Percentage calculator
Switch among three common questions: what a percent of a base is, what percent a part is of a whole, and percent change between an old and new value. Labels update automatically so you always know which box is which.
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Percents as language, not magic
A percent is literally “per hundred.” Saying fifteen percent is the same as multiplying by 0.15, which is why the “percentage of” mode divides your percent by one hundred before it touches the base. That single rule powers discounts, tax-inclusive pricing, commission schedules, and classroom word problems alike; the notation changes but the factor does not.
The part-to-whole question flips the algebra: you already know the slice and the entire pie, and you want the slice expressed in hundredths. That is how market share, test scores, and error rates are communicated. Percent change is subtly different—it always anchors on the starting value, so a move from 50 to 75 is not the same relative story as a move from 5 to 7.5 even though both add 25 absolute units in different contexts. Anchoring on zero as a starting point breaks the relative-change definition, which is why the tool guards that case.
Where quick percent math shows up
Retail workers sanity-check markups before printing shelf tags. Journalists convert raw counts into readable shares without leaning on a spreadsheet for every paragraph. Engineers translate specification tolerances into pass-or-fail ratios. Students verify homework before submitting. In each case the goal is the same: translate between fractions, decimals, and percents without losing track of which quantity is the denominator—this page simply encodes the three most common question shapes in one place.
Frequently asked questions
- What are the three modes on this percentage calculator?
- Percentage of a number multiplies the base by p÷100. Part versus whole divides the part by the whole and multiplies by 100. Percent change compares new minus old, divided by old, times 100.
- Why is percent change undefined when the original is zero?
- Relative change divides by the starting value. When that start is zero, the ratio is not a meaningful percent change in the usual business sense; the tool asks for a non-zero original in that mode.
- Can I enter negative numbers?
- Yes where mathematically sensible—for example a price drop modeled as a negative percent change path. Division by zero and empty fields are still rejected with a short message.
- Does this round like a cash register?
- It shows a readable numeric string with up to four decimal places trimmed of trailing zeros for display. Banking rounding rules and currency precision are not built in.
- How is this different from the tip calculator?
- The tip page is optimized for bills, default percents, and splitting among people. This page is generalized for homework, analytics, and any percent-of or percent-change question.