Percentage Calculator

To find a percentage, divide the part by the whole, then multiply by 100. To find what percent 25 is of 200, divide 25 by 200 to get 0.125, then multiply by 100 for 12.5%. The same two steps work for any comparison between a smaller part and a larger whole, whether you're grading a test, splitting a bill, or checking a discount.

A percent is relative to a starting value; a percentage point is a plain, direct difference between two percentages. If an interest rate rises from 5% to 6%, that's a 1 percentage point increase, but a 20% increase relative to the original 5%. Financial and political reporting blur the two constantly, so it's worth checking which one a headline actually means before repeating it.

Because the second percentage is calculated from a different, larger number. Increase $100 by 10% and you get $110. Decrease that $110 by 10% and you lose $11, not $10, leaving $99. Each percentage change resets its own base value, so equal-and-opposite percentage changes never fully cancel unless the underlying number happens to stay exactly the same, which it doesn't.

Percent change compares an old value to a new one: (new minus old) divided by old, times 100, and it's directional, showing whether something rose or fell. Percent difference compares two values with no obvious before-and-after, dividing their absolute difference by their average instead. Use percent change for tracking something over time, like a price or a score, and percent difference for comparing two separate measurements.

Divide the known result by the percentage written as a decimal. If a discounted price of $45 represents 75% of the original, divide 45 by 0.75 to get $60. This reverse calculation is the same formula rearranged to solve for the whole instead of the percentage, and it comes up often with sale prices, tips, and exam scores reported only as a final total.

Yes, whenever the part is larger than the whole you're comparing it to. If sales this month are $300 against $200 last month, that's 150% of last month's total, meaning sales are one and a half times last month's amount. Percentages over 100% are normal for growth and comparisons, but they don't make sense in situations where the whole represents a fixed maximum, like a completion rate.

Dividing by the wrong number: the part goes on top, and the number you're measuring against goes on the bottom. A close second is treating consecutive percentage changes as if they add together, so a 50% discount followed by a 25% discount feels like 75% off, when the second discount actually applies to the already-reduced price and the real total works out to 62.5% off, not 75%.

Subtract the old value from the new value, divide by the old value, then multiply by 100. A positive result is a percentage increase, a negative result is a decrease. Going from 40 to 50 is (50 minus 40) divided by 40, times 100, a 25% increase. Going from 50 back to 40 is a 20% decrease, not 25%, because the base value changed.

Not quite. A ratio compares two quantities directly, like 3 to 4, without forcing either one onto a scale of 100. A percentage is a specific kind of ratio already converted onto a base of 100, which makes it easier to compare across different totals. 3 out of 4 and 75 out of 100 describe the same proportion, but only the second one is a percentage.

Percentage error measures how far a measured or estimated value is from a known, correct value: divide the absolute difference by the correct value, then multiply by 100. Percentage difference compares two values where neither one is authoritative, using their average as the base instead. A lab measurement checked against a textbook constant calls for percentage error; comparing two competitors' prices calls for percentage difference.

Divide the percentage by 100, or just move the decimal point two places to the left. 12.5% becomes 0.125, and 6% becomes 0.06. Going the other way, multiply a decimal by 100 and add the percent sign, so 0.125 becomes 12.5%. This conversion is exactly what's happening inside the percentage formula itself, which is why decimals and percentages are really the same number written two ways.

Multiply the original price by the discount percentage written as a decimal, then subtract that from the original price. A $60 item at 25% off: 60 × 0.25 = $15, so the sale price is 60 − 15 = $45. You can also get there in one step by multiplying by what's left over, 60 × 0.75, which gives the same $45 without a separate subtraction.

Per mille (‰) and basis points (bps) are close relatives of a percentage that use a different base. Per mille means parts per thousand instead of parts per hundred, so divide the part by the whole and multiply by 1,000 instead of 100. A basis point is one-hundredth of a percentage point, or 0.01%, and it shows up constantly in finance: a rate move from 5% to 5.25% is usually written as 25 basis points, which avoids confusing that small move with a 25% change.

Yes, and that holds for any two numbers, not just this pair. Multiplication doesn't care about order, so (20 ÷ 100) × 50 and (50 ÷ 100) × 20 both simplify to 20 × 50 ÷ 100, which is 10 either way. It's a genuinely useful shortcut: if one direction is easier to do in your head, like 4% of 25 versus 25% of 4, swap the numbers and calculate whichever version is simpler.