Math

Finds the eigenvalues and real eigenvectors of a 2 x 2 or 3 x 3 matrix by solving the characteristic polynomial exactly, complex pairs included.

Gives the domain and range of seven named function families in interval notation, with the asymptote, vertex or endpoint that produces the answer.

Solves first order linear, logistic and second order homogeneous differential equations exactly from numeric coefficients and initial conditions.

Volume of a sphere, a cone or a rectangular pyramid from its radius or base and height, converted to cubic feet, cubic metres, litres and gallons.

Solves a triangle from three known parts with the sine and cosine rules, returning the missing sides and angles, area, perimeter, circumradius and inradius.

Gauss-Jordan reduction to reduced row echelon form with partial pivoting, for matrices from 2x2 to 6x8, reporting the rank and the pivot columns.

Simplify a ratio to its lowest terms, solve A : B = C : ? for the missing value, or split an amount into shares using any ratio.

Divides one polynomial by another the long way and shows every subtraction, with the quotient, the remainder and a check that rebuilds the dividend.

Evaluates limits of rational functions exactly: at a point by dividing out (x - a), and at infinity by comparing degrees and leading coefficients.

Factors a whole number into every divisor and its prime powers, or factors a one-variable polynomial up to degree 4 into linear factors.

Cylinder volume from diameter and height, plus the contents of a part-full tank standing upright or lying on its side, in litres and gallons.

Runs a Pearson chi-square test, either goodness of fit against expected counts or a contingency table, and reports the statistic, degrees of freedom and p value.

Binomial probabilities for n trials at probability p: exactly k, at most k, at least k or a range between two counts, with the mean, variance and coefficient.

Area of a rectangle, triangle, circle, trapezoid, parallelogram, ellipse or regular polygon, in the unit you enter and converted to square meters and feet.

Turns a raw value, mean and standard deviation into a z-score, or a z-score into its percentile, normal-curve area and two-tailed p-value.

Reduces a square root, cube root or higher root of a whole number to simplest radical form and shows the factor pulled out plus the decimal value.

Combines like terms and expands brackets in a single-variable algebraic expression, and reduces a fraction to its lowest terms.

Solves a right triangle from two legs, a leg and the hypotenuse, or a leg and an acute angle, returning every side, both angles, area and perimeter.

Find the chance of a single event, combine two independent events with and, or and neither, or work out the odds across repeated tries.

Splits a proper rational function into partial fractions for two or three distinct linear factors, or a repeated linear factor beside a distinct one.

Multiplies two square matrices of the same size, 2x2 or 3x3, and shows the row-by-column sum behind every entry of the product so the working is visible.

Adds, subtracts and multiplies 2x2 and 3x3 matrices and finds the determinant, with rows typed as plain numbers separated by commas and semicolons.

Works out the logarithm of a number in any base, with the natural, common and binary logs alongside it, plus an antilog mode that inverts the result.

Fit a least squares line to paired x and y data, then read off the slope, intercept, correlation and predicted values.

Inverts a 2x2 or 3x3 matrix by cofactors, showing the determinant and every entry of the inverse, and refuses a singular matrix.

Draws the curve of a polynomial up to x^4, or a sine or cosine wave, over the x range you choose, with the axis crossings marked.

Solves a single-variable linear or quadratic equation typed in as text, returning the standard form, the discriminant and the roots, complex ones included.

Finds the Pearson correlation coefficient for two lists of paired values, with r squared, the sample covariance and the least-squares regression line.

Work out the circumference of a circle from its radius or diameter, or go backwards from a known circumference to the radius, diameter and area.

Solves one equation in one variable when it reduces to linear or quadratic form, showing the standard form, the solution and a substitution check.

Solve two equations in x and y, or three in x, y and z, by elimination. Enter each coefficient and get the solution and the determinant.

Round a number to a set count of decimal places or to the nearest tenth, ten, hundred or thousand, with half up, down and up shown side by side.

Solve any quadratic equation by entering a, b and c. Returns both roots, real or complex, with the discriminant, the vertex and the axis of symmetry.

Divide two whole numbers and see every step: what the divisor goes into, what you subtract and the remainder carried to the next digit.

Differentiate a polynomial in x with the power rule, and get the second derivative, the slope at any point and the tangent line there.

Generate Fibonacci sequences with our free calculator. Find specific terms, view step-by-step calculations, and explore the mathematical properties of this fascinating sequence.

Calculate Golden Ratio proportions with our free online calculator. Find the perfect balance for design, art, architecture, and mathematics with the divine proportion (? = 1.618).

Calculate earthquake energy and impact with our Richter Scale Calculator. Convert magnitude to energy release, compare with historical earthquakes, and understand potential effects.

Instantly check if a number is prime, find its factors, and discover the nearest prime numbers with our comprehensive Prime Number Checker.

Multiply any number by pi (?) instantly. Essential for geometry, physics, and engineering calculations. Quick and accurate results.

Calculate pi (?) to any decimal place. Perfect for mathematics, engineering, and scientific calculations. Fast and precise results.

Calculate precise values of e raised to any power. Essential for mathematics, science, and engineering applications. Fast and accurate.

Calculate bandwidth and rise time relationships in electronic systems. Essential for signal analysis and circuit design. Fast, accurate results.

Easily convert fractions into precise decimal values using our online, fast and free Fraction to Decimal Calculator.

Quickly calculate confidence intervals for any dataset with our fast & accurate Confidence Interval Calculator.

Compute the cross product of two 3D vectors, including step-by-step results and detailed vector component calculations.

Quickly calculate standard deviation, variance, mean, and more for both population and sample datasets with our calculator.

Quickly solve exponential expressions and simplify complex calculations with our easy-to-use exponent calculator.