Math Calculators

Absolute Value Calculator

Find the absolute value of any positive or negative number, returning its distance from zero on the number line regardless of the original input sign.

Algebra Calculator

Solve linear equations, find both roots of a quadratic equation, or simplify an algebraic expression step by step with the full working shown each time.

Angle Between Lines Calculator

Find the angle where two lines cross, computed from their slopes or from two direction vectors, with perpendicular pairs flagged at exactly 90 degrees.

Angle Between Vectors Calculator

Find the angle between two 2D or 3D vectors using the dot product and vector magnitudes, with a full step-by-step calculation shown for each part.

Basic Calculator

Add, subtract, multiply, and divide with a calculator that rounds results to six decimal places and blocks division by zero before it produces an error.

Ceiling Calculator

Round any number up to the nearest whole integer using the ceiling function, including correct handling of negative inputs and already-whole number values.

Circle Area Calculator

Calculate a circle's area from its radius using Area = pi r squared, with a reference table listing computed areas for common radius values from 1 to 10.

Circle Circumference Calculator

Calculate the distance around a circle from its radius using Circumference = 2 pi r, with a reference table of results for common radius values from 1 to 10.

Combination Calculator

Calculate the number of unordered groups possible when selecting r items from a set of n, using the factorial-based nCr combination formula shown directly.

Cone Volume Calculator

Calculate a cone's volume from its radius and height using Volume = pi r squared h / 3, exactly one-third the volume of the matching cylinder shape.

Cosecant Calculator

Calculate the cosecant of any angle as the reciprocal of sine, entered in degrees or radians, with undefined cases at sine-zero flagged clearly each time.

Cosine Calculator

Calculate the cosine of any angle entered in degrees or radians, with results rounded to six decimal places for accuracy across trigonometry problems solved.

Cosine Rule Calculator

Find the third side of any triangle from two sides and the angle between them using the law of cosines, the general form of the Pythagorean theorem.

Cotangent Calculator

Calculate the cotangent of any angle as the reciprocal of tangent, entered in degrees or radians, with undefined cases at sine-zero flagged clearly each time.

Cramer's Rule Calculator

Solve a 2x2 or 3x3 system of linear equations using Cramer's rule, replacing each coefficient column with the constants and dividing the determinants.

Cube Root Calculator

Calculate the cube root of any positive or negative number, with real results returned correctly even for negative inputs, unlike a plain square root.

Cylinder Volume Calculator

Calculate a cylinder's volume from its radius and height using Volume = pi r squared h, with a full step-by-step worked example showing each calculation.

Decimal to Fraction Converter

Convert any decimal number into a fraction reduced to lowest terms, with an adjustable maximum denominator for repeating or irrational decimal inputs.

Distance Between Points Calculator

Calculate the straight-line distance between two coordinate points using the Pythagorean theorem, with 2D and 3D support and a step-by-step breakdown.

Distance Calculator

Find the distance between two points using 2D or 3D coordinates, or calculate great-circle distance between two latitude and longitude coordinate pairs.

Euclidean Distance Calculator

Calculate the straight-line Euclidean distance between two 2D points using the Pythagorean relationship applied directly to their given x and y coordinates.

Exponent Calculator

Raise any base to any exponent, including negative and fractional powers, with built-in checks for negative-base and division-by-zero edge cases handled.

Factorial Calculator

Calculate the factorial of any whole number from 0 to 170, returned with thousands separators for easy reading of results that grow into the millions quickly.

Floor Calculator

Round any number down to the nearest whole integer using the floor function, including correct handling of negative inputs and already-whole number values.

Fraction Calculator

Add, subtract, multiply, or divide two fractions and get the result automatically reduced to lowest terms using the greatest common divisor each time.

Fraction to Decimal Converter

Convert a fraction into its decimal equivalent, calculated to six decimal places for a numerator and denominator of virtually any size or sign combination.

Gaussian Elimination Calculator

Solve a 2x2 or 3x3 linear system using Gaussian elimination with partial pivoting, showing every row-reduction and back-substitution step along the way.

Geometry Calculator

Get area, perimeter, volume, or surface area for rectangles, circles, triangles, cubes, spheres, cylinders, cones, trapezoids, ellipses, and polygons instantly.

Graphing Calculator

Evaluate linear, quadratic, cubic, exponential, sine, or logarithmic functions at any x value from their coefficients, with the formula shown for each type.

Hypotenuse Calculator

Find the length of a right triangle hypotenuse directly from its two legs using c equals the square root of a squared plus b squared, shown step by step.

Intersection of Lines Calculator

Find the exact coordinates where two lines cross, entered as slope-intercept equations or as two points each, with parallel and identical cases flagged.

Inverse Logarithm Calculator

Calculate a natural, common, or custom base antilogarithm by raising e, 10, or any chosen base to the power you specify, reversing a logarithm calculation.

Lateral Area Calculator

Calculate the curved side area of a right cylinder or right circular cone, excluding the top and bottom caps, from the shape's radius and height.

Line Equation Calculator

Find a line's equation from two points or from a slope and one point, returned in y = mx + b form with the slope and intercept worked out step by step.

Logarithm Calculator

Calculate a natural log, common base-10 log, or custom base logarithm of any positive number using the change of base formula for any custom base inputs.

Manhattan Distance Calculator

Calculate the Manhattan distance between two points by summing the absolute horizontal and vertical differences, as used in grid-based robot navigation.

Matrix Addition Calculator

Add two 2x2 or 3x3 matrices of matching size by summing each pair of corresponding entries, with a full worked numeric example shown for every cell.

Matrix Determinant Calculator

Calculate the determinant of a 2x2 or 3x3 matrix using cofactor expansion, a value that reveals whether the matrix can be inverted or is singular.

Matrix Inverse Calculator

Find the inverse of a 2x2 or 3x3 matrix using the adjugate and determinant, flagging singular matrices with a zero determinant that have no inverse.

Matrix Multiplication Calculator

Multiply two 2x2 or 3x3 matrices using the row-times-column dot product rule, showing each resulting entry's calculation worked out step by step.

Matrix Subtraction Calculator

Subtract one 2x2 or 3x3 matrix from another of matching size by finding the difference of each corresponding entry, with a full worked numeric example.

Midpoint Calculator

Find the exact midpoint between two coordinate points by averaging their x and y values separately, useful for geometry, layout, and design work directly.

Modulo Calculator

Find the remainder of a division operation using floor-based modulo, where the sign of the result follows the divisor rather than the dividend value used.

Nth Root Calculator

Calculate the nth root of any number for any root degree, with real solutions returned for negative numbers whenever the chosen root degree is an odd number.

Parallel Line Calculator

Build the equation of a line parallel to a given line through a new point, keeping the original slope unchanged and solving only for the new y-intercept value.

Percentage Calculator

Find a percentage of a number, compare two values, calculate percentage increase or decrease, or work out a restaurant tip or discount across six modes.

Percentage Change Calculator

Calculate the percentage increase or decrease between an old and a new value, with the direction of change labeled automatically in the final calculated result.

Percentage Difference Calculator

Calculate the symmetric percentage difference between two values using their average as the base, unlike a directional before-and-after percentage change.

Permutation Calculator

Calculate the number of ordered arrangements possible when selecting r items from a set of n, using the factorial-based nPr permutation formula directly.

Perpendicular Line Calculator

Find the equation of a line perpendicular to a given line through a chosen point, using the negative reciprocal of the original line's slope value.

Polar to Cartesian Converter

Convert between polar coordinates (radius and angle) and Cartesian coordinates (x, y) in both directions, in degrees or radians, with worked examples.

Prism Volume Calculator

Calculate any prism's volume from its base cross-sectional area and height, the general formula that underlies triangular, rectangular, and other prisms.

Pyramid Volume Calculator

Calculate a square-base pyramid's volume from its base side length and height, using base area times height divided by three, with a worked example.

Pythagorean Theorem Calculator

Find a right triangle hypotenuse from its two legs, or solve for a missing leg from the hypotenuse and one known leg, using the Pythagorean theorem formula.

Quadratic Equation Calculator

Solve ax squared plus bx plus c equals zero for real or complex roots using the quadratic formula, with the discriminant shown clearly for every case handled.

Ratio Calculator

Simplify a ratio to its lowest terms using the greatest common divisor, or solve for a missing value in an A to B equals C to D proportion equation directly.

Reactor Volume Calculator

Size a continuous stirred-tank reactor (CSTR) from flow rate, target conversion, and rate constant using the first-order CSTR design equation directly.

Scientific Calculator

Compute square roots, cubes, sine, cosine, tangent, log base 10, natural log, exponentials, absolute value, and factorials from a single numeric input.

Secant Calculator

Calculate the secant of any angle as the reciprocal of cosine, entered in degrees or radians, with undefined cases at cosine-zero flagged clearly each time.

Sine Calculator

Calculate the sine of any angle entered in degrees or radians, with results rounded to six decimal places for accuracy across trigonometry problems solved.

Sine Rule Calculator

Solve for a missing triangle side using the law of sines, given one side and two angles, with the third angle computed from the 180-degree angle sum.

Slope Calculator

Calculate the slope of a line through two given points, with vertical lines correctly flagged as having a mathematically undefined slope value each time.

Sphere Volume Calculator

Calculate a sphere's volume from its radius using Volume = 4/3 pi r cubed, with a reference table showing exactly how volume scales as radius increases.

Square Root Calculator

Calculate the square root of any positive or negative number, with imaginary results returned automatically for negative inputs instead of a plain error.

Surface Area Calculator

Calculate the total surface area of a rectangular prism (cuboid) from its length, width, and height, summing all six rectangular faces of the shape.

Tangent Calculator

Calculate the tangent of any angle entered in degrees or radians, with an explicit error returned where the value is mathematically undefined at 90 degrees.

Triangle Area Calculator

Calculate triangle area from base and height, from three side lengths using Heron's formula, or from three vertex coordinates using the shoelace formula.

Triangle Solver

Solve for all three interior angles of a triangle from its three side lengths using the law of cosines, with a triangle-inequality validity check applied.

Trigonometric Equation Solver

Solve sin(x), cos(x), or tan(x) equals a given value for every angle solution between 0 and 360 degrees, returned together as a complete solution set.

Unit Circle Calculator

Find the cosine, sine, and tangent of any angle using the unit circle, with a reference table for standard angles like 30, 45, 60, and 90 degrees.

Vector Addition Calculator

Add two 2D or 3D vectors component by component to find the resultant vector, with a step-by-step breakdown of each component's calculation shown.

Vector Cross Product Calculator

Calculate the cross product of two 3D vectors to find the perpendicular vector they define, with the standard basis-vector example included for reference.

Vector Dot Product Calculator

Calculate the dot product of two 2D or 3D vectors, a scalar value that reveals how closely aligned the two vectors are, with a worked example shown.

Vector Magnitude Calculator

Calculate a vector's length (magnitude) from its 2D or 3D components using the Pythagorean-based formula, with fully worked numeric examples included.

Volume of Cube Calculator

Calculate a cube's volume from its side length using Volume = Side cubed, with a reference table showing how fast volume grows as side length increases.

Volume of Ellipsoid Calculator

Calculate an ellipsoid's volume from its three semi-axis lengths using Volume = 4/3 pi abc, which reduces exactly to a sphere when all three axes match.

Volume of Hemisphere Calculator

Calculate a hemisphere's volume from its radius using Volume = 2/3 pi r cubed, exactly half of the corresponding full sphere's total volume, with examples.

Volume of Rectangular Prism Calculator

Calculate the volume of a rectangular box from its length, width, and height by multiplying the three dimensions together, with a worked numeric example.

Volume of Torus Calculator

Calculate a torus (donut shape) volume from its major and minor radii using Volume = 2 pi squared R r squared, with a full worked example shown.

Volume of Triangular Prism Calculator

Calculate a triangular prism's volume from its triangular base dimensions and prism length, computing the triangle's area first and then extending it.

Weighted Average Calculator

Calculate a weighted average across up to five value and weight pairs, where larger weights pull the final calculated result more heavily toward themselves.

X-Intercept Calculator

Find where a line through two given points crosses the x-axis, with horizontal and vertical line special cases handled explicitly and clearly each time.

Y-Intercept Calculator

Find where a line through two given points crosses the y-axis, derived directly from the calculated line slope and one of the two known input coordinates.

The Formulas Behind Every Level of Math Class

Math calculations span an enormous range of difficulty within a single subject label — from basic arithmetic and fractions through algebra, geometry, trigonometry, and matrix operations. Over eighty calculators here cover that full range, built to check homework, solve a real-world measurement problem, or work through a formula that's easy to forget between semesters.

Popular Math Calculators

Highlights across algebra, geometry, and trigonometry:

  • Algebra Calculator — solves equations and simplifies expressions step by step.
  • Geometry Calculator — finds area, perimeter, and volume across common 2D and 3D shapes.
  • Matrix Determinant Calculator — calculates the determinant of a matrix, foundational for solving systems of equations.
  • Fraction Calculator — performs arithmetic on fractions and simplifies results automatically.
  • Distance Between Points Calculator — applies the distance formula to find the straight-line distance between two coordinates.

Why Geometry Formulas Share a Common Structure

Most 3D volume formulas are built from a simpler pattern — base area multiplied by height, adjusted by a shape-specific factor — which is why a cylinder's volume (πr²h) and a cone's volume (one-third of that same base times height) are closely related rather than unrelated formulas to memorize separately; the cone is mathematically exactly one-third the volume of a cylinder sharing the same base and height. Recognizing these relationships between shapes, rather than treating each formula as an isolated fact, is often what separates genuinely understanding geometry from just memorizing a formula sheet.

Frequently Asked Questions

Why does a matrix need a nonzero determinant to be invertible?
A zero determinant means the matrix's rows or columns are linearly dependent, collapsing the transformation into a lower dimension in a way that can't be reversed, which is exactly what makes the matrix non-invertible.

Is a scientific calculator different from a basic calculator for these purposes?
Yes — scientific calculators add trigonometric, logarithmic, and exponential functions beyond the four basic operations, which are needed for anything beyond simple arithmetic.

Explore More

Need statistics rather than pure math? See the Statistics Calculators, or check applied physics formulas in the Physics Calculators.