How to calculate a percentage
A percentage expresses a number as parts per hundred. To find 15% of 200, convert 15% to 0.15 and multiply: 0.15 x 200 = 30. To find what percentage 30 is of 120, divide the part by the whole and multiply by 100: 30 / 120 x 100 = 25%.
Percentage change: use the starting value as the base
Percentage change compares the difference with the starting value: (new - old) / |old| x 100. A price rising from 80 to 100 increased by 20, which is 25% of the original 80. Reversing the direction is different: falling from 100 to 80 is a 20% decrease because the starting base is now 100.
A change from zero has no defined percentage because the formula would divide by zero. In that case, report the absolute change or choose a meaningful nonzero reference value.
Increase or decrease a number by a percentage
For an increase, multiply by 1 + percentage / 100. For a decrease, multiply by 1 - percentage / 100. Increasing 200 by 15% gives 230. Decreasing 200 by 15% gives 170.
Successive percentage changes do not usually cancel. A 20% increase followed by a 20% decrease changes 100 to 120 and then to 96, because the second calculation uses a different base.
How reverse percentages work
Use reverse percentage when you know the final value and the percentage change but need the original. If 230 is the result after a 15% increase, divide 230 by 1.15 to recover 200. If 170 is the result after a 15% decrease, divide 170 by 0.85.
Percentage difference versus percentage change
Percentage change has a direction and uses the old value as its base. Percentage difference treats both values equally and divides the absolute gap by their average magnitude. Use percentage difference when comparing two measurements and neither is naturally the starting point.
Percent change versus percentage points
If a rate moves from 20% to 25%, it rose by 5 percentage points. Relative to the original 20%, that is a 25% increase. Stating the correct unit prevents a common source of confusion in rates, surveys and performance reports.
Practical uses
- Check a sale discount, tax, tip, markup or commission.
- Measure growth or decline between two reporting periods.
- Recover a pre-tax or pre-discount value with reverse percentage.
- Compare two experimental measurements with percentage difference.
Round only the final answer when possible. Rounding intermediate values can create a noticeably different result in multi-step calculations.