How it works
Percentage of a value multiplies the value by the percentage and divides by 100.
What-percentage divides the part by the whole and multiplies by 100.
Percentage change compares the difference between two values to the original value, so it is positive for an increase and negative for a decrease.
Reverse percentage works backwards from a value that has already been increased or decreased by a percentage, to find what it started as.
Worked through in order, a price falling from 250 to 200: subtract the original from the new value to get 200 - 250 = -50; divide by the original value, -50 ÷ 250 = -0.2; multiply by 100 to get -20. The sign carries the direction and the size of the change is 20%. The base value is the step worth watching, because dividing by 250 rather than by 200 is what separates a 20% decrease from a 25% one.
Reversing a percentage divides by the same factor a change multiplied by, so the two calculations agree exactly: a value of 120 reached by a 20% rise divides back out through 1.20 to 100. To apply a change forwards rather than undo it, use the percentage increase calculator, which multiplies by 1 + percentage ÷ 100 instead.
Formula: Percentage of a value: value × percentage ÷ 100. Percentage change: (new − original) ÷ original × 100.
Examples
Percentage of a value
20% of 150 is (20 ÷ 100) × 150 = 30.
What percentage
30 is (30 ÷ 150) × 100 = 20% of 150.
Percentage change
A price moving from 80 to 100 is a change of ((100 − 80) ÷ 80) × 100 = 25%.
Reverse percentage
A value of 120 after a 20% increase started at 120 ÷ 1.20 = 100.
Percentage decrease
A price falling from 250 to 200 gives ((200 - 250) ÷ 250) × 100 = -20, so the change is a 20% decrease.
Reversing a decrease
A value of 60 after a 25% decrease started at 60 ÷ 0.75 = 80, because a 25% decrease multiplies the starting value by 0.75.
Common uses
- Checking a test score against the total marks available.
- Working out what a figure was before a reduction, such as the price a quoted total was reduced from.
- Comparing this month's total with last month's to see whether spending rose or fell.
- Comparing two measurements where neither is the original, which needs the symmetric percentage difference calculator instead.
Things to keep in mind
- Percentage change and percentage difference are not the same calculation: change is directional and uses the original value as its base, while difference treats two values symmetrically. This page covers percentage change; see the Percentage Difference Calculator (planned) for the symmetric version.
- A percentage change cannot be calculated from an original value of zero, since there is nothing to compare the change to — the calculator explains this rather than showing an error code.
- Reversing a 100% decrease is undefined, since a 100% decrease always gives zero regardless of the starting value.
- A percentage above 100% is accepted, because 150% of 60 is 90, one and a half times the value.
- Results are rounded to 12 significant digits to remove floating-point artefacts such as 0.30000000000000004, and displayed with up to 10 decimal places.