Percentage Calculator - % of, What % & Percentage Change
25% of 200
50
How This Calculator Works
Pick a mode, enter two numbers, and results update instantly on-device. Formulas: % of = (A/100)×B, What % = (A/B)×100, % change = ((new-old)/old)×100.
FAQ
• What is percentage change? It measures increase/decrease relative to starting value.
• Why can results be negative? Negative means decline.
• Can I use decimals? Yes.
Deep Dive: The Mathematics of Percentages
Percentage is derived from the Latin 'per centum' — per hundred — and provides a standardized way to express ratios regardless of absolute size. The three fundamental percentage problems are: finding a percentage of a number (what is 15% of 80?), finding what percentage one number is of another (18 is what percent of 90?), and finding the original number given a percentage (42 is 70% of what?). Each requires a different algebraic rearrangement of: Percent × Base = Part. Students frequently confuse which quantity plays which role, leading to systematic calculation errors.
Percentage change and percentage point change are frequently confused in economic and political reporting. If unemployment rises from 4% to 6%, it has increased by 2 percentage points but by 50% in relative terms. Politicians choose whichever framing serves their narrative — '50% rise in unemployment' sounds alarming; '2 percentage point increase' sounds modest. The confusion is especially prevalent in interest rate reporting: the Fed raising rates from 2% to 3% is a 1 percentage point increase but a 50% relative increase. Clearly distinguishing these measures is basic financial literacy.
Compound percentage changes are non-linear in ways that surprise people. A stock that falls 50% and then rises 50% has not returned to its starting point — it's at 75% of original value. A 50% decline requires a 100% gain to recover. This asymmetry means volatility itself destroys value in an investment, independent of average return. The geometric mean (compound annual growth rate) is always less than or equal to the arithmetic mean for a series of returns — often significantly so for volatile assets.
Percentage thinking can be deliberately exploited in pricing psychology. A $200 item marked '50% off' at $100 feels like a great deal because our brains process the savings percentage as a signal of value. Kahneman and Tversky documented framing effects — the same economic outcome (saving $100) is valued differently depending on whether it's framed as a percentage or absolute amount. A 50% discount on a $100 item feels better than $50 off a $200 item even though the dollar savings are identical. Retailers use this systematically through reference pricing and sale framing.