Percentage Calculator

This percentage calculator covers the three questions that come up most often in daily arithmetic: what a given percentage of a number is, what share one number represents of another, and how much a value has risen or fallen between two points. Shoppers use it to price a sale item, students to convert marks into grades, and anyone dealing with tips, tax, commission or margins to avoid setting up the sum by hand. Percentage work trips people up in the detail rather than the concept, because a rise and a fall of the same percentage do not cancel out. Applying the formula consistently removes that error. The arithmetic runs in your browser as you type, so results appear immediately and nothing you enter needs to leave the page.

Every percentage question reduces to one of three relationships between a part, a whole and a rate. Finding a percentage of a number multiplies the whole by the rate divided by 100: 18 percent of 250 is 250 x 18 / 100, which is 45. Expressing one number as a percentage of another divides the part by the whole and multiplies by 100: 45 out of 250 is 45 / 250 x 100, or 18 percent. Percentage change compares an old and a new value using (new minus old) divided by old, multiplied by 100, so a move from 250 to 280 is 30 / 250 x 100, a rise of 12 percent.

A fourth case, reverse percentage, follows from the first. If a price already includes a markup or discount, you divide rather than multiply: a figure of 120 that already carries 20 percent VAT came from 120 / 1.20, which is 100. Confusing that with subtracting 20 percent from 120 is the single most common percentage mistake, because it gives 96 instead of 100.

A jacket is listed at 85.00 and the sale sign says 35 percent off. The discount itself is 85 x 35 / 100, which equals 29.75. Subtracting that from the list price leaves a sale price of 55.25. Checking the change formula in the other direction confirms the figure: (55.25 minus 85) divided by 85, times 100, is minus 29.75 / 85 x 100, or exactly minus 35 percent.

Now run the same numbers back the other way, because this is where intuition fails. To climb from 55.25 back up to 85 you need an increase of 29.75 / 55.25 x 100, which is 53.85 percent, not 35 percent. The same cash amount is a larger percentage when measured against the smaller base. That asymmetry explains why a stock that drops 50 percent needs a 100 percent gain to recover, and why stacking a 10 percent discount on top of a 20 percent discount gives 28 percent off in total rather than 30 percent.

Be clear about which number is the base before you trust a percentage. Percentage change always measures against the earlier or original value, so swapping the two inputs does not simply flip the sign. Going from 40 to 50 is a 25 percent rise, while going from 50 to 40 is a 20 percent fall, and both describe the same gap of 10.

Distinguish percent from percentage points as well. If a savings rate moves from 4 percent to 5 percent, that is a rise of one percentage point but a 25 percent increase in the rate itself. News reports mix the two freely, and the difference matters when compounding is involved.

Finally, watch the order of operations when several percentages apply. Discounts, taxes and service charges multiply rather than add, so apply each one to the running total in the sequence the seller uses. Rounding at every step also drifts; round only the final figure. These results are arithmetic, not financial advice, so check contractual terms before acting on a number.