Percent of a Number

“What is p% of N?” Use: N × (p ÷ 100). Example: 15% of 80 = 80 × 0.15 = 12.

Percent Increase

From old to new, the increase % is: ((new − old) ÷ old) × 100%.

Example: Price goes from 50 to 60 → increase = (60−50)÷50×100% = 20%.
To apply a percent increase directly: new = old × (1 + p) where p is the decimal (e.g., 0.20 for 20%).

From old to new, the decrease % is: ((old − new) ÷ old) × 100%.

Example: From 60 down to 45 → decrease = (60−45)÷60×100% = 25%.
Apply directly: new = old × (1 − p) where p is the decimal (e.g., 0.25 for 25%).

Do it instantly with our Percentage Calculator — supports percent of, increase, and decrease.

Wrong base: Always divide by the original value when computing change. If a shirt goes 40 → 50, the increase is 10 ÷ 40 = 25%, not 10 ÷ 50.
Reversing changes: A 25% increase followed by a 25% decrease does not return to the starting value (it lands lower). See compound change below.
Percent points vs percent: If a rate moves from 5% to 7%, that’s a 2 percentage-point rise, which is a 40% increase relative to 5%.

Back-to-back changes multiply, they don’t add. Use this rule:

final = start × (1 + p1) × (1 + p2) × (1 + p3) …

Sale price: price × (1 − discount). A 25% discount is × 0.75.
Tax after discount: Apply tax to the discounted price: price × (1 − d) × (1 + t).
Stacked coupons: 20% off then 10% off is × 0.8 × 0.9 = × 0.72 (overall 28% off).

To find what portion a part is of a whole: part ÷ whole × 100%. Example: 18 out of 60 = 18 ÷ 60 × 100% = 30%.