Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Calculate percentages, percentage change, and ratios with step-by-step math.
25% of 200
= (25 ÷ 100) × 200
= 50
"Percentage" questions come in several genuinely different forms -- finding X% of a number, figuring out what percent one number is of another, and calculating how much something increased or decreased in percentage terms are three distinct calculations that people often mix up. This tool handles all three, showing the step-by-step math for each so you can see exactly how the answer was reached, not just the final number.
Choose which type of percentage question you're answering -- "X% of Y," "X is what percent of Y," or "Percentage change from X to Y" -- enter your numbers, and the result (plus the full calculation steps) appears instantly.
X% of Y = (X ÷ 100) × Y
X is what % of Y = (X ÷ Y) × 100
Percentage Change = ((New − Old) ÷ Old) × 100
Shoppers calculating a discount or sale price. Students checking a test score's percentage. Anyone comparing two numbers -- a budget from one year to the next, a metric that changed over time -- and wanting the precise percentage change, not just a rough sense of "it went up."
Most percentage mistakes start with picking the wrong question. Ask yourself what you already know. If you have a rate and a total and want a portion, such as a 15 percent tip on a bill, use "X% of Y". If you have a part and a total and want the rate, such as a test score of 42 out of 50, use "X is what percent of Y". If you have two values at different times and want to know how much they moved, use "Percentage change". The three questions look alike but use different formulas, so matching the mode to the question comes first.
Discount and sale price: a jacket listed at 80 with 25 percent off. Using X% of Y gives 25% of 80 = 20, so the sale price is 80 - 20 = 60. Price with added tax: adding 8 percent to 50 gives 8% of 50 = 4, so the total is 54 (the rate here is hypothetical). Test score: 42 out of 50 is (42 / 50) x 100 = 84 percent. Decrease: a monthly bill dropping from 120 to 96 gives ((96 - 120) / 120) x 100 = -20 percent, a 20 percent decrease.
A common trap is trying to undo a percentage change with the same percentage. If a price rises by 25 percent, it must fall by only 20 percent to return to where it started, because the decrease applies to a larger number. For example, 100 up 25 percent is 125; taking 25 percent off 125 leaves 93.75, not 100. Likewise, a 50 percent drop needs a 100 percent gain to recover. Use the percentage change mode with your current and original values to find the exact figure required.
Results may contain many decimals; round to the precision your situation needs. For money, two decimals is normal, but when you compare rates or growth figures, keep at least one extra digit until the final step. For tax, interest, or grading rules that specify their own rounding method, follow the official rule from the relevant authority or institution.
Use "X% of Y" with your discount percentage and original price to find the discount amount, then subtract that from the original price for the sale price.
Percentage change measures relative change (how much bigger or smaller, proportionally); percentage points measure the raw difference between two percentages -- they're easy to confuse but often give very different-looking numbers for the same underlying change.
Yes -- a negative result means a decrease. For example, going from 150 to 120 gives a -20% change (a 20% decrease).
When the part is larger than the reference value, the ratio exceeds 1. For instance, a value of 150 compared against a base of 50 is 300 percent of it.
Percentage change cannot be calculated from zero because it would require dividing by zero. Describe the change in absolute units instead.
No. 100 rises to 120, then falls to 96, because the second change applies to the larger number.
Divide the sale price by one minus the discount rate. For instance, a sale price of 60 after 25 percent off means 60 / 0.75 = 80.