Percentage calculator — offline

Almost every real percentage problem is one of three, and they are laid out here as three independent calculators so you do not have to work out which formula applies:

• What is X% of Y? — discounts, tips, tax, commission, interest.
• What percent of Y is X? — a score as a percentage, a share of a budget, a conversion rate.
• What is the change from A to B? — growth, price rises, a drop in traffic.

All three update live and work independently, so you can keep one result on screen while working out another. It is arithmetic in your browser, so nothing is transmitted and it works offline.

Percentage change is (new − old) ÷ |old| × 100. A rise from 50 to 75 is +50%; a fall from 80 to 60 is −25%. Using the absolute value of the old figure in the denominator keeps the sign meaningful even when the starting value is negative, which matters for profit-and-loss figures.

The direction is not symmetric, and this trips people up constantly. Going from 100 to 50 is a 50% decrease, but going back from 50 to 100 is a 100% increase — the same absolute move, two different percentages, because the base changed. Whenever a percentage change is quoted, the question worth asking is "percent of what?".

A percentage of a percentage is where reporting goes wrong. If a conversion rate moves from 2% to 3%, that is a rise of one percentage point — and a 50% increase. Both are true, they mean very different things, and the larger-sounding one is the one that tends to appear in headlines.

Stacked percentages do not add either. A 20% discount followed by a further 10% off is not 30% off: the second discount applies to the already-reduced price, giving 28%. The same asymmetry means a 50% loss needs a 100% gain to recover — which is why a portfolio down by half has further to climb back than it first appears.

Related and equally local: unit converter and number base converter.