Percentage Calculator

Three questions, three formulas

Most percentage confusion comes from mixing up three different questions. “What is 20% of 80?” multiplies: 20 ÷ 100 × 80 = 16. “What percentage is 16 of 80?” divides: 16 ÷ 80 × 100 = 20%. “From 80 to 100, what is the percentage change?” divides the difference by the starting number: (100 − 80) ÷ 80 × 100 = 25% increase. The calculator above keeps the three apart with separate modes, and shows its working, because a percentage answer without its formula is hard to trust.

Worked examples

These are the cases that come up most often — a discount, a share of a total, and a price move — and each uses a different one of the three formulas.

Increase versus decrease — the base matters

The same two numbers give different percentages depending on direction, and that asymmetry trips people up constantly: £80 to £100 is a 25% increase, but £100 back to £80 is only a 20% decrease, because the base changed from 80 to 100. It also means a 50% rise followed by a 50% fall does not return you to where you started — £100 up 50% is £150, down 50% from there is £75. Whenever a percentage change sounds too good or too bad, check which number it was calculated from.

Percentage points are not percent

If a rate moves from 20% to 25%, it has risen by five percentage points, but by 25% in relative terms (5 ÷ 20 × 100). News reports and loan documents use both, and confusing them understates or overstates the change fivefold in this example. When precision matters — interest rates, tax bands, exam pass marks — say which one you mean, and expect the other party to mean the other.