Percentage Calculator

Percentage problems break into three flavors that get confused with each other: "what's 15% of 80?", "15 is what percent of 80?", and "if 80 increased by 15%, what's the result?". Each has a different formula. Mixing them up — or eyeballing — is how mental math errors quietly creep into invoices, tip splits, and discount calculations.

Three input modes here, each with the right formula behind it: percent of a number, the percent that one number is of another, and percent change between two values. Whichever question you have, pick the matching mode rather than trying to talk yourself through which division goes which way.

Percent change in particular is asymmetric — going from 100 to 150 is a 50% increase, but going from 150 back to 100 is only a 33% decrease. That asymmetry trips people up regularly, and seeing both numbers explicitly helps internalize it.

The three core formulas: (1) percent of a number = number × (percent / 100); 15% of 80 = 80 × 0.15 = 12. (2) percent that x is of y = (x / y) × 100; 15 is 18.75% of 80. (3) percent change from a to b = ((b − a) / a) × 100; from 80 to 92 is 15%. The formulas look similar enough that people use the wrong one without noticing — particularly between (1) and (3), where a "15% increase" applied to 80 gives 92, while "15% of 80" gives 12. The calculator's three modes force you to pick the right formula by selecting the right question.

Worked example for percent change asymmetry: a stock goes from $100 to $130, then back to $100. The first move is +30%, the second is −23%. Same dollar amounts, asymmetric percentages. People intuit "+30% then −30% returns me to start" and are surprised when they don't. The math: the second percentage's denominator is the larger ($130) value, not the smaller ($100). For the round trip to actually return to start, the second move would need to be −23.08%, not −30%. This asymmetry compounds over multiple moves and is why investment "average annual returns" can hide losses (a 50% drop followed by a 50% gain leaves you down 25%, not even).

Percentage points versus percent is a related trap. An interest rate going from 4% to 5% is "1 percentage point" higher, which is also "25% relative increase" in the rate. News articles and political claims routinely conflate these. "Inflation rose 1%" might mean the inflation rate went from 3% to 4% (1 percentage point) or from 3% to 3.03% (1 percent of 3%). The calculator labels each form so you can tell them apart, but in everyday reading you have to interpret carefully.

For compound percentages, the multiplicative form matters. Two consecutive 10% increases multiply: 1.10 × 1.10 = 1.21, a 21% total increase. A 50% increase followed by a 30% decrease: 1.50 × 0.70 = 1.05, only a 5% net gain. Discount stacking ("20% off plus an extra 30% off") compounds the same way: 0.80 × 0.70 = 0.56, a 44% total discount, not 50%. Sales advertising routinely exploits this confusion. The calculator can handle one operation at a time; chaining multiple percentages is a sequence of operations, not a sum.