Percentage Calculator

What is x% of y, reverse percent, and increase or decrease a number by p%. For old value → new value, use percentage change.

What is x% of y?

%

15% of 80

12

From an old value to a new value? Use the percentage change calculator.

More: reverse percent and apply ±p%

x is what % of y?

12 is what % of 80

15%

Increase or decrease a number by p%

%

After applying p%

92

  • Increase by 15%92
  • Decrease by 15%68

This percentage calculator answers the three questions people actually search for: what is x% of y, x is what percent of y, and what happens when you increase or decrease a number by p%. Each answer appears as you type, in its own panel.

The word percentage covers at least four different problems, and mixing them up is the most common arithmetic error outside a spreadsheet. Below are the formulas for each, a worked example, and a note on when you want percentage change instead.

How to calculate a percentage

  1. Turn the percent into a decimal: 15% becomes 0.15.
  2. Multiply by the whole: 0.15 × 80 = 12.
  3. Going the other way, divide the part by the whole and multiply by 100: 12 / 80 × 100 = 15%.
  4. To apply a change, multiply by 1 + p/100 or 1 − p/100: 80 × 1.15 = 92, 80 × 0.85 = 68.

Example

15% of 80 is 12. 12 is 15% of 80. Increasing 80 by 15% gives 92, and decreasing it by 15% gives 68. The two operations are not inverses: 92 reduced by 15% is 78.2, not 80, because the second 15% is taken from a larger base.

Percentage formulas

x% of y = (x/100) × y. x is what % of y = (x/y) × 100. Increase: y × (1 + p/100). Decrease: y × (1 − p/100). Original from a post-change value: original = new / (1 ± p/100).

How to use this calculator

  1. Open the panel that matches your question — the first one is what is x% of y.
  2. Type the percent and the whole; the result updates on each keystroke and the URL keeps your numbers.
  3. For x is what percent of y, put the part first and the whole second; the answer is always a percentage of the second field.
  4. For increase or decrease, enter the starting value and the percent. The sign decides the direction, so use -15 for a 15% drop.

The four percentage problems

Almost every percentage question is one of these, and each uses a different denominator — which is why a calculator that answers one often gets the others wrong.

  • Part of a whole: multiply. 15% of 80 = 12.
  • Ratio as a percent: divide, then × 100. 12 / 80 = 15%.
  • Change between two values: divide the difference by the starting value. (72 − 60) / 60 = 20%.
  • Apply a percent: multiply by 1 ± p/100. 80 × 1.15 = 92.

Percentage change vs. percentage difference

Percentage change has a direction and a fixed reference: the starting value. Percentage difference has neither — it divides by the average of the two numbers and is always positive, which suits comparing two measurements of the same thing (two rulers, two labs). Sales rose 20% is change; the two methods differ by 3% is difference.

Mixing them is how a 20% rise followed by a 20% fall gets reported as flat, when it is actually a 4% loss.

Reverse percentages

If a price is $92 after a 15% increase, the original was 92 / 1.15 = $80, not 92 × 0.85 = $78.20. The 15% was taken from the smaller base, so undoing it means dividing by 1.15. The same trap appears with VAT, sales tax, and discounts: to strip a tax out of a gross figure, divide by 1 + rate, never multiply by 1 − rate.

A note on terminology

Percent, percentage, and percentage point are not interchangeable. A move from 4% to 6% is a 2 percentage point gain but a 50% increase. A basis point is a hundredth of a percentage point, so 25 bps is 0.25%. When a headline says a rate rose 2%, check whether it means 2 points or 2% of the old value.

What this calculator leaves out

It does not compound. Applying 10% twice is not 20% but 21%, because the second 10% is taken from the larger amount. For repeated growth use the compound interest calculator; for a change from an old value to a new one, use percentage change.

Common mistakes

  • Adding percentages that apply to different bases. A 20% discount followed by another 10% off is 28% off, not 30%.
  • Undoing an increase by subtracting the same percentage. 80 + 15% = 92, but 92 − 15% = 78.2.
  • Confusing percentage points with percent. Going from 4% to 6% is +2 points, which is +50%.

FAQ

What is 15% of 80?

12. (15 / 100) × 80 = 12.

How do I find what percent 12 is of 80?

15%. 12 / 80 = 0.15, and 0.15 × 100 = 15%.

How do I increase a number by a percentage?

Multiply by 1 + p/100. 80 increased by 15% is 80 × 1.15 = 92. To reverse it, divide by 1.15 rather than subtracting 15%.

How do I decrease a number by a percentage?

Multiply by 1 − p/100. 80 decreased by 15% is 80 × 0.85 = 68.

What is the difference between percent and percentage point?

One percentage point is the arithmetic difference between two percentages: 4% to 6% is 2 points. In relative terms that is a 50% increase, because 2 is half of 4.

How do I calculate a percentage in Excel?

A1/B1 formatted as a percentage gives the ratio; A1*0.15 gives 15% of A1; (B1-A1)/A1 gives the percentage change from A1 to B1.

How do I add 20% to a price?

Multiply by 1.2, so $50 becomes $60. To take 20% off, multiply by 0.8, giving $40. Adding then removing 20% does not return the original: 50 → 60 → 48.

What is 20% of 50?

10. A fifth of 50 is 10, just as half of 50 is 25.

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