Percent of, change, and off

Four percent questions.

Compute percent of a value, percent change, what percent X is of Y, and percent off a price. Pure browser; no login.

Percent of

% of

50

What percent is A of B

of

8%

Percent change

→

50%

Percent off a price

-

Final: 60.00 (saved 20.00)

Four percentage calculations, explained

Percentages describe a part of something as a share of 100. They show up in discounts, tips, tax, interest, test scores, salary rises and statistics, and each of those uses one of a handful of formulas. Mixing the formulas up is how a 20% discount turns into a wrong total at the till.

This calculator puts the four everyday percentage questions side by side, each with its own inputs and an instant answer, so you can pick the question you actually have.

How to use it

  1. Find the box that matches your question: percent of a value, what percent one number is of another, percent change, or percent off a price.
  2. Type your numbers into that box's two fields.
  3. Read the result straight away; it updates as you type.
  4. Use a dot as the decimal separator, for example 19.99.

Example: the four questions with everyday numbers

Input
15% of 80
12 is what percent of 80
Change from 80 to 100
20% off 79.99
Output
12
15%
25%
Final: 63.99 (saved 16.00)

The first two questions are mirror images of each other. The discount comes to 15.998, which rounds to 16.00 for display.

The formulas behind each box

Percent of a value is percent ÷ 100 × value: 15% of 80 is 0.15 × 80 = 12. What percent A is of B is A ÷ B × 100: 12 ÷ 80 × 100 = 15%. Percent change is (new − old) ÷ old × 100: from 80 to 100 is 20 ÷ 80 × 100 = 25%. Percent off is price × (1 − percent ÷ 100): 20% off 79.99 leaves 63.99.

Why going up and coming back down are not equal

A rise from 80 to 100 is 25%, but the fall from 100 back to 80 is only 20%, because the change is measured against a different starting value each time. The same trap catches investors: a stock that falls 50% needs to rise 100% to get back to where it was.

Stacked percentages multiply rather than add. A 20% discount followed by another 10% off the reduced price is 28% off in total, not 30%, because 0.8 × 0.9 = 0.72.

Percent or percentage points?

When an interest rate moves from 2% to 3%, it has risen by one percentage point, but by 50% in relative terms. News reports and contracts mix the two up often. If the difference matters, write points for the absolute change and percent for the relative one.

Questions

Why does percent change show a dash?

A change from 0 cannot be expressed as a percentage, because the formula divides by the starting value. The tool shows a dash instead of a misleading number.

How do I add VAT or sales tax to a price?

Use percent of a value to get the tax, then add it to the price. For 19% VAT on 50, the tax is 9.50 and the total 59.50.

How do I remove VAT from a gross price?

Divide by 1 plus the rate, not by subtracting the percentage: 59.50 ÷ 1.19 = 50. Subtracting 19% of 59.50 would give 48.20, which is wrong.