Percentage Calculator (% of, what %, % change)

The three percentage operations

Almost every real-world percentage problem reduces to one of three patterns: 'X% of Y' (a discount or tax), 'X is what % of Y' (a ratio expressed as a percent), or the percent change from A to B (year-over-year growth, weight loss, exam score improvement).

This calculator exposes all three in a single interface. Switch the mode at the top, then plug in the two values. The math is simple but the bookkeeping — which number goes where — is where most mistakes happen, so labels here are explicit about which input is the part and which is the whole.

How percent change is computed

Percent change = (new − old) / old × 100. A positive result means an increase, a negative result means a decrease. Notice the formula uses the old value, not the new one or the average — that's why a 50% drop followed by a 50% gain doesn't bring you back to where you started: it ends at 75% of the original.

When the old value is zero, percent change is undefined (you can't divide by zero). The calculator returns no result in that case rather than showing 'infinity', because the answer to 'how big is the change relative to nothing' isn't meaningful.

Common pitfalls

Compounding percentages. A 10% raise after a 10% raise is 21%, not 20% (1.10 × 1.10 = 1.21). Use the percent-of mode twice or the percent-change mode for the final ratio.

Percentage points vs percent. If a poll moves from 40% to 42%, that's a change of 2 percentage points but a 5% relative increase. The calculator's 'percent change' mode reports the relative change.

Discount stacking. A '20% off' coupon applied after a '20% off' sale is 36% off the original (0.8 × 0.8 = 0.64), not 40%. Run the calculator twice in 'percent of' mode to see this directly.