Fill in any two fields in each section and the third is computed instantly. Every section is bidirectional — enter the answer and one input to work backwards. The four sections cover the most common percentage calculations.
What Is a Percentage?
A percentage is a dimensionless ratio expressed as a fraction of 100. The word comes from the Italian per cento, meaning "for a hundred". The symbol % literally stands for /100, so 5% = 5/100 = 0.05.
Percentages are useful because they put quantities of different sizes on a common scale. Knowing a company earned $1,000,000 more than last year says little without context. Knowing it earned 100% more tells an immediately clear story. This is why percentages appear everywhere — finance, medicine, statistics, shopping, and everyday comparisons.
The Three Percentage Formulas
| Question | Formula | Rearranged as |
|---|---|---|
| What is p% of x? | y = x × p / 100 | find the part |
| x is what percent of y? | p = x × 100 / y | find the percentage |
| x is p% of what? | y = x × 100 / p | find the whole |
Finding a Percentage of a Number
To find p% of x, multiply x by p and divide by 100. This is the same as multiplying x by the decimal form of p (p ÷ 100).
Example: what is 40% of 20? Calculate 20 × 40 / 100 = 8. Alternatively, 40% = 0.40, and 0.40 × 20 = 8.
Another example: you scored 27 out of 30 on a test. Your percentage score is 27 × 100 / 30 = 90%.
Finding What Percent One Number Is of Another
To find what percent x is of y, divide x by y and multiply by 100.
Example: Gavin's rent is $1,245 and his monthly budget is $4,000. His rent is 1,245 × 100 / 4,000 = 31.125% of his budget.
Reverse: Gavin wants rent to be no more than 25% of $4,000. Maximum rent = 25 × 4,000 / 100 = $1,000.
Finding the Base Value
To find the whole when you know the part and the percentage: y = x × 100 / p.
Example: 10 is 5% of what number? Answer: 10 × 100 / 5 = 200.
Example: you spent $12 on gum, which was 30% of your pocket money. Total budget = 12 × 100 / 30 = $40.
Percentage Increase and Decrease
To increase a value by p%, multiply it by (100 + p) / 100. To decrease by p%, multiply by (100 − p) / 100.
Example: a candy bar priced at $5 increased in price by 30%. New price = 5 × (100 + 30) / 100 = 5 × 1.30 = $6.50.
Reverse: a discounted item costs $44 after a 10% discount. Original price = 44 × 100 / (100 − 10) = 44 × 100 / 90 ≈ $48.89.
Percentage vs. Percentage Points — Example
| Description | Value |
|---|---|
| Initial value | 10% |
| Final value | 12% |
| Change in percentage points | 12 − 10 = 2 pp |
| Percentage increase | (12 − 10) / 10 × 100 = 20% |
Per Mille and Basis Points
Two smaller units of proportion are used in specific fields:
- Per mille (‰) — per thousand. 1‰ = 0.1% = 0.001. Used in blood-alcohol limits, salinity measurements, and some financial contexts.
- Basis point (‱) — per ten thousand. 1 basis point = 0.01% = 0.0001. Used in finance to describe changes in interest rates and investment returns.
To convert basis points to percent, divide by 100. To convert per mille to percent, divide by 10.
Quick Reference — Common Percentage Calculations
| Calculation | Formula | Example |
|---|---|---|
| Find p% of x | y = x × p / 100 | 40% of 20 = 8 |
| Find what % x is of y | p = x × 100 / y | 8 is 40% of 20 |
| Find the base | y = x × 100 / p | 8 is 40% of 20 |
| Increase x by p% | y = x × (100 + p) / 100 | 20 + 10% = 22 |
| Decrease x by p% | y = x × (100 − p) / 100 | 20 − 10% = 18 |
| Find percent change | p = (final − initial) / |initial| × 100 | 20 → 22 = +10% |
This percentage calculator solves four common percentage problems. Fill in any two fields in a section and the third is calculated automatically. Every section works in reverse — enter the result and one input to find the missing value.