Math Calculators

Math calculators that show their work: arithmetic, algebra, statistics, and a calculus calculator for derivatives and integrals, with exact answers in fractions and radicals where they exist.

Arithmetic and numbers

• Percentage CalculatorA percentage calculator for all seven percentage questions, from X% of Y to percentage change and difference, each with the work shown.
• Percent to Decimal ConverterThe percent to decimal calculator divides by 100 and gives the fraction in lowest terms beside it: 12.5% is 0.125, which is 1/8.
• Fraction CalculatorThe fraction calculator gives exact answers in lowest terms, with the common denominator written out. 1/3 + 1/6 is 1/2 here, not 0.49999999999999994.
• Decimal to Fraction CalculatorExact fractions, repeating decimals included: the decimal to fraction calculator turns 0.41(6) into exactly 5/12, not a rounding of it.
• Average CalculatorThe average calculator gives the mean, median, mode, range, count and sum of a list, plus weighted averages, averages of percentages, and the score you need on the tests left.
• Rounding Calculator2.675 to two places is 2.68. Most software says 2.67. This rounding calculator works on the number you typed, not its binary approximation, and shows the digit that decides it.
• Significant Figures CalculatorThe significant figures calculator marks every digit significant or not, with the rule that decides it. That includes the zeros in 1500, which nobody can count without more information.
• Scientific Notation CalculatorConvert both ways with this scientific notation calculator, engineering form and SI prefix included. 4.7e4 and 47 kilo are the same statement.
• Square Root CalculatorThe square root calculator gives the simplest radical form as well as the decimal: the square root of 72 is 6 times the root of 2, or 8.485281374.
• Exponent CalculatorA power is repeated multiplication until the exponent stops being a whole number. Then it is a root. The exponent calculator explains which case you are in.
• Log CalculatorA logarithm answers one question, what power turns the base into this number, and a log calculator answers it in any base.
• Absolute Value CalculatorThe absolute value calculator isolates the bars, splits the problem into its two cases, and solves each one exactly. It also gives the absolute value of a single number.
• Factorial CalculatorEnter n and the factorial calculator multiplies every whole number from n down to 1, exactly, then counts the digits and the zeros at the end.
• GCF and LCM CalculatorThe GCF and LCM calculator finds both at once, with the prime factorization that produces them. The GCF takes the lowest power of each shared prime and the LCM takes the highest.
• Prime Factorization CalculatorEnter a number and the prime factorization calculator returns its prime factors, the division steps that found them, and the divisor count that falls out of the exponents.
• Long Division CalculatorThe long division calculator writes every step out the way it goes on the page: bring down, divide, multiply, subtract, repeat.
• Long Multiplication CalculatorLong multiplication by the column method: one row per digit of the bottom number, the carries written out, and the partial products added at the end.
• Order of Operations CalculatorType an expression into the order of operations calculator and see it reduced one operation at a time: parentheses, exponents, multiplication and division, then addition and subtraction. The expression is rewritten after every step.
• Expanded Form CalculatorThe expanded form calculator writes a number as the sum of what each digit is worth, and lists each digit's place value beside it.
• Multiplication ChartEvery product from 1 x 1 to 12 x 12 in one multiplication chart, with the row, the mirror fact, the neighbors and the pattern behind any fact.
• Ratio CalculatorThe ratio calculator simplifies a ratio to lowest terms, solves a proportion for the missing term, scales a ratio, and splits a total in a given ratio.
• Aspect Ratio CalculatorEnter a width and a height and the aspect ratio calculator reduces them to lowest terms, or give it one new side and it finds the other at the same shape.

Algebra and calculus

• Algebra CalculatorSolve for x or simplify an expression in an algebra calculator that writes the steps out and the answer as an exact fraction, not a decimal that nearly works.
• Quadratic Formula CalculatorThe quadratic formula calculator gives both roots as decimals and in exact form (fractions or surds), plus the discriminant, the vertex and the factored form.
• System of Equations CalculatorTwo or three equations at once: the system of equations calculator returns exact fractions, and a straight answer when the lines are parallel instead of a misleading number.
• Factor CalculatorThe factor calculator lists every factor of a number in the pairs that multiply to it, with the prime factorization, the divisor count, and whether it is prime, perfect or abundant.
• Matrix CalculatorType a matrix, pick an operation, and the matrix calculator answers in exact fractions with the work shown. Where the answer is 1/3, it says 1/3, not 0.333333.
• Vector CalculatorGive the vector calculator two vectors and it returns the dot product, the cross product's determinant expansion, the angle and the projection, exact where the components are whole numbers.
• Derivative CalculatorA derivative calculator that differentiates symbolically, names every rule it uses, and gives the slope and tangent line at any point.
• Integral CalculatorAn integral calculator with steps: antiderivatives worked by rule, every step named and checked by differentiation, and definite integrals between any two bounds.
• Arithmetic Sequence CalculatorGive the arithmetic sequence calculator a first term and a common difference, or any two terms, and it finds the nth term, the sum, and both formulas, exactly.
• Pascal's TrianglePascal's triangle to any row, with an entry C(n, k) worked out, the row's sum, and the binomial expansion of (a + b)^n. Each number is the sum of the two above it.

Statistics and probability

• Standard Deviation CalculatorSample and population side by side in one standard deviation calculator, because dividing by n when you meant n-1 understates the spread and nobody notices.
• Probability CalculatorTwo events, binomial trials, or combinations in one probability calculator, with the overlap that stops P(A or B) being a simple sum.
• Combination CalculatorEnter n and r and the combination calculator counts the ways to choose, with the formula worked through. It also gives the permutation count and both counts with repetition, so you can see which one your question needs.
• Dice Probability CalculatorPick the dice and a target total, and this dice probability calculator gives the exact chance of rolling exactly, at least or at most that total, with every total's odds in a table.
• Expected Value CalculatorType each outcome with its probability and this expected value calculator gives the EV, variance and standard deviation, after checking that the probabilities add up to 1. Switch to betting for the EV of a bet at posted odds.
• Z Score CalculatorEnter a value, the mean and the standard deviation, and this z score calculator gives the z score, its percentile and the area on each side, then points to its row and column in the z-table.
• Normal Distribution CalculatorGive a mean and standard deviation, pick a range, and this normal distribution calculator returns its probability and shades it on the bell curve. Switch to inverse to get the value at any probability.
• Confidence Interval CalculatorEnter a sample mean, SD and size, or a count of successes, and this confidence interval calculator returns the interval and its margin of error at any confidence level, with t when the SD comes from the sample and Wilson for a proportion.
• Sample Size CalculatorSet a margin of error and a confidence level, and this sample size calculator says how many responses a survey needs, corrected for a small population. For an experiment, it sizes each group from the power and alpha.
• Percentile CalculatorPaste a list and the percentile calculator finds the value at any percentile and the percentile rank of any value, with quartiles, IQR and outliers. Three methods are shown side by side, because they disagree on small lists.
• Correlation Coefficient CalculatorEnter paired x and y values and the correlation coefficient calculator returns Pearson's r, r-squared and Spearman's rho, with a p-value and a 95% interval to show how sure the number is.
• Linear Regression CalculatorThe line through your data, and the numbers that say how much to trust it. The linear regression calculator adds a residuals table, because the summary statistics alone can hide a curve or an outlier.
• Chi Square CalculatorType a table of counts and the chi square calculator tests whether rows and columns are independent, or test observed counts against expected ones. Every cell's expected count and contribution is shown.
• T Test CalculatorPaste your data or enter the means, SDs and sample sizes. The t test calculator gives the t statistic, the degrees of freedom, the p-value for every tail, a confidence interval and the decision.
• P Value CalculatorEnter the test statistic, pick its distribution and give the degrees of freedom. The p value calculator returns the two-tailed, right-tailed and left-tailed p-values and the critical value at your alpha.
• Test Statistic CalculatorThe test statistic calculator gives the statistic, its p-value both ways, the critical value and the interval. It also says what a p-value does not tell you, which is most of what people read into it.
• Box Plot GeneratorPaste the numbers and the box plot generator draws the plot and the figures behind it. It also says which quartile method it used, because four common ones give four different boxes on small data.
• Poisson Distribution CalculatorEnter the average rate λ and a count k, and this Poisson distribution calculator gives the chance of exactly, at least, at most or between k events, with the formula worked through.
• Hypergeometric CalculatorThis hypergeometric calculator gives the chance of exactly, at least or at most k successes when you draw without putting anything back, such as the 34.12% chance of at least one ace in a 5-card hand.
• Gini Coefficient CalculatorOne number for how unevenly something is shared out: the Gini coefficient calculator shows the work, and the shares behind it, because two very different distributions can have the same Gini.
• Monty Hall ProblemIn the Monty Hall problem you pick one of three doors, the host opens another to show a goat, and switching wins 2 times in 3. Play up to a million games and watch the count land on the exact odds.

Grades

• GPA CalculatorThe GPA calculator gives your term and cumulative GPA, unweighted or weighted for honors and AP courses, and the term GPA you need next to hit a target.
• Grading CalculatorThe grading calculator turns the questions on a test and the number wrong into a percent and a letter grade, with an easy grader chart for every possible score.

More categories

• Geometry CalculatorsGeometry calculators for shapes, lines and angles, with the formula behind each answer explained.
• Chemistry Calculators, Physics and Lab ToolsChemistry calculators, physics calculators and molecular biology tools for the bench and the problem set.
• Conversion CalculatorsConversion calculators for unit conversion, number bases, Roman numerals and angles. The unit converter shows the factor it used and a conversion chart for the values around yours.
• Date and Time CalculatorsDate and time calculators for counting days, adding hours, converting time zones and reading other calendars.
• Business CalculatorsBusiness calculators for pricing a product and for the unit economics behind a company: margin, markup, break-even, ROI, CAC, LTV and churn.
• Random GeneratorsRandom generators that draw fairly, from your browser's cryptographic generator: numbers, names, teams, coin flips and dice.
• Everyday Cost CalculatorsCost calculators for what a meal, a drive or an appliance actually costs: tips, split bills, fuel, electricity and EV charging.
• Free Online ToolsFree online tools for codes and text, run in your browser with nothing uploaded.