Percentage formulas explained
A single reference sheet for each formula behind the calculators, with one worked example apiece.
Core formulas
Percentage of a value: Part = (Percent ÷ 100) × Whole. 12% of 350 = 42.
Percentage one number is of another: Percent = Part ÷ Whole × 100. 42 of 350 = 12%.
Percentage change: (New − Original) ÷ Original × 100. From 350 to 392 is +12%.
Comparison and money formulas
Percentage difference: |A − B| ÷ ((|A| + |B|) ÷ 2) × 100. Comparing 40 and 60 gives 40%.
Discount: Final = Original × (1 − Rate ÷ 100). $89.99 at 25% off is $67.49.
Tip: Total = Bill × (1 + Rate ÷ 100), then divide by the number of diners.
Tax: Gross = Net × (1 + Rate ÷ 100), and Net = Gross ÷ (1 + Rate ÷ 100).
Reversing a percentage
To undo a change, divide instead of multiply. A price of $180 after a 28% cut was $180 ÷ 0.72 = $250.
This is the step most people get wrong: subtracting the same percentage does not take you back to the start. The Reverse Percentage Calculator works through it for you.
Put it to work