Percentage calculator
Calculate a percentage of an amount, what percentage one value represents of another, and the percentage change between two values.
What this calculator does
This calculator solves the three most common percentage problems: finding a percentage of an amount (for example, 15% of $200), finding what percentage one value represents of another (for example, what percent 30 is of 200), and measuring the percentage change between two values (for example, how much a price rose from $200 to $250).
The result updates instantly as you type, and you can always see the formula applied with your own numbers to understand where each figure comes from.
Who it is for
- Anyone who needs to work out discounts, tips, or surcharges when buying or selling.
- Students who want to check math homework and understand the procedure, not just the answer.
- Shop owners and entrepreneurs adjusting prices, computing margins, or comparing sales between periods.
- People analyzing increases or decreases: salaries, utility bills, savings performance.
What information you need
- For a percentage of an amount: the percentage you want to apply and the base amount.
- To find what percent X is of Y: the partial value and the total reference value.
- For the percentage change: the initial and final values you want to compare.
How it is calculated
A percentage is a fraction with denominator 100: 15% means 15 out of every 100. To apply a percentage to an amount, the calculator multiplies the amount by the percentage and divides by 100.
To find what percentage a value represents of a total, the partial value is divided by the total and multiplied by 100. The total must be non-zero: division by zero is undefined.
The percentage change compares the difference between the final and initial values against the initial value. A positive result means an increase and a negative one a decrease. The initial value must be non-zero.
Percentages are rounded to 4 decimal places and amounts to 2, always rounding ties up (half up), applied once on the final result.
Formula
- X% of an amount
result = amount × percent ÷ 100- What percent X is of Y
percent = (partial value ÷ total value) × 100- Percentage change
change % = ((final value − initial value) ÷ initial value) × 100
Worked example
A store offers a 15% discount on a $200 purchase. How much is the discount and what do you pay in the end?
- Turn the percentage into a fraction: 15% = 15 ÷ 100 = 0.15.
- Multiply the amount by that fraction: $200 × 0.15 = $30. That is the discount.
- Subtract the discount from the original price: $200 − $30 = $170.
The discount is $30 and the final price is $170.
How to interpret the result
In "X% of an amount" mode, the result is in the same units as the base amount: enter dollars, get dollars.
In the other two modes the result is percentage points. A percentage change of 25% means the final value is a quarter larger than the initial one; −20% means it shrank by a fifth.
A change of −100% means the final value dropped to zero. Values above 100% are perfectly valid: going from $50 to $150 is a 200% increase.
Common mistakes
- Confusing percentage points with percent: going from 10% to 15% is an increase of 5 percentage points, but 50% in relative terms.
- Assuming percentages reverse symmetrically: a 50% increase followed by a 50% discount does not return to the original value ($100 → $150 → $75).
- Using the final value as the base of a percentage change: the formula always divides by the initial value.
- Adding chained percentages: two successive 10% discounts are not a 20% discount, but a 19% one.
Frequently asked questions
How do I find a percentage of an amount without a calculator?
Multiply the amount by the percentage and divide by 100. A useful shortcut: 10% is found by moving the decimal point one place ($250 → $25), and from there you can compose other percentages (5% is half of 10%, 20% is double).
Why can I not use zero as the total or initial value?
Both formulas divide by that value, and division by zero is undefined in mathematics. If your initial value is zero, a percentage change does not exist: any final value would represent an "infinite" increase. In that case, express the change in absolute units instead.
Can I use negative values?
Yes. Negative values are useful, for example, to compare losses or balances. Keep in mind that with a negative initial value the sign of the percentage change follows the rules of algebra and can feel unintuitive: check the calculation breakdown to confirm the interpretation.
What is the difference between percentage change and what percent X is of Y?
Percentage change measures how much a value moved relative to its starting point (it can be negative). "What percent X is of Y" expresses a proportion between two values at the same moment: 30 out of 200 is 15%, regardless of any increase or decrease.
How do I calculate a 15% increase directly?
Multiply the amount by 1.15 (that is, 1 + 15 ÷ 100). For a 15% discount, multiply by 0.85. It is the same calculation this calculator performs in two steps: finding 15% and adding or subtracting it.
Sources
- Last reviewed:
- July 20, 2026
- Calculation version:
- 1.0.0
Important notice
The results of these calculators are informative estimates and may differ from official calculations. They do not constitute legal, tax, or financial advice. Always verify with the competent institutions or a professional.