How to use this calculator
Enter the known part and the percentage that part represents of the original whole. Divide the part by the percentage expressed as a decimal. For a price after a 20% discount, enter the sale price as the part and 80% as the percentage, because 80% of the original price remains.
Formula
Part ÷ (Percentage ÷ 100)
Worked example
If 30 is 15% of a whole, the whole is 30 ÷ 0.15 = 200. If a sale price of 80 remains after 20% off, enter part 80 and percentage 80 to recover the original 100.
Assumptions and limitations
A percentage of zero cannot recover a unique whole, including when the part is also zero. Signed percentages and parts are allowed for arithmetic but may not describe a meaningful price. The known percentage is the retained share, not necessarily a discount rate.
Frequently asked questions
How do I undo a percentage increase?
If a value rose by 25%, the new value is 125% of the old value. Enter the new value as the part and 125 as the percentage to recover the old value. Subtracting 25% from the new value would give a different answer.
How precise are these results?
Calculations use ordinary floating-point arithmetic. Results show up to six decimal places; very small nonzero values use scientific notation. They are estimates for everyday arithmetic, not arbitrary-precision accounting.
Can I use decimals and negative numbers?
Yes where the input allows them. Percentage change requires a nonnegative starting value; difference uses nonnegative values; discount requires a nonnegative price and a rate between 0% and 100%.
Keep the same units for both values. Amounts have no assumed currency.