What is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred." Percentages are used everywhere in daily life — from calculating discounts and tips to understanding tax rates, interest rates, exam scores, and statistical data. When we say "25%," we mean 25 out of every 100, which is equivalent to the fraction 1/4 or the decimal 0.25.
Percentage Formulas
Percentage of a Number
Result = (Percentage / 100) * Number25% of 200 = (25 / 100) * 200 = 50
What Percent X is of Y
Percentage = (X / Y) * 10030 is what % of 150? (30 / 150) * 100 = 20%
Find the Whole from a Part
Whole = X / (Percentage / 100)50 is 25% of what? 50 / (25 / 100) = 200
Percentage Change
Change = ((New - Old) / |Old|) * 10080 to 100: ((100 - 80) / 80) * 100 = +25%
Percentage Difference
Diff = (|A - B| / ((A + B) / 2)) * 10040 vs 60: (20 / 50) * 100 = 40%
Increase / Decrease by %
Result = Number * (1 +/- Percentage / 100)Increase 80 by 25%: 80 * 1.25 = 100
Common Percentage Calculations
| Percent | of 100 | of 200 | of 500 | of 1000 |
|---|---|---|---|---|
| 5% | 5 | 10 | 25 | 50 |
| 10% | 10 | 20 | 50 | 100 |
| 15% | 15 | 30 | 75 | 150 |
| 20% | 20 | 40 | 100 | 200 |
| 25% | 25 | 50 | 125 | 250 |
| 33.33% | 33.33 | 66.67 | 166.67 | 333.33 |
| 50% | 50 | 100 | 250 | 500 |
| 75% | 75 | 150 | 375 | 750 |
| 100% | 100 | 200 | 500 | 1000 |
Tips for Working with Percentages
Quick Mental Math
To find 10% of any number, just move the decimal one place to the left. To find 5%, halve the 10% result. To find 1%, move the decimal two places left. Combine these to estimate any percentage quickly.
Reverse Percentages
If an item costs $75 after a 25% discount, the original price is $75 / (1 - 0.25) = $100. Always divide by (1 - discount rate) to reverse a decrease, or (1 + rate) to reverse an increase.
Avoid Common Mistakes
A 50% increase followed by a 50% decrease does NOT return to the original value — it results in 75% of the original. Percentage operations are not symmetric, so always be careful with sequential changes.
Frequently Asked Questions
To find X% of Y, convert the percentage to a decimal by dividing by 100, then multiply by the number. For example, 25% of 200 = (25 / 100) * 200 = 50.
Percentage change measures how much a value has increased or decreased relative to its original value. The formula is ((New - Old) / |Old|) * 100. A positive result means an increase, and a negative result means a decrease.
Percentage change compares a new value to an old value and has direction (increase or decrease). Percentage difference compares two values without an implied direction, using the average of the two values as the base: (|A - B| / ((A + B) / 2)) * 100.
Divide the part by the whole and multiply by 100. For example, to find what percent 30 is of 150: (30 / 150) * 100 = 20%. So 30 is 20% of 150.
To increase a number by a percentage, multiply the number by (1 + percentage / 100). For example, to increase 80 by 25%: 80 * (1 + 25/100) = 80 * 1.25 = 100.
To decrease a number by a percentage, multiply the number by (1 - percentage / 100). For example, to decrease 80 by 25%: 80 * (1 - 25/100) = 80 * 0.75 = 60.
A basis point (bps) is one hundredth of a percentage point, or 0.01%. It is commonly used in finance to describe small changes in interest rates or yields. For example, a change from 3.00% to 3.25% is an increase of 25 basis points.
Yes. This percentage calculator runs 100% in your browser using client-side JavaScript. No data is sent to any server. You can even use it offline once the page has loaded.
Yes. A percentage greater than 100% simply means the value exceeds the reference amount. For example, if sales grew from 50 to 150, that is a 200% increase, meaning the new value is 300% of the original.