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| Calculate discounts, final sale prices, and percentage changes quickly and easily with this free online calculator. |
You see "35% off" on a price tag, a colleague says prices rose "about 12%", or a test result comes back as 42 out of 60. Each of these needs a different percentage calculation, and it is surprisingly easy to use the wrong one. This free calculator handles the four questions people ask most: what a percentage of a number is, what percent one number is of another, what a discounted price comes to, and how much a value rose or fell in percent.
Everything runs in your browser. Nothing you type is sent to a server or saved by the tool. After the calculator you will find worked examples, the formulas behind each mode, and the mistakes that cause most wrong answers.
Percentage and Discount Calculator
Privacy: calculations happen in your browser. The tool does not send, save or store what you enter.
How to use the calculator
- Pick a calculation. The four cards at the top switch the form below them.
- Type your two numbers. Use a dot for decimals. A comma is accepted only as a thousands separator, so 2,000 and 1,250.50 work, while 12,5 is rejected on purpose, because it could mean 12.5 or 125.
- Choose a currency if the numbers are money. It is optional and only changes how amounts are displayed. Leave it on "None" for scores, weights, distances or any other plain numbers.
- Press Calculate. The result appears with the formula that produced it. Use Copy Result to paste it into a message or spreadsheet, or Reset to start over.
- Percentage of a number: answers "what is 15% of 2,000?"
- What percent is it? answers "45 is what percent of 180?"
- Discount and final price: gives the amount you save and what you pay.
- Percentage change: shows whether a value rose or fell, and by how many percent.
Worked examples
These examples are calculated with the same formulas the tool uses, so you can check your own results against them.
Example 1: a percentage of a number
What is 15% of 2,000? Multiply 15 by 2,000 and divide by 100: 15 × 2,000 ÷ 100 = 300.
Example 2: what percent one number is of another
You answered 45 of 180 questions correctly in a practice set. 45 × 100 ÷ 180 = 25%.
Example 3: a discount and the final price
A jacket costs 1,000 and is 20% off. The discount is 1,000 × 20 ÷ 100 = 200, so the final price is 1,000 − 200 = 800. A shortcut: paying 80% of the price means 1,000 × 0.80 = 800.
Example 4: percentage change
A subscription goes from 80 to 92: (92 − 80) × 100 ÷ 80 = +15%. A price drops from 250 to 200: (200 − 250) × 100 ÷ 250 = −20%.
Example 5: two discounts in a row
A store takes 20% off 1,000 and then an extra 10% off the sale price. The first step gives 800. The second discount applies to 800, not to 1,000: 800 × 10 ÷ 100 = 80, so you pay 720. The total saving is 280, which is 28%, not 30%. In the calculator, run Discount mode twice and type the first final price as the second original price.
Example 6: why +50% then −50% does not get you back
Start with 100 and add 50%: you have 150. Remove 50% of 150 and you have 75, which is 25% below where you started. To get from 75 back to 150 you would need a +100% change. A percentage always refers to the value it is applied to.
The formulas behind each mode
- Percentage of a number: result = (percentage × number) ÷ 100
- What percent it is: percent = (part × 100) ÷ whole
- Discount: discount amount = (price × discount%) ÷ 100, and final price = price − discount amount
- Percentage change: change% = ((new − old) × 100) ÷ |old|, where |old| is the starting value without its sign
Two related calculations are not separate modes, but you can do them by hand. To find the original price when you know the final price and the discount, divide the final price by (1 − discount ÷ 100): 800 ÷ 0.80 = 1,000. And to compare rates, remember that a rise from 5% to 7% is 2 percentage points but a 40% relative increase, because (7 − 5) × 100 ÷ 5 = 40.
Accuracy, assumptions and limitations
- Rounding is for display only. The tool calculates with full precision and then shows money to two decimals and other results to at most four. A shop may round each item separately, so a receipt can differ from the calculator by a cent or two.
- Taxes, shipping and fees are not included. The discount is applied to the price you type. If your price already includes tax, the result does too.
- The currency selector is a label. It does not convert exchange rates.
- Percentage change needs a non-zero starting value. Going from 0 to anything cannot be expressed as a percentage, so the tool shows a message instead of a number. For a negative starting value, the percentage is based on its absolute size.
- Size limit. Numbers must be below one quadrillion in absolute value.
- Browser requirement. The calculator needs JavaScript. If it is turned off, the form will not respond.
Common mistakes
- Dividing a change by the new value instead of the old one. The base is always the starting value.
- Adding two discounts together. Successive discounts multiply, as in Example 5.
- Mixing up percent and percentage points when comparing interest rates, tax rates or survey results.
- Trusting the "original price" on a sale tag without checking it. The calculator can confirm the arithmetic, but not whether the former price was real. In the United States, the Federal Trade Commission's Guides Against Deceptive Pricing say a former-price comparison is legitimate when that price was the actual price offered to the public on a regular basis for a reasonably substantial period of time. Rules differ in other countries.
When this calculator is useful
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| Use the calculator to find percentage values, work out discounts, calculate final prices, and compare percentage changes. |
- Comparing two offers. 30% off 80 gives 56, while 25% off 70 gives 52.5, so the "smaller" discount is cheaper here.
- Checking a pay rise. Going from 3,500 to 3,745 is a +7% change.
- Turning scores into percentages. 42 out of 60 is 70%.
- Splitting a service charge. A 10% charge on a bill of 48.50 is 4.85.
- Tracking a budget. Cutting a monthly expense from 400 to 340 is a −15% change.
Frequently asked questions
Can I type numbers with commas?
Yes, as thousands separators: 2,000 or 1,250.50. A comma used as a decimal mark, such as 12,5, is rejected and the tool asks you to use a dot, because the same text could mean two different numbers.
Why do I get an error for percentage change from zero?
The formula divides by the starting value, and dividing by zero is undefined. If something grows from 0 to 50, the change cannot be written as a percentage, so the tool tells you instead of showing a misleading figure.
How do I calculate two discounts in a row?
Use Discount mode twice. Enter the first discount, then type the final price from the first result as the original price for the second discount. Twenty percent followed by ten percent off 1,000 ends at 720.
Does the currency selector convert my amount?
No. It only adds a currency symbol or code to the display. Choose "None" when your numbers are not money.
Does the calculator store or send what I enter?
No. The calculation runs in your browser and the tool does not save or transmit your numbers. As with any page on this site, the page itself may load ads or analytics, which are described in our Privacy Policy.
Conclusion
Whether you are checking a sale, a grade or a price change, the right calculation depends on what your percentage is measured against. Use the tool above, check it against the examples, and keep the common mistakes in mind. If you like practical everyday tools, read our guide to the best productivity apps for everyday tasks, or browse more guides on the Mundo News 24h home page.
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