How this calculator works
- Step 1Start with the whole1,000Keep both quantities in matching units.
- Step 2Turn percent into a fraction0.2Divide the percentage by one hundred.
- Step 3Multiply the whole200This is the portion, not the amount left.
A percentage tells you a quantity per hundred. The important part is choosing the base: the whole for a share, the old value for a change, or the pair’s mean for a symmetric difference.
Choose Find a percentage to multiply a number by a rate. Choose What percent to divide a part by a whole. A share can exceed the whole; that simply gives a result above one hundred percent.
Worked example: find a portion
- Percentage of a number
portion = whole × percentage ÷ 100
- wholeStarting number 1,000
- percentageRate per hundred 20%
- Starting whole1,000
- Percentage divided by one hundred0.2
- Whole multiplied by the fraction200
The answer is the requested portion. If you want the amount left after a reduction, choose Decrease a number instead. To work backwards from a discounted value, choose Find the original before a discount.
A change is directional; a difference is symmetric
- From 80 to 10025%The old, smaller value is the base.
- From 100 to 80-20%The old, larger value is now the base.
- Between 80 and 12040%Symmetric difference uses the mean of the pair.
Reversing an increase does not produce an equal percentage decrease because the denominator changes. A negative change means the new value is lower. The symmetric difference has no direction and stays the same when you swap its inputs.
The symmetric convention here is absolute difference divided by the arithmetic mean. It is not a universal definition for every subject. If a report gives its own definition of percentage difference, follow that report’s convention.
Recovering an original value
The worked reverse example recovers an original of 1,000 from a final value of 800 after a discount. You divide by the fraction still retained; simply adding the discount percentage to the final value uses the wrong base.
A full discount leaves no information about the original amount. The reverse question therefore accepts only discounts below one hundred percent. Likewise, a change from zero and a share of a zero whole are undefined here, not zero-percent answers.
Assumptions and limits
Both inputs accept values up to one trillion. For decrease, the percentage cannot exceed one hundred. The tool does not handle signed starting bases, annualise a change, choose a tax rate or interpret a change as investment performance.
Results retain full floating-point precision during calculation. Only the displayed result is rounded, to at most six decimals. Very small and large results use scientific notation so a nonzero result does not appear to be zero.
Common percentage mistakes
Mistake: Enter a decimal fraction where the field asks for a percentage.
Instead: Enter the rate per hundred; the calculator converts it for you.
Mistake: Treat a percentage change as percentage points.
Instead: Percentage points subtract two rates; relative change divides their difference by the old rate.
Mistake: Compare amounts in different units.
Instead: Convert both inputs to matching units before calculating.
Mistake: Subtract a discount and then add the same percentage to undo it.
Instead: Use the reverse question, which divides by the retained fraction.
Related percent tools
Most money questions are percent questions with a name: discounts, GST, interest and hikes.
For stacked discounts, use the discount calculator, and to add or remove tax, the GST calculator. The salary hike calculator works out a raise, and the percent error calculator compares a measurement with its expected value.
Checking the method
The equations follow OpenStax’s percentage and discount methods, with reverse calculations obtained by rearranging those equations. Tests check manual golden values, proportional identities, symmetric comparisons and discount round trips. Primary sources and review details appear below.
Read how we test our calculators, or browse more maths calculators.