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Percentage Calculator

Three percentage calculations in one place: X% of a number, what percentage X is of Y, and the percentage change between two values.

Result
12.675
15% of 84.5 = 84.5 × 15/100

Every result shows its formula so you can verify the math instantly. Calculations run locally.

Three Problems That Look Identical and Are Not

Almost every percentage mistake is a direction mistake. "15% of 84.50" scales a number down — a multiplication. "43 out of 50 is what percent?" divides the part by the whole and rescales to 100. "From 50 to 60" compares a change against the starting value — and that starting value is where most people slip, because after a change has happened the base is the old number, not the new one.

The three modes in this calculator mirror those three questions. Choosing the mode first — before typing — is what keeps the answer honest, and the formula display with your numbers substituted shows exactly which operation ran.

Percentage Errors That Reach the Real World

  • Price drop then rise: −20% then +20% lands at 96% of the start, not 100% — the bases differ.
  • Survey margins: "60% of respondents" with 12 answers is 7.2 people — check the base before quoting.
  • Compound discounts: 30% off then 20% off is 44% total, not 50% — the second percentage applies to the reduced price.
  • Small percentages on huge bases: 0.5% of a national budget is enormous money; percent size and absolute size are independent.

The Formula Behind the Result

  1. Choose the calculation type: percent of a number, percentage of total, or percent change.
  2. Enter the two values relevant to that mode.
  3. The result appears instantly with the formula written out, so you can verify the math.
  4. Switch modes freely — inputs carry over where they apply.
Formula & Technical Standard
X% of Y = Y × X/100 · X is what % of Y = X/Y × 100 · % change = (new − old)/|old| × 100

Worked Example

Tip on a bill
Input: 15% of 84.50
Output: 12.68
Percent-of mode multiplies the base by the fraction; the formula display shows the exact multiplication.
Exam score as a percentage
Input: 43 points out of 50
Output: 86%
Percentage-of-total mode divides and scales to 100 — the reverse direction of the first mode.

Common Questions

How is percentage change different from percentage of?

"20% of 50" scales a number down (result 10). "From 50 to 60" as a change is +20% because the delta is compared to the starting value.

What happens with a negative old value in percent change?

The change is divided by the absolute value of the old number, which keeps the direction of the change intuitive.

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