Percentage Calculator
Find X% of Y, percent change, discounts, and more — free and instant.
Percentage calculator
Result
30
20% × 150 = 30
Popular calculators
Essential calculators
Direct links to the percentage, money, and grade tools people use most. Each page shows the formula and a worked example.
- Percentage of a number20% of 150 = 30
- Percentage increaseOld value to new
- Percentage decreaseHow far a value fell
- Percentage changeUp or down, with a sign
- What percentage is A of B30 is 20% of 150
- Reverse percentageFind the original amount
- DiscountSale price after % off
- Profit margin$50 to $100 is 50%
- MarkupPrice from cost plus markup
- VATAdd or remove VAT
- TipTip and tax on a bill
- Grade percentageScore out of a total
- Percentage differenceCompare two numbers
- Percentage pointsPoint gap, not percent change
- Salary increaseRaise from old pay to new
- Price increase$10 to $12 is 20%
- Sales taxTax amount and total
- InflationWhat money is worth over time
- BMIBody mass index
- Weighted gradeScores with different weights
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Percentage calculator: the short answer
A percentage is a count out of 100. What is 20% of 150? Multiply: 150 × 20 ÷ 100 = 30. What percent is 30 of 150? Divide: 30 ÷ 150 × 100 = 20%. The box above switches between those questions. The arithmetic is short; the usual miss is which number is the whole.
Change uses the starting number as the denominator. From 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%. From 100 back to 80 is (80 − 100) ÷ 100 × 100 = −20%. The gap is 20 either way. The rates differ because the base changed. Adding 15% to 80 is 80 × 1.15 = 92. That is a different question from “how much did it change?”
Formula
Part = whole × percent ÷ 100. Percent = part ÷ whole × 100. Change = (new − old) ÷ old × 100.
Worked examples
Each line shows the step, not only the result. Type the same numbers into the calculator above to see them again.
1. 20% of 150, and the reverse
150 × 0.20 = 30. The reverse question, “30 is what percent of 150?”, is 30 ÷ 150 × 100 = 20%. People swap these and multiply when they should divide. If the sentence says “percent of”, multiply. If it says “what percent”, divide. Both live on percentage of a number and what percent is A of B.
2. Up 25%, back down is not 25%
80 to 100 is 20 ÷ 80 = 25%. 100 to 80 is 20 ÷ 100 = 20%. After a 25% rise the value is 125% of the start, so the trip home is 25 ÷ 125 = 20% of the new value. A raise and a later cut of the “same” percent do not cancel. Use percentage increase or percentage decrease when you only want one direction, and percentage change when you want the sign.
3. Two discounts, and a tax add-on
20% off and then 10% off $200 is 200 × 0.80 × 0.90 = $144. Adding the rates to 30% would leave $140. The $4 gap is the second rate applied to $160, not to $200. The order of two percent rates does not matter; adding them does. A single sale price is on the discount calculator: 25% off $80 is $60. Adding 20% tax to $100 is 100 × 1.20 = $120, which is VAT, not a discount.
4. Percentage difference, not change
When neither number is the original, divide the gap by the average. 90 and 110 average 100. |110 − 90| ÷ 100 × 100 = 20%. Swapping the order leaves 20%. Change would say 22.22% one way and 18.18% the other, because each way picks a different base. That comparison is the percentage difference.
5. Percentage points
A rate moving from 4% to 6% rose by 2 percentage points. The relative increase is (6 − 4) ÷ 4 × 100 = 50%. News copy often means the points. The relative figure is larger when the starting rate is small. The percentage points page keeps the subtraction separate from the division.
Common cases
| Question | Arithmetic | Result |
|---|---|---|
| 20% of 150 | 150 × 20 ÷ 100 | 30 |
| 30 is what % of 150 | 30 ÷ 150 × 100 | 20% |
| 80 → 100 | (100 − 80) ÷ 80 | 25% |
| 100 → 80 | (80 − 100) ÷ 100 | −20% |
| Add 15% to 80 | 80 × 1.15 | 92 |
| $200, 20% off then 10% off | 200 × 0.80 × 0.90 | $144 |
Typical mistakes
Dividing by the new value
From 8 to 10 the gap is 2. 2 ÷ 10 = 20%, but the start was 8, so 2 ÷ 8 = 25%. The 20% figure answers “2 is what percent of 10?”, which is a different sentence.
Treating the return trip as the same rate
A 25% increase from 80 lands on 100. Cutting that 100 by 25% lands on 75, not 80. The cut that returns to 80 is 20% of 100.
Adding stacked discounts
20% then 10% off $200 leaves $144, not $140. You save $56, which is 28% of $200, not 30%. The second percent applies to what is left.
Removing tax as a plain percent of the gross
A $120 price with 20% tax included is $100 before tax and $20 of tax. Subtracting 20% of $120 removes $24 and leaves $96. Divide by 1.20. The included share is 20/120, which is one sixth, not one fifth.
Which calculator to open
The six modes above cover the everyday questions. Open a dedicated page when you want the formula next to a name that matches a receipt, a raise, or a syllabus.
- Percentage of a number — 20% of 150 = 30
- What percent is A of B — 30 is 20% of 150
- Percentage increase — from 80 to 100 is 25%
- Percentage decrease — from 100 to 80 is 20%
- Percentage change — the same formula, with a sign
- Discount — sale price and the amount saved
- Reverse percentage — 30 is 20% of 150
- All calculators — the full list, grouped by job
Common questions
How do you find a percent of a number?
Divide the percent by 100 and multiply by the number. 20% of 150 is 30. Adding that percent instead is 150 × 1.20 = 180, which is the new total, not the part.
Why is an increase of 25% not undone by a 25% decrease?
From 80 to 100 is 25% because you divide by 80. From 100, a 25% decrease goes to 75. The decrease that returns to 80 is 20% of 100. Each rate uses its own starting value.
How do you calculate percentage change?
Subtract the original from the new value, divide by the original, and multiply by 100. From 80 to 100 is 25%. From 100 to 80 is −20%. A starting value of 0 makes the division undefined.
Do stacked discounts add?
No. 20% off and then 10% off $200 leaves $144. Adding the rates to 30% would leave $140. The second rate applies to the price after the first rate. The order of two pure percentages does not change the result.
What is the difference between percent and percentage points?
From 4% to 6% is 2 percentage points. The relative change is 2 ÷ 4 × 100 = 50%. Points are a subtraction. A percent change is a division by the starting rate.
How do you remove 20% tax from a price?
Divide by 1.20. $120 with 20% tax included is $100 before tax and $20 of tax. Subtracting 20% of $120 leaves $96, which is $4 too low.
How do you reverse a percentage?
Divide the part by the percent. If 30 is 20% of a number, the number is 30 ÷ 0.20 = 150. A percent of 0 cannot be reversed, because that would divide by zero.