20% × 500 = 100. Enter 20 in the percentage field and 500 in "of value" in the first panel above to see this calculated directly.

Why isn't a 20% pay cut undone by a 20% pay rise?

Because each percentage is taken from a different base. A 20% cut on £2,000 leaves £1,600; a 20% rise on £1,600 is only £320, giving £1,920 — not back to £2,000. Use the "Percentage change" panel to see this with your own numbers.

What's the difference between a percentage and a percentage point?

If a rate moves from 5% to 7%, that's a rise of 2 percentage points, but a 40% percentage increase relative to the original 5% — the two figures describe the same change differently, and mixing them up is a common source of confusion in news reporting on rates and statistics.

Percentage Calculator

Calculate percentages, percentage change, and one number as a percentage of another.

Runs entirely in your browser — nothing you enter is uploaded.

Percentage of a number

What is 15% of 250?

Percentage

Of value

Result

37.50

Percentage change

From 80 to 100, measured against the original.

Original value

New value

Increase

+25.00%

A change of 20.00 on a base of 80.00

X as a percent of Y

45 is what percent of 180?

Part

Whole

Result

25.00%

How this works

Three distinct questions get called 'percentage' and they are not interchangeable. Taking a percentage of a value is straightforward multiplication. Percentage change compares a new value against an original one and always divides by the original. Expressing one number as a percentage of another divides the part by the whole. The tool keeps them separate because using the wrong denominator is where nearly all percentage errors come from.

part = whole × (p ÷ 100); change = (new − old) ÷ old × 100; proportion = part ÷ whole × 100

Assumptions

Percentage change is always measured against the original value, not the new one.
Results are rounded for display; the underlying calculation uses full precision.

Worked example

A price rises from £80 to £100, then falls back to £80.

Original value: £80
New value: £100
Result: +25% increase, then −20% decrease

Going up, the £20 change is divided by the original £80, giving 25%. Coming back down, the same £20 is divided by £100, giving 20%. The two percentages differ even though the money is identical, because the denominator changed. This is why a 50% loss needs a 100% gain to recover.

How to read the result

Always check what the percentage is being taken of. A percentage increase followed by the same percentage decrease never returns you to where you started. When someone quotes a change without stating the base, the figure is not yet meaningful — and percentage point differences (5% to 7% is two percentage points, not 2%) are a separate thing again.

Limitations

Percentage change cannot be calculated from an original value of zero — the division is undefined.
Very large percentage changes from tiny bases are technically correct but rarely informative.
Does not compound: applying 10% three times is not a 30% increase.

Frequently asked questions

What is 20% of 500?: 20% × 500 = 100. Enter 20 in the percentage field and 500 in "of value" in the first panel above to see this calculated directly.
Why isn't a 20% pay cut undone by a 20% pay rise?: Because each percentage is taken from a different base. A 20% cut on £2,000 leaves £1,600; a 20% rise on £1,600 is only £320, giving £1,920 — not back to £2,000. Use the "Percentage change" panel to see this with your own numbers.
What's the difference between a percentage and a percentage point?: If a rate moves from 5% to 7%, that's a rise of 2 percentage points, but a 40% percentage increase relative to the original 5% — the two figures describe the same change differently, and mixing them up is a common source of confusion in news reporting on rates and statistics.