Free online math calculators for percentages, fractions, roots, averages, subsets, and more. Step-by-step solutions with formulas shown.
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Math calculators take the routine out of arithmetic so you can focus on the problem instead of the bookkeeping. Whether you're working out what percentage one number is of another, simplifying a fraction, finding a square root by hand was going to take all afternoon, or counting subsets of a set, the tools here do it instantly with the formula and worked example shown alongside the answer.
Every calculator on this page is free, requires no signup, and works on your phone. Inputs are processed in your browser — nothing is sent to a server. If you ever want to understand how a result was reached, scroll down on any calculator: the math is spelled out, not hidden behind a black box.
To find X percent of Y, multiply Y by X and divide by 100. For example, 15% of 80 = (80 × 15) ÷ 100 = 12. Our percentage calculator does this in both directions — you can find a percentage of a number, find what percent one number is of another, or calculate percentage increase and decrease, all in one place.
What's the difference between a fraction and a decimal?
A fraction expresses a number as a ratio of two integers (3/4), while a decimal expresses it positionally (0.75). They're interchangeable representations of the same value: 3/4, 0.75, and 75% all describe the same quantity. Fractions are exact for ratios like 1/3, while decimals are exact for sums of tenths, hundredths, and so on.
How do you find the square root of a number without a calculator?
For perfect squares (4, 9, 16, 25...) the square root is the integer you'd need to multiply by itself: √25 = 5. For non-perfect squares, you can estimate by finding the two nearest perfect squares: √20 is between √16 (= 4) and √25 (= 5), so about 4.47. For an exact value, our root calculator handles square roots, cube roots, and any n-th root.
What is a subset of a set?
A subset of a set S is any collection of elements that all come from S. The empty set ∅ and S itself are both considered subsets of S. A set with n elements has exactly 2ⁿ subsets in total. For example, {a, b} has four subsets: ∅, {a}, {b}, and {a, b}. Proper subsets exclude the original set, so {a, b} has three proper subsets.