Percentage Calculator
Type a word problem, or pick a question. Read the big red answer, then the steps.
Write the problem the way a teacher would say it.
Tip, tax, or a piece of a whole.
How to Use This Percentage Calculator
A percentage is a number out of 100. The symbol is %.
25% means 25 out of every 100, or the decimal 0.25. Pick the question that sounds like your homework or your receipt.
| You are asking | Open this tab |
|---|---|
| What is 15% of 80? | Word problem or % of a number |
| 12 is what percent of 80? | is what % |
| 15 is 25% of what number? | is % of what |
| The price went from 80 to 100 | up or down |
| 20% off $50, or a 15% tip | off / tax / tip |
| I scored 42 out of 50 | test marks |
| Compare two numbers with no “start” | difference |
| Lab true value vs measured value | lab error |
| Turn 1/4 into a percent | convert |
Type the numbers and press Calculate, or paste the full sentence in Word problem. The big red number is the answer. The steps under it are the working you can copy into an exercise book.
The One Idea Behind Every Percentage Question
Every basic percentage problem is the same three-part family:
Part = (Percent ÷ 100) × Whole
If you know any two of those three things, you can find the third.
- Know the percent and the whole → find the part.
- Know the part and the whole → find the percent.
- Know the part and the percent → find the whole.
That last one is the reverse question. Many simple calculators skip it. This one does not.
Formula 1 — What Is P% of X?
Answer = (P ÷ 100) × X
Example: What is 15% of 80?
- 15 ÷ 100 = 0.15
- 0.15 × 80 = 12
- Check: 12 is 15% of 80.
Use this for a tip, a slice of a class, or the amount of a discount before you subtract it.
Formula 2 — Y Is What Percent of X?
Percent = (Y ÷ X) × 100
The whole cannot be zero. You cannot divide by nothing.
Example: 12 is what percent of 80?
- 12 ÷ 80 = 0.15
- 0.15 × 100 = 15%
Use this for test scores written as “12 right out of 80 questions,” market share, or “how much of the bag is left.”
Formula 3 — Y Is P% of What? (The Reverse)
Whole = Y ÷ (P ÷ 100) = Y × (100 ÷ P)
Percent cannot be zero here. Zero percent of a number is never a real piece.
Example: 15 students failed. That was 25% of the class. How big is the class?
- 25% = 0.25
- 15 ÷ 0.25 = 60
- Check forwards: 25% of 60 = 15.
This is the gap on many ranking pages that only ask “what is P% of X.”
Formula 4 — Percent Change (Up or Down)
Change % = [(New − Old) ÷ |Old|] × 100
A plus sign means increase. A minus sign means decrease. The starting number is the one you divide by — not the new number, and not the average.
Example: A price goes from 80 to 100.
- Change in money: 100 − 80 = 20
- 20 ÷ 80 = 0.25
- 0.25 × 100 = 25% increase.
Example: 50 falls to 40.
- 40 − 50 = −10
- −10 ÷ 50 = −0.2
- −20% decrease.
If the start is 0, percent change is not defined. The calculator will say so instead of printing Infinity.
Formula 5 — Take Off a Percent or Add a Percent
First find P% of the start. Then subtract for a sale, or add for a tip or tax.
Amount = (P ÷ 100) × Start
Final = Start ± Amount
Example: A shirt is $50 with 20% off.
- 20% of 50 = 10
- Sale price = 50 − 10 = 40
Example: Add a 15% tip to an $80 bill.
- 15% of 80 = 12
- Total = 80 + 12 = 92
Two discounts in a row are not added. 20% off then 10% off is not 30% off. The second percent acts on the new price. This page does one percent at a time on purpose, so the working stays honest.
Formula 6 — Test Marks
Marks % = (Marks Obtained ÷ Maximum Marks) × 100
Example: 42 out of 50.
- 42 ÷ 50 = 0.84
- 0.84 × 100 = 84%
The band under the answer is a guide, not your school’s official grade boundary. Schools set their own pass marks.
Change, Difference, and Error Are Not the Same
People mix these three words. The calculator keeps them on separate tabs.
Percent change needs an original value. “From 80 to 100” is a 25% increase.
Percent difference has no original. It compares two values using their average:
Difference % = |A − B| ÷ |(A + B) ÷ 2| × 100
Example: Compare 26 and 14.
- Gap = 12
- Average = 20
- 12 ÷ 20 × 100 = 60% different.
Percent error is for a science measurement against a known true value:
Error % = |Measured − True| ÷ |True| × 100
Example: True value 50, measured 47.
- Miss = 3
- 3 ÷ 50 × 100 = 6% error.
If a question says “increased from,” use up or down. If it says “how different are these two readings,” use difference. If it says “accepted value,” use lab error.
Convert a Percent, a Decimal, and a Fraction
25% = 0.25 = 1/4
Move the decimal point two places to turn a percent into a decimal, or two places the other way to turn a decimal into a percent. The convert tab also accepts a fraction such as 1/4.
Worked Word Problems
These match the example chips in the tool. Solve them on paper, then check the Word problem tab.
1. Shopping
A bag costs $50. It is 20% off. What do you pay?
20% of 50 = 10. Pay $40.
2. Tip
Dinner is $80. You leave 15%. What is the tip, and what is the total?
Tip = $12. Total = $92.
3. Class
12 of 80 pupils walk to school. What percent walk?
12 ÷ 80 × 100 = 15%.
4. Reverse
15 is 25% of a number. Find the number.
15 ÷ 0.25 = 60.
5. Growth
A plant was 80 mm. Now it is 100 mm. What is the percent change?
25% increase.
6. Test
42 marks out of 50.
84%.
Mistakes This Calculator Blocks
- Dividing by the new number instead of the old number when you want percent change.
- Treating 0:0 style zeros as a real answer. A whole of 0, a start of 0, or 0% as a reverse whole is rejected.
- Adding two sale percents as if they were one.
- Calling change, difference, and error the same thing.
- Writing a percent without × 100 after you divide.
Percent Versus Percentage Point
If a rate goes from 10% to 12%, that is a rise of 2 percentage points.
The percent change of the rate itself is:
2 ÷ 10 × 100 = 20%
News headlines often blur that. The calculator’s change tab always uses the formula above, so you can see which story you are telling.
Frequently Asked Questions
How Do I Calculate a Percentage of a Number?
Multiply the number by the percent, then divide by 100. 15% of 80 is 80 × 15 ÷ 100 = 12.
How Do I Find What Percent One Number Is of Another?
Divide the part by the whole, then multiply by 100. 12 of 80 is 15%.
How Do I Find the Original Amount After a Percent?
Divide the known piece by the percent as a decimal. If 15 is 25% of a class, the class is 60.
What Is the Percent Change Formula?
(New − Old) ÷ |Old| × 100. From 80 to 100 is a +25% change.
How Do I Work Out a Discount?
Find that percent of the price, then subtract. 20% off $50 is $40.
How Do I Work Out a Test Percentage?
Marks you got ÷ marks on the paper × 100.
Is Percent Difference the Same as Percent Change?
No. Change uses a starting value. Difference uses the average of two values.
Can a Percentage Be More Than 100%?
Yes. 50 is 200% of 25. The bar on screen stops at 100% only as a picture, not as a math limit.
Do My Numbers Leave This Page?
No. The calculator runs in the browser.
What If the Word Problem Is Not Read Correctly?
Use an example chip, or open the matching tab and type the two numbers yourself. The math is the same.
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