- Result
- 30
How it works
Equal gains and losses do not cancel
A value rising 20% and then falling 20% goes from 100 to 120 to 96. The second change uses the larger base, so the combined result is a 4% loss, not a return to 100.
Choosing the correct percentage question
A percentage of a number, a percentage change, and a percentage difference use different comparison bases. Select the mode that matches the wording of the problem before entering values. When reversing a percentage change, work from the relationship to the original amount rather than subtracting the same percentage from the final amount. The displayed formula shows which value serves as the base.
A rate rising from 5% to 6% increases by 1 percentage point and by 20% relative to the original rate. Percentage points subtract the two rates; percentage change divides that difference by the original rate.
If an item costs 80 after a 20% discount, the original price was 100: divide 80 by 0.8. Adding 20% to 80 gives 96, because that percentage uses a different base.
Percentage of a number: formula and assumptions
Result = percentage ÷ 100 × number.
Convert a percentage to a decimal, then multiply by the original number.
What percentage?: formula and assumptions
Percentage = part ÷ whole × 100.
The whole is the comparison base and cannot be zero.
Percentage change: formula and assumptions
Change = (new − original) ÷ |original| × 100%.
A positive result is an increase and a negative result is a decrease. This tool uses the magnitude of the original value as its base.
Percentage difference: formula and assumptions
Difference = |a − b| ÷ ((a + b) / 2) × 100%.
Use percentage difference to compare two nonnegative values without assigning either as the original.
Increase or decrease: formula and assumptions
New value = original × (1 ± percentage / 100).
Apply the change once to the original value.
Find the original whole: formula and assumptions
Whole=part×100/percentage.
Use this when the part and its percentage are known.
Reverse a percentage change: formula and assumptions
Original=final/(1+change/100).
Use a negative change for a decrease. A 100% decrease cannot determine the original value.
Worked example
Using the Percentage of a number example:
- Percentage (%)
- 15
- Number
- 200
Result = percentage ÷ 100 × number.
Example result
Result: 30
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
How is percentage difference different from percentage change?
Change uses an original value as its base. Difference compares two nonnegative values using their average as the base.
Can I reverse a 100% decrease to find the original value?
No. Every original value becomes zero after a 100% decrease, so the final value does not identify a unique original.
Prepared by Finflo. See our methodology and editorial policy.