Percentage Calculator

• % of: (X ÷ 100) × Y
• Increase: X × (1 + P ÷ 100)
• Decrease: X × (1 − P ÷ 100)
• Change: ((Y − X) ÷ |X|) × 100
• Difference: (|A − B| ÷ ((|A| + |B|) ÷ 2)) × 100
• Reverse: X ÷ (P ÷ 100)

Every percentage question is really one ratio in disguise. “Percent of” scales a number down to a slice. “Change” compares a new value against an old baseline. “Difference” compares two values symmetrically — you don't need to decide which one came first. Switching modes above just rephrases the same arithmetic to match the question you actually have.

The most common confusion is between change and difference. Change has direction (up or down) and uses the original value as the baseline. Difference is unsigned and uses the average of the two values, which makes it the right choice when neither value is more “correct” than the other.

• Tips & sales tax — “What's 18% of $54.30?” uses percent of.
• Discounts — “25% off $79” is a percent decrease.
• Pay raises & price hikes — “$58k bumped 6%” is a percent increase.
• Investment returns — “Bought at 80, now 100” is percent change.
• A/B comparisons — comparing two metrics fairly is percent difference.
• Reverse-engineering totals — “VAT was $12 at 20%, what's the pre-tax price?” uses reverse percentage.

• Treating +10% then −10% as zero change. It's actually a 1% loss because the second percent is taken from a larger number.
• Confusing percentage points with percent. Going from 10% to 12% is a 2-point rise, but a 20% increase.
• Using the wrong baseline for percent change. It's always the original (the “from” value), not the new one.
• Mixing up “X% of Y” with “Y% of X”. They're only equal when X = Y.