Percentage Calculator
Calculate percentages, percentage change, and more.
15% of 200
30
200 × 0.15 = 30
How It Works
- 1
Choose a calculation mode
Select from three modes: 'X% of Y', 'X is what % of Y', or '% Change'.
- 2
Enter your values
Input the numbers for your chosen mode. The result updates instantly.
- 3
Read the result and formula
See the calculated answer with the formula shown for reference.
Worked example: three common percentage problems
Find 15% of 240, find what percent 45 is of 180, and find the percent change from 80 to 100.
- Part of whole: 15% of 240 = 240 × 0.15 = 36.
- Percent of: 45 is (45 ÷ 180) × 100 = 25% of 180.
- Percent change: ((100 − 80) ÷ 80) × 100 = 25% increase.
- Reverse check: a 20% decrease from 100 is 100 × 0.80 = 80 (not the same as a 20% increase from 80, which lands at 96).
15% of 240 is 36; 45 is 25% of 180; 80 → 100 is a 25% increase.
Percentage formulas
part = whole × (percent ÷ 100) percent = (part ÷ whole) × 100 change % = ((new − old) ÷ old) × 100
- part
- the portion you are finding or comparing
- whole
- the base amount (100%)
- percent
- rate out of 100
- old / new
- starting and ending values for percent change
Percent change always divides by the old value. Percentage points measure absolute gaps between rates (e.g. 10% to 12% is +2 points, a 20% relative increase).
Quick percentage reference
| Percent | Of $200 | Meaning |
|---|---|---|
| 5% | $10 | 1/20 of the whole |
| 10% | $20 | 1/10 of the whole |
| 15% | $30 | 3/20 of the whole |
| 25% | $50 | 1/4 of the whole |
| 50% | $100 | 1/2 of the whole |
Common percentage mistakes
Using the wrong denominator. Percentage change uses the old value, while percentage difference uses the average of both values.
Calling percentage points a percent change. Moving from 5% to 7% is 2 percentage points, but a 40% relative increase.
Assuming increases and decreases are symmetric. A 25% increase followed by a 25% decrease does not return to the original value.
Rounding too early. Keep extra digits until the final result when comparing rates, discounts, or margins.
How Percentages Work
Percentages are one of the most frequently used mathematical concepts in everyday life, from calculating discounts and tax rates to understanding statistics and financial returns. The word 'percent' literally means 'per hundred', so 25% means 25 out of every 100. Our calculator handles the three most common percentage operations: finding X% of a number (multiply the number by X/100), determining what percentage one number is of another (divide the part by the whole and multiply by 100), and calculating percentage change between two values ((new − old) ÷ old × 100). Percentage change is particularly important in finance and economics: a stock that rises from $80 to $100 has gained 25%, while one that falls from $100 to $80 has lost only 20%, illustrating why percentage changes are not symmetric. Our calculator provides instant results for all three modes, showing the formula used alongside the answer.
Frequently Asked Questions
How do I calculate a percentage of a number?
To find X% of Y, multiply Y by X/100. For example, 15% of 200 is 200 × 0.15 = 30.
How do I find what percentage one number is of another?
To find what percent X is of Y, divide X by Y and multiply by 100. For example, 30 is (30 ÷ 120) × 100 = 25% of 120.
How do I calculate percentage change?
Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. A positive result means an increase, and a negative result means a decrease. For example, from 80 to 100 is ((100 − 80) ÷ 80) × 100 = 25% increase.
What is the difference between percentage points and percent change?
Percentage points are the arithmetic gap between two rates: moving from 10% to 12% is a rise of 2 percentage points. Percent change is relative to the starting rate: (12 − 10) ÷ 10 = 20%. Confusing the two overstates or understates moves in interest rates, polls, and margins.
How do I find the original amount before a percentage increase?
Divide the new amount by (1 + rate). If a price is $120 after a 20% markup, the original is 120 ÷ 1.20 = $100. For a decrease, divide by (1 − rate): $80 after a 20% discount came from 80 ÷ 0.80 = $100.
When should I use a percentage calculator vs a discount calculator?
Use this percentage calculator for part-of-whole, percent-of, and percent-change math. Use the discount calculator when you need sale price, savings amount, or stacked markdowns on a retail price.
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Calculation record
How this result is maintained
Calcflux publishes the formula, assumptions, limits, and primary references behind its tools. Automated tests guard the implemented calculation paths and known-answer cases.
- Maintained by
- Calcflux
- Verification
- Formula tests and boundary checks