
2. Find what percent one number is of another
Use this when you know the part and the whole and want the rate, share, or proportion.
3. Find percent increase or decrease
Use this for price changes, revenue growth, cost increases, score improvements, inflation, or any comparison between an old value and a new value.
Worked Examples
Result: $12
Result: 12 is 15% of 80
Result: 15% increase
Common Use Cases
- Shopping: estimate discounts, sale prices, coupons, and tips.
- Business: calculate markup, margin, revenue growth, conversion rates, and churn.
- Finance: compare rates of return, fee percentages, and interest changes.
- School: calculate grades, weighted scores, and test performance.
- Everyday planning: compare before-and-after numbers without being misled by the size of the base value.
For quick calculations, use the Percentage Calculator. For school-related percentages, the Grade Calculator and GPA Calculator can help with weighted outcomes.
Common Percentage Mistakes
- Using the new value as the denominator when calculating percent change instead of the original value.
- Confusing percentage points with percentage change. Moving from 5% to 7% is a 2 percentage-point increase, but a 40% relative increase.
- Applying a discount and then a tax in the wrong order for the situation being modeled.
- Forgetting to convert the percent into a decimal before multiplying.
- Assuming a 20% decrease followed by a 20% increase returns to the original value. It does not.
Frequently Asked Questions
What is the basic percentage formula?
The basic formula is part divided by whole times 100. For example, 12 divided by 80 times 100 equals 15%.
How do I calculate percent increase?
Subtract the original value from the new value, divide by the original value, and multiply by 100.
What is the difference between percent and percentage points?
Percentage points measure the absolute difference between two percentages. Percent change measures the relative change compared with the starting percentage.
Can I use the percentage calculator for discounts?
Yes. Use it to find a percent of a number, then subtract that amount from the original price to estimate the discounted price.
Calculate percentage of a number, percent change, and related percentage questions without setting up the formula manually.
Open Percentage Calculator →