Formulas and sources
Each formula this calculator uses, where it comes from, and what it leaves out. "How it works" shows the same formula with your own numbers.
X% of Y
% of mode
- Result
- the part
- A
- the percentage as typed (20 means 20%)
- B
- the whole
Source: Standard formula; no single publisher.
X is what % of Y
is % of mode
- Result %
- the percentage
- A
- the part
- B
- the whole, not zero
Source: Standard formula; no single publisher.
Percent change
% change mode
- % Change
- the change, as a percentage
- New
- the later value
- Old
- the starting value, not zero
The card gives the size of the change and says Increase or Decrease. For a positive Old, |Old| is Old, the usual formula. For a negative Old, dividing by its size keeps the word on the direction of the move: −50 to 25 is a 150% increase.
Source: Uses the formula in the US Bureau of Labor Statistics’ guide to percent changes [1] for a positive starting value. The rule for a negative one is CalcTrail’s own; no publisher.
Add X% to Y
add % mode
- Result
- the value with the percentage added
- Base
- the value
- A
- the percentage to add
Source: Standard formula; no single publisher.
Subtract X% from Y
minus % mode
- Result
- the value with the percentage taken off
- Base
- the value
- A
- the percentage to subtract; above 100 the result is negative
Source: Standard formula; no single publisher.
X% of Y%
% of % mode
- Result %
- the combined percentage
- A
- the first percentage
- B
- the second percentage
50% of 20% is 10%.
Source: Standard formula; no single publisher.
Reverse percentage
reverse mode
- Original
- the whole you are looking for
- A
- the known part
- B
- the percentage the part stands for, not zero
Source: Standard formula; no single publisher.
The question box
Every mode
It reads five forms: what is X% of Y, X is what % of Y, X is Y% of what, increase X by Y%, and decrease X by Y%. Each uses the formula above for that question. It does not read negative numbers, the word "percent", or "20% of 500" without "what is".
Source: CalcTrail’s own reading rules; no publisher.
Figures beside the result, and rounding
Every mode
The figures beside the result (the remaining amount, the difference, New ÷ Old and the like) come from the same two numbers. The card shows up to three decimals, and six significant digits below 0.001, so 0.1% of 0.2 shows 0.0002. "How it works" rounds to two decimals, four for % of %.
Source: CalcTrail’s own figures and display rules; no publisher.
Sources
- US Bureau of Labor Statistics. Calculating percent changes, Consumer Price Index fact sheet, Tables 1, 2 and 4. Last modified February 9, 2023.
What this calculator does not cover
- Single-step percentage arithmetic only. It does not compound percentages over several periods (a savings or investment calculator does that) or convert percentages to fractions; the Fraction Calculator handles fractions.
- A change in a figure that is itself a percentage, such as a rate going from 4% to 5%, is a rise of one percentage point. This tool does not label points: it answers 25%, because 5 is 25% above 4.
- Markup and margin differ by their base. Add % is a markup on the value you enter; there is no margin mode.
Sources checked on .