Math Calculators with Steps

Arithmetic and Geometric Sequence Calculator Find the nth term and the sum of an arithmetic or geometric sequence, the infinite sum for |r| < 1, or d and r from two terms, with steps.

Bayes' Theorem Calculator Find the chance that a condition is present after a positive result, from how common the condition is and two test rates. Steps shown.

Binomial Probability Calculator Work out the probability of exactly, at most or at least k successes in n trials, with the mean, the variance, a table and a chart of the distribution.

Chi-Square Test Calculator Run a chi-square test of independence on a table of counts, or a goodness-of-fit test against expected shares, with expected counts, χ², df and a p-value.

Combinations and Permutations Calculator Count combinations and permutations of n objects taken k at a time, with and without repetition: exact results, the formula and working, and Pascal's row.

Complex Number Calculator Add, subtract, multiply and divide complex numbers, find powers and n-th roots, modulus and argument, and convert rectangular, polar and exponential forms.

Confidence Interval Calculator Calculate a confidence interval for a mean (z or t) or a proportion (Wald or Wilson) at any confidence level, with each step of the working.

Correlation Calculator Find the Pearson correlation r and the Spearman rank correlation ρ of x, y pairs, with the t test of significance, its p-value and each step.

Definite Integral Calculator with Error Estimate Find the area under a function between two limits with Simpson's rule. Get the value, an error estimate and the steps of the working.

Derivative Calculator with Steps Differentiate a polynomial, sine, cosine, exponential, logarithm or square root. See each rule used, the derivative, and its value at a point.

Expected Value Calculator Enter each outcome with its chance in percent. Get the expected value, a check that the chances add up to 100%, and the contributions.

Fraction Calculator Add, subtract, multiply or divide fractions, mixed numbers and decimals. Each step is shown: common denominator, operation and simplifying with the GCD.

GCD and LCM Calculator Find the greatest common divisor (GCD) and least common multiple (LCM) of two or more whole numbers, with Euclid's algorithm and the prime factors shown.

Linear Equation System Solver Solve two to six linear equations by Gaussian elimination, with exact fractions, every step shown, and Cramer's rule for two or three equations.

Linear Interpolation Calculator Find y between two known points, or along a table of x and y values, with the slope and each step. Values outside the table are flagged.

Linear Regression Calculator Find the least-squares line through your x and y pairs, with the slope, intercept, correlation, R², standard errors, residuals, a chart and every step.

Long Division Calculator Divide one decimal number by another with long division. See each step, the quotient, the remainder and repeating decimals, in the Turkish or the US layout.

Matrix Calculator Add, subtract, multiply and transpose matrices, and find the determinant, inverse, rank and reduced row echelon form, with every step shown.

Modular Arithmetic Calculator Find a mod n for negative numbers, the modular inverse by extended Euclid, a^e mod n by square-and-multiply, and the Chinese remainder theorem, with steps.

Multiplication Table Generator Print multiplication tables from 1 to 20, or make a practice sheet of random questions with an answer key. Each table is shown with its working.

Poisson Probability Calculator Find the Poisson probability of exactly, at most or at least k events for an average rate λ, with the mean, the variance, a table and a chart.

Polynomial Root Calculator Find real and complex roots of a polynomial up to degree 6, with rational root test, synthetic division, exact roots where possible and a residual check.

Prime Factorization Calculator Find the prime factors of a whole number up to 10¹⁵, with the factor tree, the number of divisors, the sum of divisors and a primality test.

Quadratic Equation Solver Solve ax² + bx + c = 0 with the quadratic formula. Get the discriminant, real or complex roots, exact roots such as 2√3, the vertex and a graph.

Quartile and Box Plot Calculator Find Q1, the median, Q3, the interquartile range and the outliers of a data set by Tukey's hinges or linear interpolation, with a box plot in text.

Roman Numeral Converter Convert numbers from 1 to 3999 into Roman numerals and back, check whether a Roman numeral is in standard form, or write a date in Roman numerals.

Sample Size Calculator Find the sample size for a survey proportion at 90, 95 or 99% confidence, with the finite population correction, or the margin of error of a given sample.

Significant Figures Calculator Count the significant figures of a number, round it to n figures, and add, subtract, multiply or divide two numbers with the precision rules shown.

Statistics Calculator Enter a list of numbers and get the mean, median, mode, range, quartiles, variance, standard deviation and outliers, with each step of the working.

t-Test Calculator Run a one-sample, Welch, pooled or paired t-test on raw data or summary statistics, and get t, the degrees of freedom, the p-values and the conclusion.

Triangle Solver Solve a triangle from any three sides and angles (SSS, SAS, ASA, AAS, SSA). Get the other sides and angles, the area by Heron, heights and type.

Truth Table Generator Type a logic formula with not, and, or, if-then and if-and-only-if, and get every row of its truth table, with whether it is a tautology or a contradiction.

Vector Calculator Add vectors, find the dot and cross product, length, unit vector, angle, projection and triple product in 2D or 3D, with every step shown.

Weighted Average Calculator Work out a weighted average: each value times its weight, summed and divided by the total weight. Use it for course grades by credits or prices by quantity.

Z-Score Calculator Find the z-score of a value, the share of a normal distribution below, above or between two values, or the value at a percentile.

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