CodeMaster AcademyThe three percentage problems people actually search for
"Percentage calculator" hides at least three distinct questions, and confusing them is the most common source of wrong answers when doing this by hand. First: what is X% of Y? (e.g., what is 15% of 200 — used for tips, discounts, taxes). Second: X is what percent of Y? (e.g., 30 out of 200 is what percent — used for grades, completion rates). Third: what is the percentage change from X to Y? (e.g., a price moved from 200 to 230 — what's the percent increase). Each uses a different rearrangement of the same underlying ratio, which is why a single "percentage formula" memorized without understanding often gets misapplied.
The formulas behind each case
For "X% of Y," multiply Y by (X ÷ 100) — 15% of 200 is 200 × 0.15 = 30. For "X is what percent of Y," divide X by Y and multiply by 100 — 30 ÷ 200 × 100 = 15%. For percentage change, subtract the original from the new value, divide by the original, and multiply by 100 — (230 − 200) ÷ 200 × 100 = 15% increase. Percentage decrease uses the identical formula; a negative result simply indicates a decrease rather than an increase.
Where the confusion usually happens
The most common real-world mistake is percentage change math on discounts and markups. If a $100 item is marked up 20% to $120, then discounted 20%, people often expect to land back at $100 — but 20% of $120 is $24, not $20, so the discounted price is $96, not $100. Percentage increases and decreases aren't symmetric once the base number changes. This trips up shoppers comparing "was $X, now Y% off" deals, and it trips up anyone tracking compounding changes over multiple periods.
Using this calculator
Select which of the three calculation types matches your question, enter the numbers, and the result computes instantly. All math happens locally in your browser — nothing is sent to a server.
Common questions
Why did reversing a discount and markup not return the original price?
Because percentage is always calculated against the current base number, not the original one — a 20% increase followed by a 20% decrease lands below the starting value, not back at it.
How do I calculate percentage points vs. percent change?
Going from 20% to 25% is a 5 percentage-point increase, but a 25% relative increase (5 ÷ 20 × 100). These describe different things and are easy to conflate in statistics or news reporting.
Can this handle negative percentages or values over 100%?
Yes — percentage change calculations naturally support negative results (decreases) and values over 100% (more than doubling), since the formula doesn't cap at any particular range.
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Page last reviewed: July 2026