About this calculator
Six everyday percentage questions in one place: a percentage of a number, what percentage one value is of another, the percentage change from an old to a new value, increasing or decreasing by a percentage, the reverse percentage (finding the original number) and the percentage difference between two values.
Formula
P% of a number
R = P ÷ 100 × X
A is what % of B
P = A ÷ B × 100%
% change A → B
% change = (B − A) ÷ |A| × 100%
A is the old value and B the new value. The multiplier is B ÷ A.
Increase / decrease by %
R = X × (1 ± P ÷ 100)
Reverse (X is P% of ?)
Original = X ÷ (P ÷ 100)
Example: if a price including 20% tax is the known value, it is 120% of the price before tax, so enter P = 120.
% difference
% difference = |A − B| ÷ ((A + B) ÷ 2) × 100%
Use it when neither value is the “old” one. For a before-and-after comparison use % change instead.
Worked example
- 15% of 240 = 0.15 × 240 = 36
- 45 is 45 ÷ 60 × 100 = 75% of 60
- Change from 45 to 60: (60 − 45) ÷ 45 × 100 = 33.33% increase
- 240 increased by 15% = 240 × 1.15 = 276
- 276 is 115% of 276 ÷ 1.15 = 240
- % difference of 45 and 60 = 15 ÷ 52.5 × 100 = 28.57%
Assumptions and limitations
- Percentages are entered as numbers of percent (15 means 15%, not 0.15).
- Two successive percentage changes do not add: +10% then −10% gives 0.99 × the start value, not the same value.
- Results are shown to 10 significant figures; full precision is kept in the calculation.
References
- Standard arithmetic of percentages and proportional change.