Percentage Calculator
30 is X% of Y
Three Different Percentage Questions, One Formula Family
"Percentage" problems almost always reduce to the same relationship, part = percent × whole, just solved for a different variable. Finding X% of Y multiplies Y by X/100. Finding what percent X is of Y divides X by Y and multiplies by 100. Both are direct applications of the definition of percent as "per hundred" (Latin per centum) — a ratio scaled so the whole equals 100 parts.
Percentage Change Is Not the Same as Percentage Points
Going from 150 to 180 is a 20% increase, calculated as (180 − 150) ÷ 150 × 100. That's different from saying the values differ by "20 percentage points," which only applies when comparing two percentages directly (for example, an interest rate moving from 5% to 7% is a 2 percentage point increase, but a 40% relative increase). Mixing up percentage change and percentage points is one of the most common statistics reporting errors, so this calculator always reports true relative percentage change.
Related Tools
If you need to work with the fractional form of a percentage instead (like converting 3/4 to a percent or back), try the fraction calculator. For comparing a measured value against an expected one rather than a before/after change, the percent error calculator uses a related but distinct formula.
Frequently Asked Questions
What is the formula for percentage increase or decrease?
Percentage change equals (New Value minus Old Value) divided by the absolute value of the Old Value, multiplied by 100. A positive result is a percentage increase and a negative result is a percentage decrease. The old (starting) value must be nonzero for the formula to be defined.
What is the difference between percentage change and percentage points?
Percentage change is a relative measure: going from 5% to 7% is a 40% relative increase (2/5 x 100). A percentage point difference is a simple subtraction of two percentages: 7% minus 5% is a 2 percentage point increase. The two describe the same move but with very different-sounding numbers, so they should never be used interchangeably.