Percentage Calculator Guide: How to Calculate Percentages for Everyday Life

Almost every percentage problem is one of six questions, and each has one formula. You are either finding a percentage of a number, finding what percent one number is of another, finding the percent change between two numbers, adding a percentage to a number, taking a percentage off a number, or working backward from a result to the original number. This guide lists all six with computed answers, so you can find the one that matches your problem and check your own arithmetic against it.

The six percentage problems and their formulas

A percent is a fraction out of 100, so 15% means 15 / 100 = 0.15. Every formula below is that one idea applied in a different direction. The first five question types match the five modes of the TheCalcUniverse percentage calculator; the sixth, the reverse problem, has no mode of its own, but you can check it with the calculator by running the answer forward.

Every answer in the table was computed rather than estimated. The calculator's percent-change mode divides by the absolute value of the starting number, which only matters when the starting number is negative (covered below).

A worked example for each situation

• Percent of a number: a 7.5% commission on a 64-unit order is 0.075 x 64 = 4.8 units.
• Percent above 100%: 120% of 45 is 1.2 x 45 = 54. Percentages over 100 are normal when something has grown.
• What percent: you scored 42 of 50, so 42 / 50 = 0.84, which is 84%.
• Share of a total: if 18 of 60 survey answers were "yes", that is 18 / 60 x 100 = 30%. The other 42 answers are 70%, and 30% + 70% = 100%.
• Change over time: a price of 240 that falls to 210 changed by (210 - 240) / 240 = -0.125, which is a 12.5% decrease.
• Tax added: 8.5% tax on a 120 purchase is 10.20, so the total is 130.20.
• Discount taken off: 35% off a 90 item removes 31.50, leaving 58.50.
• Working backward: a price of 68 after a 20% discount was 68 / 0.80 = 85 before the discount.

Working backward is the one people get wrong

Suppose a total of 138 includes a 15% increase and you want the amount before the increase. The tempting move is to take 15% of 138 and subtract it, which gives 138 x 0.85 = 117.30. That is wrong, because the 15% was calculated on the smaller original number, not on 138. The correct step is to divide: 138 / 1.15 = 120. Check it by going forward: 120 x 1.15 = 138. The same applies to a discount, where you divide by (1 - rate) instead of subtracting.

Common mistakes

• Using the wrong base. Percent change always divides by the starting value. Going from 75 to 50 is a 33.3% decrease, but going from 50 back to 75 is a 50% increase. The same gap of 25 units gives two different percentages because the starting values differ.
• Treating a rise and a matching fall as cancelling. Start at 100, add 20% to reach 120, then take 20% off: 120 x 0.80 = 96, not 100. To undo a 20% fall you need a 25% rise.
• Adding percentages that apply to different bases. A 10% rise followed by another 10% rise is 1.10 x 1.10 = 1.21, so 21% in total, not 20%. A 50% rise followed by a 50% fall leaves you at 1.5 x 0.5 = 0.75, which is a 25% loss.
• Confusing percent with percentage points. A rate moving from 10% to 15% is up 5 percentage points but up 50% in relative terms.
• Rounding too early. Keep full precision through the calculation and round only the final answer, especially for money, so that fractions of a cent are rounded once, at the end.

When a plain percentage is not enough

The formulas above assume a single step on a single base. Percent change is undefined when the starting value is zero, because you cannot divide by zero; report the absolute change instead. When the starting value is negative, the result needs care: the calculator treats a move from -50 to -25 as +50% because it divides by the absolute value of -50, which reads as an improvement, but plain division by -50 would show -50%. Many analysts avoid percent change altogether for values that can be zero or negative. Repeated percentages, such as interest earned every year, compound rather than add, so use a compound interest tool instead. Tax brackets, tiered pricing and sliding-scale fees apply different percentages to different slices of an amount, so one percentage multiplication will not reproduce them.

Which guide to read next

This guide is the reference for the basic types. For a deeper treatment of percent change, percentage points and reverse percentages, read the guide on calculating percentage increase and decrease. For shortcuts to do these sums without a calculator, read the guide on percentage mental math. For stacked discounts and sales tax together, use the discount guide and the percent off calculator.