Am I comparing percentages or proportions?
State the original base before interpreting a change, reduce ratios without changing their meaning, and preserve exact fractions.
Everyday mathematics
Everyday mathematics
Calculate percentages, fractions, averages, powers and integer factors. Review the formulas, exact results, rounding rules and worked examples before use.
10 calculatorsEnglish and ChineseNo account required
From question to result
Choose a path for your question
Calculate first, understand the formula and example, then compare your options. Each link answers a different question.
When should an average or rounded result be used?
Keep legitimate zeros and investigate outliers before averaging. Round only at the reporting step using a stated tie rule.
How are roots and powers related?
Check the real-number domain before using inverse operations; negative exponents and principal square roots have specific rules.
Which integer operation solves this problem?
Use prime factors to understand GCD and LCM, but distinguish factorization from factorial products and their exact integer bounds.
Calculator set
Everyday mathematics calculators
Open a calculator for an immediate estimate, then use its method notes, examples, limits, and sources to understand the result.
Percentage CalculatorFind a percentage of a number, express a part as a share of a whole, or compare percentage change from a positive original value. Choose the relationship first, then enter A and B.CalculateAverage CalculatorCalculate arithmetic mean, median, minimum, maximum and count for a finite set of numbers. Retain zero and negative observations rather than dropping them.CalculateFraction CalculatorAdd, subtract, multiply or divide two integer fractions. The rational result is reduced exactly using integer arithmetic; a decimal approximation is also displayed.CalculateSquare Root CalculatorFind the non-negative real square root of a number and check it by squaring the result. This is the principal root; an equation y² = x can also have the negative solution.CalculateRatio CalculatorReduce an integer ratio and scale both original terms by the same factor. The reduced ratio expresses relative size; scaled terms retain the chosen numerical scale.CalculateGCD & LCM CalculatorFind greatest common divisor and least common multiple across a list of integers using the Euclidean algorithm and exact integer arithmetic.CalculateExponent CalculatorRaise a non-negative base to a power, including negative and fractional exponents when defined. Negative bases accept integer exponents only; the result must be finite.CalculateRounding CalculatorRound to decimal places or powers of ten. This tool uses the explicitly stated midpoint-away-from-zero rule: −1.5 rounds to −2 at zero decimal places.CalculatePrime Factorization CalculatorDecompose an integer into a product of prime factors using bounded trial division. Negative values retain a factor of −1, making the displayed product reproduce the original input.CalculateFactorial CalculatorCompute the exact factorial of a non-negative whole number using arbitrary-size integer arithmetic rather than letting large results overflow to Infinity.Calculate
Understand, then calculate
Make sense of the key numbers in Everyday mathematics
The operation and its domain matter as much as the numbers. Percentages are ratios expressed per hundred, a fraction is an exact numerator-to-denominator relationship, and a real square root denotes the non-negative principal root. A finite decimal displayed on screen need not be the exact mathematical value: irrational roots and many decimal fractions cannot be represented exactly by binary floating point. Keep full internal precision when calculating, then round at the display or reporting step.
Integer problems have different rules from real-number problems. Prime factorization, factorials and greatest common divisors require whole numbers, so a decimal such as 3.8 must not silently become 3. Euclid’s remainder algorithm reduces GCD efficiently; exact large-integer arithmetic keeps products precise where a floating-point integer would lose digits. Bounds limit interactive work and do not change the underlying equation. For ratios and averages, retain valid zero observations and reject an undefined denominator instead of substituting a plausible-looking result.
What you can work out here
Identify the decision first, then open the calculator that answers it.
- Percentage Calculator
- Find a percentage of a number, express a part as a share of a whole, or compare percentage change from a positive original value. Choose the relationship first, then enter A and B.
- Average Calculator
- Calculate arithmetic mean, median, minimum, maximum and count for a finite set of numbers. Retain zero and negative observations rather than dropping them.
- Fraction Calculator
- Add, subtract, multiply or divide two integer fractions. The rational result is reduced exactly using integer arithmetic; a decimal approximation is also displayed.
- Square Root Calculator
- Find the non-negative real square root of a number and check it by squaring the result. This is the principal root; an equation y² = x can also have the negative solution.
Core terms in plain language
Understand the recurring inputs and results instead of reading only the final number.
- Input domain
- The values for which an operation is defined, such as a nonzero denominator.
- Exact value
- An integer or fraction represented without decimal rounding within the tool’s bounds.
- Principal square root
- The nonnegative real root; solving x² = a may also require its negative counterpart.
- Rounding midpoint
- A halfway value handled by a declared tie rule rather than an unstated assumption.
Choose with context
Which calculator should you use?
Use these distinctions to move through the Everyday mathematics tools without comparing unrelated results.
- 01
Use percentage change for a before-and-after comparison and ratios for proportional quantities.
- 02
Use fractions for exact rational arithmetic; inspect the median when an average is affected by outliers.
- 03
Use integer tools for GCD, LCM, factors and factorials; roots and powers have different real-number domains.
Check the stated input format, calculation convention and limits before using the result.
Common questions
What else to know about Everyday mathematics
These answers explain how to use the estimates and where their limits begin.
How do I choose a tool?
Use percentage change for a before-and-after comparison and ratios for proportional quantities. Use fractions for exact rational arithmetic; inspect the median when an average is affected by outliers. Use integer tools for GCD, LCM, factors and factorials; roots and powers have different real-number domains.
Are displayed decimals always exact?
Integer and fraction outputs can preserve an exact value within the supported bounds; irrational roots and floating-point decimals may be rounded. Review the selected domain and rounding rule before comparing results.