MihsabaPercentage, discount or percentage change?
Finding a percentage of a number is different from a discounted final price or a percentage change between two dates.
Use this calculator for: Finding X% of a value, the percentage represented by a part, and simple percentage increases or decreases.
- Calculate a sale price after discounts — Find savings and final price after one or two discounts, with optional tax.
- Calculate percentage change — Compare old and new values using (new − old) ÷ old × 100.
- Add or remove VAT — Find net price, tax amount and tax-inclusive total using a chosen rate.
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How to Calculate Percentages: Formula & Worked Examples
How to use
Percentage calculations involve six distinct questions: finding a percentage of a value, calculating a part-to-whole ratio, recovering an unknown original amount, increasing a number, applying a discount or measuring change between two values. Select the question that matches your inputs. The calculator displays a substituted formula, making it easier to verify which value forms the base instead of treating every percentage as the same operation.
- Select the matching mode rather than forcing every question into a part-to-whole calculation.
- Enter the rate and known amount, or the old and new amounts when calculating change.
- Check the substituted formula and denominator before interpreting the displayed answer.
- Try a nearby input to verify the direction of change and retain the units or currency when sharing.
How it is calculated
Example
To find 15% of 240, multiply 240 by 0.15 to get 36. A part of 45 out of 60 is 75%. If 30 represents 20% of an unknown total, then 30 ÷ 0.20 = 150. Increasing 200 by 12% yields 224, and discounting 150 by 20% gives 120. Changing from 80 to 100 is (100 − 80) ÷ 80 × 100 = a 25% increase based on the starting 80.
Important notes
A percentage discount and a percentage increase need not undo each other: a 20% increase followed by a 20% decrease takes 100 to 120 and then 96. Profit margin and markup also use different denominators. A ratio cannot be calculated with a zero total, and conventional percentage change cannot be evaluated when the starting amount is zero. Always identify the reference amount and avoid confusing percentage points with relative percentages.
Worked examples and interpreting results
First choose the question: a percentage of a number, a part as a percentage of a total, or a value after an increase. The same numbers can answer different questions.
| Case | Calculation | Result |
|---|---|---|
| 20% of 150 | 150 × 20 ÷ 100 | 30 |
| 30 out of 150 | 30 ÷ 150 × 100 | 20 % |
| 150 after a 20% increase | 150 × (1 + 20 ÷ 100) | 180 |
How to check the result
A 20% increase followed by a 20% decrease does not undo itself: 150 becomes 180, then 144. The second percentage uses 180 as its base.
Further cases: decimal rates, reverse percentages and percentage points
Percentage problems can involve fractional rates or an unknown starting value. A change between two percentage rates must also distinguish percentage points from relative change.
- Find 7.5% of 80: 80 × 7.5 ÷ 100 = 6
- 90 is 75% of which original value?: 90 ÷ 0.75 = 120
- Relative change from 10% to 12%: (12 − 10) ÷ 10 × 100 = 20% relative increase
Percentage points versus relative percentage
A rate moving from 10% to 12% increases by 2 percentage points, or 20% relative to the starting rate. Standard percentage change is undefined when its original value is zero.
Frequently asked questions
How do I find 15 percent of 240?
Multiply 240 by 15 and divide by 100. The result is 36 before any separate sales tax or fees.
How do I find what percentage one amount is of another?
Divide the part by the total and multiply by 100: 45 ÷ 60 × 100 = 75%. The total must not be zero.
Do equal percentage increases and decreases cancel?
No. A 20% increase on 100 creates 120, and a 20% decrease on 120 produces 96 because the base changed.