Percentage Calculator
Calculate percentages instantly — find a percent of a number, figure out what percent one number is of another, or calculate percent change.
By Evan Carter · Updated August 15, 2026
15% of 200
30
One Tool, Three Percentage Problems
A percentage is just a ratio expressed out of 100. The word comes from the Latin "per centum," meaning "per hundred," so 25% literally means 25 out of every 100. This tool handles the three percentage questions you actually run into day to day: finding a percent of a number, working out what percent one number is of another, and measuring the percent change between two values. Pick the mode that matches your question, enter your numbers, and the result updates as you type.
The Three Core Calculations
1. Finding a Percent of a Number
To find X% of Y, multiply Y by X and divide by 100. This is the math behind tips, discounts, sales tax, commissions, and interest. For example, 15% of 200 is 200 x 15 / 100 = 30. A 20% discount on an $80 item is 80 x 20 / 100 = $16 off, leaving a final price of $64. Because the operation is just multiplication, a percentage over 100 produces a result larger than the original: 150% of 40 is 60.
2. Working Out What Percent One Number Is of Another
Divide the part by the whole, then multiply by 100. If you answered 45 of 60 questions correctly, your score is 45 / 60 x 100 = 75%. If 18 of 24 seats in a room are filled, that is 18 / 24 x 100 = 75% occupancy. This is the right mode for test scores, survey results, completion rates, and any "X out of Y" situation.
3. Measuring Percent Change
Percent change compares a new value against an old one using the formula ((New - Old) / Old) x 100. The starting value is always the base you divide by. Going from 200 to 250 is a 25% increase, because the $50 gain is one quarter of the original 200. Going from 250 back to 200 is a 20% decrease, because the same $50 is now measured against the larger 250. That is why an increase and the matching decrease almost never share the same percentage.
Reverse Percentages: Finding the Original Amount
One of the most common real-world tasks is undoing a percentage to recover the original number. The key idea is to divide instead of multiply. If a receipt total of $120 already includes a 20% markup, the pre-markup price was 120 / 1.20 = $100. If a sale price of $80 reflects a 20% discount, the original ticket price was 80 / 0.80 = $100. A frequent mistake is adding the discount percentage back onto the sale price — adding 20% to $80 gives $96, not the true original of $100, because the discount was taken from a larger base.
Mental Math Shortcuts
- 10%: move the decimal one place left, so 10% of 240 is 24.
- 15%: take 10% and add half of it, so 15% of 240 is 24 + 12 = 36.
- 20%: double the 10% value, or just divide by 5.
- 25%: divide by 4; 50%: halve it; 5%: take half of 10%.
- Add or subtract: turn the percentage into a multiplier. To add 15%, multiply by 1.15; to remove 15%, multiply by 0.85.
Percentage vs. Percentage Points
These two phrases are easy to mix up but mean different things. When a rate moves from 5% to 8%, that is a 3 percentage point increase (the plain gap between the numbers) but a 60% relative increase (3 measured against the original 5). News coverage of interest rates, poll numbers, and unemployment often blurs the line, so it pays to ask whether a figure is a difference in points or a relative percent change before drawing a conclusion.
Common Mistakes to Avoid
- Dividing by the wrong base. Percent change always uses the old value, not the new one, as the denominator.
- Assuming a percentage increase and decrease cancel out. A 50% drop needs a 100% gain to recover, not another 50%.
- Stacking discounts by adding them. Two 20% discounts are not 40% off; applied in sequence they leave 0.80 x 0.80 = 64% of the price, a 36% total reduction.
When Percentages Are Not Quite the Question
This tool is built for general percentage math. If you are specifically figuring out a restaurant gratuity, the tip calculator adds per-person splitting. For sales tax on a purchase, a dedicated sales tax calculator applies the correct state rate. And for growth that compounds over many periods, such as savings or investments, a compound interest calculator handles the repeated percentage gains that a single percent-change figure cannot capture.
Frequently Asked Questions
How do I calculate a percentage of a number?
To find X% of Y, multiply Y by X and divide by 100. For example, 15% of 200 = 200 x 15 / 100 = 30. The same method powers everyday tasks like tips, discounts, sales tax, and commission. If the percentage is over 100, the result is simply larger than the original number.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100. If you scored 45 out of 60 on a test, that is 45 / 60 x 100 = 75%. The smaller number is usually the part and the larger is the whole, but the formula works either way and will return a value above 100% when the part exceeds the whole.
What is the difference between percentage and percentage points?
If a rate moves from 5% to 7%, that is a 2 percentage point increase but a 40% relative increase. Percentage points measure the plain arithmetic gap between two percentages, while percent change measures the relative difference between them. Financial and political reporting frequently confuses the two, so the distinction matters.
How do I calculate percent change?
Percent change = ((New Value - Old Value) / Old Value) x 100. A positive result means an increase and a negative result means a decrease. For example, going from 200 to 250 is a 25% increase, while going from 250 back to 200 is a 20% decrease. The base you divide by is always the starting (old) value.
How do I reverse a percentage to find the original number?
When a number already includes a percentage, divide rather than multiply. If a price is $120 after a 20% markup, the original was 120 / 1.20 = $100. If $80 is left after a 20% discount, the original was 80 / 0.80 = $100. Adding the percentage back to a discounted price will not return the original amount.
How do I add or subtract a percentage from a number?
To add 15% to 200, multiply by 1.15 to get 230. To subtract 15%, multiply by 0.85 to get 170. Turning the percentage into a multiplier (1 plus or minus the rate as a decimal) is faster and less error-prone than calculating the percentage separately and then adding or subtracting it.
Why does a 50% drop need a 100% gain to recover?
Because the base shrinks. If a $100 value falls 50%, it is now $50. To get back to $100 it must double, which is a 100% gain on the smaller base. This asymmetry is why a 25% loss needs a 33% gain to break even, and why large drawdowns are so damaging to investments and budgets.
Can a percentage be more than 100%?
Yes. A percentage simply expresses a ratio out of 100, so values above 100% are valid whenever the part is larger than the reference whole. Sales that triple are a 200% increase, and 150% of 40 is 60. Percentages below 0% are also valid and represent decreases relative to the starting value.
This calculator provides estimates for informational purposes only. Results should not be considered as financial advice. Actual amounts may vary based on additional factors not included in this calculator. Consult a qualified financial advisor for personalized advice.
Tax data is based on 2026 federal and state rates (IRS Rev. Proc. 2025-32, Tax Foundation). State bracket thresholds may differ slightly from official figures due to rounding and inflation adjustments. Data is updated annually and may not reflect mid-year legislative changes.
See how we calculate and our editorial policy for the formulas, sources, and review process behind this tool.