Percentage Calculator
Calculation type
How to use
- Select the calculation type using the tabs above.
- Enter your numbers - the result updates instantly as you type.
- Check the step-by-step section to see the full working.
- Switch modes at any time to solve a different percentage problem.
How to calculate percentages
What percent is Y of X?
Formula: (Y / X) x 100. Divide the part by the whole, then multiply by 100.
Example: Scored 68 out of 80 on a test -> (68 / 80) x 100 = 85%.
What is X% of Y?
Formula: (X / 100) x Y. Convert the percentage to a decimal, then multiply.
Example: 30% off a $240 jacket -> (30 / 100) x 240 = $72 discount.
Percentage change from A to B
Formula: ((B - A) / |A|) x 100. Positive = increase, negative = decrease.
Example: Revenue $8,500 -> $10,200 -> (1,700 / 8,500) x 100 = +20%.
Quick reference - additional formulas
| Problem type | Formula | Example |
|---|---|---|
| Find the original price | Value / (1 - discount%/100) | $68 after 15% off -> $80 original |
| New value after % increase | Value x (1 + rate%/100) | $100 + 7% = $107 |
Memory trick: the percentage triangle
Cover the value you want to find - the other two corners tell you the operation (multiply if adjacent; divide if stacked).
- Find the Part -> Part = Whole x (Percent / 100)
- Find the Whole -> Whole = Part / (Percent / 100)
- Find the Percent -> Percent = (Part / Whole) x 100
What is a percentage?
A percentage is a number expressed as a fraction of 100. The word comes from the Latin per centum - "out of a hundred." When you say 40%, you mean 40 out of every 100, or the decimal 0.4.
Percentages provide a shared scale that makes unlike things comparable. A teacher grading papers and a bank calculating interest rates are doing completely different things - but both can express results as a percentage, making them instantly comparable.
Every percentage problem has three elements: a part, a whole, and a percent value. Know any two, and the third is simple arithmetic. The three modes in this calculator cover every variation.
Interpreting your result
When the result exceeds 100%
A percentage can exceed 100 whenever the part is larger than the whole - for example, a sales team hitting 118% of their target. The calculator labels these "exceeds total" so the context is always clear.
Positive vs. negative percentage change
Positive means the value grew from A to B; negative means it shrank. The direction badge is shown automatically. Keep in mind: increases and decreases are not symmetric - a 50% drop requires a 100% gain to recover.
Percentage change vs. percentage points
An interest rate moving from 3% to 5% is a change of 2 percentage points, but a 66.7% increase in the rate itself. Both are accurate; they measure different things. Be precise, especially in financial or scientific reporting.
When the result is exactly 0%
In % change mode, 0% means A and B are equal - no change occurred. In "what % is Y of X" mode, 0% means Y is zero. The calculator labels both as "no change" rather than leaving the field blank.
Real-world percentage examples
Salary and pay raises
A raise is always calculated on your current salary, not your target. On $52,000 with a 5% raise: (5 / 100) x 52,000 = $2,600 raise, new salary $54,600.
To evaluate an offer: jumping from $52,000 to $56,000 is ((56,000 - 52,000) / 52,000) x 100 = 7.7% increase.
Survey and poll results
312 out of 400 survey respondents agreed with a proposal: (312 / 400) x 100 = 78% approval.
Percentages let you compare approval across surveys of different sizes - 78% approval in a 400-person poll and 78% in a 10,000-person poll carry the same proportional meaning, but the larger sample is far more reliable.
Budgeting and spending limits
You have a $3,200 monthly take-home pay and want to cap housing at 30%. How much can you spend? (30 / 100) x 3,200 = $960 maximum rent.
The same logic applies to any category: 15% on food = $480, 10% on transport = $320. Percentages let you allocate a budget systematically without needing to recalculate from scratch each time income changes.
Quick mental percentage tricks
For everyday estimates when you don't have a calculator:
- 10% - move the decimal one place left. 10% of $85 = $8.50
- 5% - find 10%, then halve it. 5% of $85 = $4.25
- 20% - find 10%, then double it. 20% of $85 = $17
- 15% - 10% + half of 10%. 15% of $80 = $8 + $4 = $12
- 25% - divide by 4. 25% of $60 = $15
- 1% - move the decimal two places left. 1% of $240 = $2.40
- Any % - combine the above. 18% of $50 = 10%($5) + 5%($2.50) + 3x1%($1.50) = $9
These shortcuts cover most everyday situations: splitting a bill, estimating tax, checking a discount, or calculating a tip without a phone.
Common percentage mistakes
Using the wrong base for percentage change
Always divide by the original value. A price rising from $200 to $250 is (50 / 200) x 100 = 25% - not (50 / 250) x 100 = 20%.
Stacking discounts incorrectly
20% off then 10% off is not 30% off. A $100 item at 20% off = $80; 10% off $80 = $72. The effective combined discount is 28%, not 30%.
Confusing percent with percentage points
An interest rate rising from 4% to 6% is +2 percentage points, but a 50% increase in the rate itself ((6-4)/4x100). Both accurate; both different. Financial headlines often use whichever figure is more dramatic.
Assuming increases and decreases are symmetric
A 100% increase doubles a value. A 100% decrease zeros it. An investment gaining 50% then losing 50% ends up 25% below the starting point - not back to zero.