Everyday math

Percentage calculator

Three small questions share one page: a percent of a number, what percent one number is of another, and the percent change from one number to another.

Last updated . How we check formulas

Inputs

Results update as you type. The link in the address bar keeps the inputs so you can share it.

What this means

  • 15% of 80 is 12
  • X is the percent, not a fraction. 15 means 15%, which is 0.15 times Y.

What if

If the percent were 10 Keep Y and set X to 10. 10% of 80 is 8
If Y were doubled The percent stays the same. 15% of 160 is 24

About this calculator

What this calculator does

It answers one of three percent questions. Pick the question first so X and Y mean the right things. The labels under the inputs change with the question.

How it is calculated

What is X% of Y:

result = (X / 100) * Y

X is what percent of Y:

result = (X / Y) * 100

Percent change from X to Y:

result = ((Y - X) / X) * 100

How to read the result

The sentence is the full answer. The numeric result is the same quantity without words, so you can compare it. For percent change, a minus sign means a decrease.

Common mix-ups

Percent change is not the same as percent of. A move from 80 to 100 is a 25% increase, while 80 is 80% of 100. The base of a change is the starting number.

Sources and method

Standard arithmetic with no outside data. The formula is shown under How it is calculated, and unit tests check worked examples, including edge cases.

This page uses arithmetic only, with no outside data.

Questions

What is the difference between the three modes?

The first takes a percent of a number. The second asks what percent one number is of another. The third measures the change from a start value to an end value.

Why can't the starting value be zero for percent change?

Percent change divides by the starting value. Division by zero is undefined, so the calculator asks you to use a different start.

Is a negative result an error?

Not for percent change. It means the ending value is lower than the starting value.

How does percent change work from a negative start?

The page divides by the size of the starting value, ignoring its sign. From -10 to -5 is a 50% increase, because the value went up.

Do I enter 15 or 0.15 for 15%?

Enter 15 in the percent field. The calculator divides by 100.

How is this different from margin and markup?

Margin and markup are business ratios with named bases. Use the profit margin calculator for those. This page is general percent math.

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