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Percentage Calculator

A multi-mode percentage calculator: find X% of Y, find what percent A is of B, calculate percent increase or decrease, and reverse-percentage problems.

15% of 200 =
30
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How to use Percentage Calculator

  1. Choose the mode that matches your question: "X% of Y", "X is what % of Y", or "% change".
  2. Enter the two numbers — the field labels change to match the selected mode.
  3. Read the answer instantly; it updates as you type.
  4. Switch modes to solve a related question with the same numbers, for example to verify a result.

Percentage calculator: three modes, one clear answer

Percentages express a part out of a hundred, but the same word covers several distinct calculations that people frequently mix up. This tool separates them into three modes so you always get the right answer. Below is what each mode does, the formulas behind them, and the percentage pitfalls that trip up even careful people.

Mode 1: X% of Y

Finds a portion of a whole. The formula is (X ÷ 100) × Y. Use it for tax, tips, commissions, and discounts — anywhere you need "a percentage of an amount." For example, 8.25% of $60 is 0.0825 × 60 = $4.95.

Mode 2: X is what percent of Y

Turns a ratio into a percentage. The formula is (X ÷ Y) × 100. This is the mode for grades (38 out of 50 = 76%), progress ("how much of the goal is done"), and budget shares ("rent is what percent of income").

Mode 3: percent change

Measures how much a value rose or fell relative to its starting point. The formula is (New − Old) ÷ |Old| × 100. Stock moves, salary raises, price hikes, and traffic growth are all percent-change problems. A jump from 200 to 260 is a +30% change.

The asymmetry trap

Percentage increases and decreases do not cancel, because each is measured against a different base:

  • A 50% gain followed by a 50% loss leaves you at 75% of where you started, not 100%.
  • To undo a 25% drop you need a 33% rise, not another 25%.
  • To undo a 20% gain you need a 16.7% cut.

The rule: to reverse a change of r, the offsetting change is 1 ÷ (1 + r) − 1.

Percent vs percentage points

These are not interchangeable. If an interest rate goes from 4% to 5%, that is a rise of one percentage point but a 25% relative increase. Headlines that blur the two can make a small move sound dramatic or hide a large one. When precision matters, state both: "up 1 point, a 25% increase."

Reversing a percentage

To recover an original amount after a percentage was applied, divide rather than multiply. A bill of $113 that includes 13% tax came from $113 ÷ 1.13 = $100. A sale price of $90 after 25% off came from $90 ÷ 0.75 = $120. Switching this calculator between modes makes it easy to set up and check these reverse problems.

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Frequently asked questions

What does "X is what % of Y" mean?
It tells you what fraction X represents of Y, expressed as a percentage. The formula is X ÷ Y × 100. For example, 15 is 7.5% of 200. This is the mode for test scores, market shares, and "what portion is complete" questions.
How is percent change calculated?
Percent change is (New − Old) ÷ |Old| × 100. A positive result is an increase, a negative result is a decrease. Going from 80 to 100 is a +25% change; going from 100 to 80 is a −20% change.
Why isn't a 25% increase cancelled by a 25% decrease?
Because each percentage applies to a different base. 100 increased by 25% is 125; 125 decreased by 25% is 93.75, not 100. To fully reverse a 25% rise you need a 20% cut (1 ÷ 1.25 = 0.8).
What is the difference between percentage points and percent?
If a rate moves from 10% to 12%, that is a rise of 2 percentage points, but a 20% increase in relative terms (2 ÷ 10). Confusing the two is a common source of misleading statistics.
How do I add or subtract a percentage from a number?
Use the "X% of Y" mode to find the amount, then add or subtract it. To add 15% tax to $80, find 15% of 80 ($12) and add it for $92. As a shortcut, multiply by 1.15 to add 15% or by 0.85 to subtract 15%.
Can I work with negative or decimal numbers?
Yes. All three modes accept decimals, and percent change uses the absolute value of the original number so the sign of the result reflects direction (up or down) rather than the sign of the inputs.
How do I reverse a percentage to find the original amount?
If a price after a 20% discount is $80, the original is $80 ÷ 0.80 = $100. Divide the known amount by (1 minus the discount rate) for a markdown, or by (1 plus the rate) to strip an added percentage like tax.

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