Percentage Calculator
The three percentage questions everyone actually asks: what is X% of Y, X is what percent of Y, and what is the percentage change from X to Y. One tool, all three.
Three questions hide inside the word 'percentage'
Almost every percentage problem is one of three shapes: a percentage of a whole (15% of 200), a share (30 is what % of 200?), or a change (from 200 to 230 is what %?). They use different formulas, and picking the wrong shape — not arithmetic — is where percentage errors live.
Of: A ÷ 100 × B · Share: A ÷ B × 100 · Change: (B − A) ÷ A × 100
Example: 15% of 200 is 30. 30 as a share of 200 is 15%. A change from 200 to 230 is +15% — but the change back from 230 to 200 is −13.04%, not −15%: change is measured against where you start, and the asymmetry fools adults daily.
Percent vs percentage points
A rate rising from 4% to 5% rose by one percentage point — and by 25 percent. News, banking and politics exploit the ambiguity; the defense is to always ask 'percent of what?' The three modes here force that question to be answered before any number appears.
How this is calculated
The three closed forms above, applied to your two numbers with the mode you select. Percentage change divides by the absolute starting value and keeps the sign of the direction. Results are stated with the sentence they answer, so the output names its own meaning instead of floating as a bare figure.
Frequently asked questions
Why is a 50% loss not undone by a 50% gain?
Because the bases differ: $100 → $50 is −50%; $50 → $100 needs +100%. Losses and gains are asymmetric in percentage terms — the deeper the loss, the steeper the climb (a 90% loss needs a 900% gain).
How do I calculate a reverse percentage (price after 20% off was $80)?
Divide by the surviving fraction: 80 ÷ 0.8 = $100. 'Of' mode run backwards — or the discount page, which is built for the retail version of this shape.
What is a basis point?
One hundredth of a percent: 0.01%. Finance uses it to speak precisely about rate changes — 'the Fed raised 25 basis points' means +0.25%, avoiding the percent-of-percent confusion entirely.
Percent of a percent — how?
Multiply them as decimals: 20% of 5% is 0.2 × 0.05 = 0.01 = 1%. This is how layered fees and nested discounts actually compose, as the discount calculator demonstrates in retail dress.
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