How to Calculate a Percentage Increase, Decrease, or Change (With Formulas)

Most percentage confusion doesn't come from bad math — it comes from answering the wrong question with the wrong formula. "Percentage" problems almost always fall into one of three categories: finding a percentage of a number (what's 15% of 80?), finding what percent one number is of another (20 is what percent of 80?), and finding the percentage change between two numbers (a price went from 80 to 100 — what's the percent increase?). Each has its own formula, and using the wrong one for the situation is where most errors actually come from — not arithmetic mistakes.

Percentage of a number: (Percent ÷ 100) × Number. 15% of 80 is (15 ÷ 100) × 80 = 12.

What percent X is of Y: (X ÷ Y) × 100. 20 is what percent of 80? (20 ÷ 80) × 100 = 25%.

Percentage change from an old value to a new value: (New − Old) ÷ Old × 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25% increase.

• "Of a number" → multiply
• "What percent is X of Y" → divide X by Y, then ×100
• "Percent change from A to B" → divide the difference by the original value A, then ×100

Plugging a decrease into the percentage change formula produces a negative number, and that's the correct, expected result — not something to strip out or flip. A price dropping from 100 to 80 gives (80 − 100) ÷ 100 × 100 = −20%, meaning a 20% decrease. The negative sign is the formula correctly telling you the direction changed. The one detail worth double-checking every time: the denominator is always the original (old) value, never the new one — dividing by the wrong value is the most common way this calculation quietly goes wrong.

“The denominator in a percentage change is always the starting value — never the ending one.”

Here's the question that catches almost everyone at least once: if a $100 item is discounted 50%, then the discounted price is later increased 50%, is it back to $100? No — it's $75. The 50% discount brings $100 down to $50. The 50% increase is then calculated on that new $50 base, not the original $100, adding back only $25 — landing at $75, not $100. A percentage increase and decrease of the same size never fully cancel each other out, because each one is calculated on a different base. This isn't an edge case; it's how percentage math always works, and it applies just as much to stock prices, salary cuts followed by "raises," and any other back-to-back percentage change.

This distinction gets blurred constantly in headlines, and it changes the actual meaning of a statistic. If an interest rate moves from 10% to 12%, that's a 2 percentage point increase — a simple subtraction, 12 − 10. But expressed as a relative percentage increase, it's 20%, because (12 − 10) ÷ 10 × 100 = 20%. Both numbers are technically correct descriptions of the same change; they just answer different questions, and swapping one for the other — intentionally or not — can make an identical change sound twice as small or twice as large.

A common real-world question: an item costs $60 after a 25% discount — what was the original price? The instinct is often to add 25% of $60 back on, which gives the wrong answer ($75) because 25% of the discounted price isn't the same as 25% of the original price. The correct approach: the $60 represents 75% of the original price (100% − 25% discount), so the original price is $60 ÷ 0.75 = $80. Reverse-percentage problems need division by the remaining percentage as a decimal, not simple addition — this comes up constantly with sale prices, tax-inclusive totals, and tip-inclusive bills.

The same handful of formulas cover almost every everyday percentage question: calculating a tip or sales tax (percentage of a number), figuring out how much a grade improved between two tests (percentage change), comparing a raise in dollars to a raise in percent (percentage change, watch the base), and working out a pre-discount price from a sale tag (reverse percentage). The Percentage Calculator runs all of these — of a number, percent change, and reverse percentage — directly, so the formula never has to be memorized or re-derived under pressure.