Percentage Calculator
Calculate percentages in the most useful everyday and classroom ways: what is X% of Y, X is what % of Y, percentage increase or decrease, value after a % change, and reverse percentages. See clean steps, quick interpretations, and a simple visual breakdown.
Background
A percentage is just a way to compare a number to 100. For example, 25% means 25 out of every 100, which is the same as 0.25. Percentage problems show up everywhere: discounts, grades, tips, tax, growth, decline, test scores, business metrics, and finance.
How to use this calculator
- What is X% of Y? Use this when you want the actual amount represented by a percentage.
- X is what % of Y? Use this when you want to convert a part-to-whole comparison into a percentage.
- % increase / decrease Use this when comparing an old value to a new value.
- Value after % change Use this to apply an increase or decrease directly to a starting amount.
- Reverse percentage Use this when you know the final value and want the original value before the increase or decrease.
How this calculator works
- It converts percentages into decimals by dividing by 100.
- For what is X% of Y, it uses result = (p / 100) × y.
- For X is what % of Y, it uses percent = (x / y) × 100.
- For % increase / decrease, it uses % change = ((new − old) / old) × 100.
- For value after % change, it multiplies the starting value by 1 ± p/100.
- For reverse percentages, it divides the final value by 1 ± p/100 to recover the original value.
Formula & Equations Used
What is X% of Y? result = (p / 100) × y
X is what % of Y? percent = (x / y) × 100
Percentage change: % change = ((new − old) / old) × 100
Value after increase: final = start × (1 + p / 100)
Value after decrease: final = start × (1 − p / 100)
Reverse increase: original = final / (1 + p / 100)
Reverse decrease: original = final / (1 − p / 100)
Example Problems & Step-by-Step Solutions
Example 1 — What is 20% of 150?
- Convert 20% to a decimal: 20 / 100 = 0.20.
- Multiply by the base value: 0.20 × 150 = 30.
- So, 20% of 150 is 30.
Example 2 — 45 is what % of 180?
- Divide the part by the whole: 45 / 180 = 0.25.
- Convert to a percentage: 0.25 × 100 = 25%.
- So, 45 is 25% of 180.
Example 3 — Percentage increase from 80 to 100
- Find the change: 100 − 80 = 20.
- Divide by the original value: 20 / 80 = 0.25.
- Convert to a percentage: 0.25 × 100 = 25%.
- So, the value increased by 25%.
Example 4 — Reverse percentage
A price after a 20% decrease is 92. What was the original price?
- After a 20% decrease, the final value is 80% of the original.
- Write that as a multiplier: 0.80.
- Divide the final value by the multiplier: 92 / 0.80 = 115.
- So, the original value was 115.
Frequently Asked Questions
Q: What is the easiest way to find a percentage of a number?
Convert the percentage to a decimal by dividing by 100, then multiply by the number. For example, 15% of 200 = 0.15 × 200 = 30.
Q: What is the difference between “what is X% of Y” and “X is what % of Y”?
The first finds an amount from a percentage. The second finds the percentage that one value represents of another.
Q: How do I tell whether it is an increase or a decrease?
Compare the new value to the old one. If the new value is larger, it is an increase. If the new value is smaller, it is a decrease.
Q: Why does reverse percentage use division instead of multiplication?
Because the final value already includes the percentage change. To recover the original value, you undo the multiplier by dividing.
Q: Can percentages be greater than 100%?
Yes. A value can be more than the whole it is compared with. For example, if a quantity doubles, that is a 100% increase. If it triples, that is a 200% increase.
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