Three common percentage calculations in one place.
Percentage calculations come up constantly in everyday finance — from figuring out a tip or discount, to understanding how much your salary increased, to checking loan interest rates. The three core formulas are: X% of Y = (X/100) × Y; X as a percentage of Y = (X/Y) × 100; and percentage change from X to Y = ((Y−X)/X) × 100.
A common mix-up is confusing 'percentage of' with 'percentage change' — a 20% discount and a price that changed by 20% use different formulas, and getting them mixed up is a common source of errors when comparing prices or growth figures.
A percentage point is the arithmetic difference between two percentages (e.g., going from 10% to 15% is a '5 percentage point' increase), while a percentage change describes the relative change (that same move is a 50% increase relative to the starting 10%).
Use the formula ((New Value − Old Value) / Old Value) × 100. A positive result means an increase, a negative result means a decrease.
Percentages are relative to their base value — a 50% decrease followed by a 50% increase doesn't get you back to the original number, because the second 50% is calculated on a smaller base than the first.