Short answer: A percentage is just a fraction out of 100. So 20% of 250 is 50 (because 20 ÷ 100 × 250 = 50), 45 is 25% of 180, and a rise from 80 to 100 is a 25% increase. This free calculator answers all three questions — what is X% of a number, what percent one number is of another, and how much something changed in percent — plus what a number becomes after a percentage increase or decrease.
Last updated: 30 October 2026 · Estimate only — not financial advice.
1. What is X% of a number?
2. X is what percent of Y?
3. Percentage increase or decrease
4. Increase or decrease a number by a percentage
How the math works
- X% of a number = X ÷ 100 × number. So 20% of 250 = 20 ÷ 100 × 250 = 50.
- X as a percent of Y = X ÷ Y × 100. So 45 as a percent of 180 = 45 ÷ 180 × 100 = 25%.
- Percentage change = (new − old) ÷ old × 100. A rise from 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%; a fall from 100 to 80 is (80 − 100) ÷ 100 × 100 = −20%. Note the asymmetry: the same 20 move is 25% one way and 20% the other, because the starting point differs.
- Increase a number by P% = number × (1 + P ÷ 100). Decrease by P% = number × (1 − P ÷ 100). So 200 decreased by 15% = 200 × 0.85 = 170.
- Rounding: results are rounded to two decimal places, so 1 ÷ 3 as a percent shows as 33.33%, not 33.333…%.
Worked examples (illustrative — not real people's figures, not advice)
Discount in a shop. A jacket costs $80 and is marked 25% off. 25% of 80 = 20, so you save $20 and pay $80 − $20 = $60. That is calculator 1 followed by calculator 4 (80 decreased by 25% = 60).
Exam or test score. You score 45 out of 180 marks. 45 ÷ 180 × 100 = 25% — calculator 2.
Price rise. A subscription goes from $80 a month to $100 a month. (100 − 80) ÷ 80 × 100 = +25% — calculator 3. If it later falls back from $100 to $80, that is a 20% decrease, not 25% — the base changed.
Common traps
Percent vs percentage points. If a rate rises from 20% to 25%, that is a rise of 5 percentage points — but a 25% relative increase (5 ÷ 20 × 100). News reports and lenders use both, and mixing them up is the most common percentage mistake there is.
Two discounts in a row don't add. 50% off, then another 50% off, is not free: the second 50% applies to the already-halved price, so you pay 25% of the original (a 75% total discount). The same logic applies to a 20% rise followed by a 20% fall — you end below where you started.
Percentages over 100% are real. If something doubles, it grew by 100%; if it triples, it grew by 200%. And a part can exceed 100% of a whole only if the "whole" you picked is not actually the whole — check the base first.
FAQ
How do I work out a percentage on paper?
For X% of a number, divide by 100 and multiply: 15% of 200 = 0.15 × 200 = 30. For a share, divide the part by the whole and multiply by 100. For a change, divide the difference by the old value and multiply by 100 — always divide by the starting value, never the new one.
What is the difference between a percentage increase and a percentage-point increase?
A move from 20% to 25% is +5 percentage points, or +25% in relative terms. Use "percentage points" when both numbers are already percentages; use "percent" for the relative change. See the traps section above.
How do I calculate a tip?
Take the bill, pick a percent, and use calculator 1: 20% of a $45 bill = $9, so $54 total. For a quick check, 10% is just the bill moved one decimal place ($4.50), and 20% is double that ($9).
Can a percentage be more than 100%?
Yes — for growth and change. A price that doubles has increased by 100%; one that triples has increased by 200%. But a part of a whole cannot exceed 100% of that whole: if your calculation says 130%, the base (the "of" number) is wrong.
Related from Bia Crypto
- Is a Crypto-to-Crypto Swap Taxable in the US? IRS Rules, Worked Examples and the 1099-DA Trap (2026) — the latest guide: swapping one crypto for another is a taxable event, even if you never touch a dollar.
- Mortgage Calculator — monthly payments, total paid and total interest for a home loan.
- Loan Payment Calculator — the same amortization math for any fixed-rate loan.
- Compound Interest Calculator — percentages compounding over time: how small rates grow large.
- US Paycheck Calculator — what actually lands per paycheck after tax and deductions.
Sources
- Khan Academy — Percent problems (introduction to percentages)
- BBC Bitesize — Percentages (how to find a percentage of an amount and percentage change)
- Math is Fun — Introduction to Percentages
Disclaimer: This tool is for education only. It is not financial or tax advice. Percentages shown are arithmetic results from the numbers you enter — always check the figures that matter against the original bill, contract or statement.
— Adrian Cole, Bia Crypto
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