# Algebra, geometry & advanced math calculators

> Calculators for quadratic equations, triangles, circles, areas and volumes, logarithms, matrices, number bases and other advanced maths.

Page: https://calculators.geekmidst.com/categories/advanced-math

- [Polynomial Roots Calculator](https://calculators.geekmidst.com/calculators/polynomial-roots-calculator.md): Find every real and complex root of a polynomial up to degree 20, with exact multiplicities for repeated roots and a residual check.
- [Cubic Equation Calculator](https://calculators.geekmidst.com/calculators/cubic-equation-roots-calculator.md): Solve any cubic equation with the trigonometric method or Cardano’s formula, with the discriminant, depressed cubic and real or complex roots.
- [Quartic Equation Calculator](https://calculators.geekmidst.com/calculators/quartic-equation-roots-calculator.md): Solve a fourth-degree equation with Ferrari’s method: the depressed quartic, its resolvent cubic and all four real or complex roots.
- [Polynomial Long Division Calculator](https://calculators.geekmidst.com/calculators/polynomial-long-division-calculator.md): Divide one polynomial by another and get the exact quotient and remainder, with each long-division step and fractional coefficients kept exact.
- [Synthetic Division Calculator](https://calculators.geekmidst.com/calculators/polynomial-synthetic-division-calculator.md): Divide a polynomial by x − r using synthetic division: the full tableau, the quotient, the remainder and P(r) by the remainder theorem.
- [Complex Number Addition Calculator](https://calculators.geekmidst.com/calculators/complex-number-addition-calculator.md): Add or subtract two complex numbers a + bi and c + di, with the result in rectangular form, its modulus and its argument in degrees.
- [Complex Number Multiplication Calculator](https://calculators.geekmidst.com/calculators/complex-number-multiplication-calculator.md): Multiply or divide two complex numbers, with the result in rectangular form, its modulus and argument, and a check in polar form.
- [Complex Number Polar Form Converter](https://calculators.geekmidst.com/calculators/complex-number-polar-conversion-calculator.md): Convert a complex number between rectangular form a + bi, polar form r∠θ and exponential form re^(iθ), with the angle in degrees or radians.
- [Complex Number Modulus Calculator](https://calculators.geekmidst.com/calculators/complex-number-modulus-calculator.md): Find the modulus (absolute value) of a complex number as an exact simplified surd and a decimal, plus its conjugate, unit vector and argument.
- [Matrix Eigenvalues Calculator](https://calculators.geekmidst.com/calculators/matrix-eigenvalues-calculator.md): Find all eigenvalues of a square matrix up to 10 × 10, real and complex, with the exact characteristic polynomial and exact multiplicities.
- [Gaussian Elimination Calculator](https://calculators.geekmidst.com/calculators/linear-system-gaussian-elimination-calculator.md): Solve a system of linear equations by Gaussian elimination with partial pivoting, showing every row operation, with exact fractional answers.
- [Cramer’s Rule Calculator](https://calculators.geekmidst.com/calculators/linear-system-cramer-rule-calculator.md): Solve a square system of linear equations with Cramer’s rule: det(A), each replaced-column determinant and the exact solution, up to 6 unknowns.
- [Vector Dot Product Calculator](https://calculators.geekmidst.com/calculators/vector-dot-product-calculator.md): Find the dot product of two vectors of any dimension, their magnitudes, the angle between them, and whether they are orthogonal or parallel.
- [Vector Cross Product Calculator](https://calculators.geekmidst.com/calculators/vector-cross-product-calculator.md): Find the cross product of two 3D vectors, its magnitude, the parallelogram and triangle areas they span, and the unit normal vector.
- [Vector Projection Calculator](https://calculators.geekmidst.com/calculators/vector-projection-calculator.md): Project one vector onto another: the vector projection, the scalar projection (component), and the perpendicular rejection, in any dimension.
- [Vector Angle Calculator](https://calculators.geekmidst.com/calculators/vector-angle-calculator.md): Find the angle between two vectors in degrees and radians from their dot product and magnitudes, and see whether they are perpendicular or parallel.
- [Vector Magnitude Calculator](https://calculators.geekmidst.com/calculators/vector-magnitude-calculator.md): Work out the magnitude (Euclidean length) of a vector from its components, plus its squared length, taxicab (L1) norm and maximum norm.
- [Unit Vector Calculator](https://calculators.geekmidst.com/calculators/unit-vector-calculator.md): Normalise a vector by dividing each component by its magnitude to get the unit vector in the same direction, with the 2D direction angle.
- [Line Intersection Calculator](https://calculators.geekmidst.com/calculators/line-intersection-calculator.md): Find the point where two lines cross from slope-intercept or ax + by = c form, the angle between them, and whether they are parallel or the same line.
- [Parabola Vertex Calculator](https://calculators.geekmidst.com/calculators/parabola-vertex-calculator.md): Enter y = ax² + bx + c to get the vertex, axis of symmetry, focus, directrix, vertex form and whether the vertex is a minimum or maximum.
- [Ellipse Eccentricity Calculator](https://calculators.geekmidst.com/calculators/ellipse-eccentricity-calculator.md): Find an ellipse’s eccentricity, focal distance, flattening, latus rectum, area and perimeter from its semi-major and semi-minor axes.
- [Hyperbola Asymptotes Calculator](https://calculators.geekmidst.com/calculators/hyperbola-asymptotes-calculator.md): Get the two asymptote equations of a hyperbola in standard form, plus its foci, vertices, focal distance and eccentricity, for any centre.
- [Arc Length Calculator](https://calculators.geekmidst.com/calculators/arc-length-calculator.md): Find the length of a circular arc from the radius and central angle in degrees or radians, with the chord, sector area and segment area.
- [Sector Area Calculator](https://calculators.geekmidst.com/calculators/sector-area-calculator.md): Work out the area of a circle sector from the radius and either the central angle or the arc length, with the angle, arc and perimeter.
- [Cylinder Surface Area Calculator](https://calculators.geekmidst.com/calculators/cylinder-surface-area-calculator.md): Find a cylinder’s curved (lateral) area, end area, total closed surface and open-top surface from its radius or diameter and height.
- [Cone Surface Area Calculator](https://calculators.geekmidst.com/calculators/cone-surface-area-calculator.md): Find a cone’s lateral (curved) area, base area and total surface from the radius and either the vertical height or the slant height.
- [Sphere Volume Calculator](https://calculators.geekmidst.com/calculators/sphere-volume-calculator.md): Find the volume of a sphere or ball from its radius, diameter, circumference or surface area, with the hemisphere volume and capacity in litres.
- [Torus Volume Calculator](https://calculators.geekmidst.com/calculators/torus-volume-calculator.md): Find the volume and surface area of a torus (ring or doughnut shape) from its major and tube radii, or from its inner and outer radii.
- [Trapezoid Area Calculator](https://calculators.geekmidst.com/calculators/trapezoid-area-calculator.md): Find a trapezoid’s (trapezium’s) area from its parallel sides and height, or from all four side lengths when the height is unknown.
- [Rhombus Area Calculator](https://calculators.geekmidst.com/calculators/rhombus-area-calculator.md): Find a rhombus’s area, side, perimeter, height, both diagonals and angle from its diagonals, its side and height, or its side and an angle.
- [Regular Polygon Calculator](https://calculators.geekmidst.com/calculators/regular-polygon-area-calculator.md): Find the area and perimeter of any regular polygon (hexagon, octagon, n-gon) from its side, circumradius or apothem, plus its interior angle.
- [Heron’s Formula Calculator](https://calculators.geekmidst.com/calculators/heron-triangle-area-calculator.md): Find a triangle’s area from its three side lengths with Heron’s formula, step by step, plus the semiperimeter, all three heights and the triangle type.
- [Triangle Inradius Calculator](https://calculators.geekmidst.com/calculators/triangle-inradius-calculator.md): Find the radius of the largest circle that fits inside a triangle (the incircle) from its three sides or from its area and perimeter.
- [Triangle Circumradius Calculator](https://calculators.geekmidst.com/calculators/triangle-circumradius-calculator.md): Find the radius of the circle through a triangle’s three corners from its three sides, one side and the opposite angle, or vertex coordinates.
- [Law of Sines Calculator](https://calculators.geekmidst.com/calculators/triangle-law-of-sines-calculator.md): Solve a triangle with the law of sines from two sides and a non-included angle (finding 0, 1 or 2 triangles) or from two angles and a side.
- [Trigonometric Identity Checker](https://calculators.geekmidst.com/calculators/trigonometric-identity-verification-calculator.md): Type both sides of a trigonometric identity and test them numerically at 400 angles to see whether they agree, with a counterexample if they do not.
- [Radians to Degrees Converter](https://calculators.geekmidst.com/calculators/radians-to-degrees-calculator.md): Convert radians to degrees or degrees to radians, with the angle as a multiple of π, in degrees-minutes-seconds, turns and gradians.
- [Degrees Minutes Seconds Converter](https://calculators.geekmidst.com/calculators/degrees-minutes-seconds-conversion-calculator.md): Convert decimal degrees to degrees, minutes and seconds (DMS) or back, for coordinates and angles, with the degrees-decimal-minutes form too.
- [Great Circle Distance Calculator](https://calculators.geekmidst.com/calculators/great-circle-distance-calculator.md): Shortest distance between two latitude/longitude points over a spherical Earth by the haversine formula, in kilometres, miles and nautical miles.
- [Bearing Between Coordinates Calculator](https://calculators.geekmidst.com/calculators/bearing-between-coordinates-calculator.md): Find the initial and final great-circle bearing from one latitude/longitude to another, in degrees from true north, with the compass point.
- [Coordinate Midpoint Calculator](https://calculators.geekmidst.com/calculators/coordinate-midpoint-calculator.md): Find the true midpoint of two latitude/longitude points on the globe, or the geographic centre of up to 200 points, without the errors of simple averaging.
- [Slope-Intercept Form Calculator](https://calculators.geekmidst.com/calculators/slope-intercept-form-calculator.md): Write a line as y = mx + b from two points, a point and a slope, or standard form Ax + By = C, with fractions, the x-intercept and standard form.
- [Distance from Point to Line Calculator](https://calculators.geekmidst.com/calculators/distance-point-to-line-calculator.md): Find the shortest (perpendicular) distance from a point to a line in the plane, and the foot of the perpendicular, from ax + by + c = 0, two points or y = mx + b.
- [Modular Exponentiation Calculator](https://calculators.geekmidst.com/calculators/modular-exponentiation-calculator.md): Compute a to the power b modulo m exactly for whole numbers up to 300 digits, by square-and-multiply, including negative exponents via the modular inverse.
- [Chinese Remainder Theorem Calculator](https://calculators.geekmidst.com/calculators/chinese-remainder-theorem-calculator.md): Solve a system of congruences x ≡ r (mod m) with the Chinese remainder theorem, including moduli that share factors, with exact big-integer arithmetic.
- [Extended Euclidean Algorithm Calculator](https://calculators.geekmidst.com/calculators/extended-euclidean-algorithm-calculator.md): Find gcd(a, b) and integers x, y with ax + by = gcd, the modular inverse when it exists, and every step of the extended Euclidean algorithm.
- [Euler Totient Calculator](https://calculators.geekmidst.com/calculators/euler-totient-calculator.md): Compute Euler’s totient φ(n), the count of integers from 1 to n that are coprime to n, from the prime factorisation, for n up to 10¹⁵.
- [Prime Sieve Calculator](https://calculators.geekmidst.com/calculators/prime-sieve-calculator.md): List and count every prime between two limits up to 10 million with the sieve of Eratosthenes, with their sum, twin-prime pairs and density.
- [Triangle Calculator](https://calculators.geekmidst.com/calculators/triangle-calculator.md): Solve any triangle from three sides, two sides and the included angle, or two angles and a side: all sides, angles, area, perimeter and type.
- [Area Calculator](https://calculators.geekmidst.com/calculators/area-calculator.md): Find the area of a rectangle, square, triangle, circle, ellipse, trapezoid, parallelogram or sector, with the result in m² and ft² too.
- [Volume Calculator](https://calculators.geekmidst.com/calculators/volume-calculator.md): Calculate the volume and surface area of a box, cube, cylinder, cone, sphere or pyramid, with the capacity in litres and US gallons.
- [Binary Calculator](https://calculators.geekmidst.com/calculators/binary-calculator.md): Do arithmetic and bitwise operations on binary numbers of any length, with the answer in binary, decimal and hexadecimal.
- [Hex Calculator](https://calculators.geekmidst.com/calculators/hex-calculator.md): Add, subtract, multiply, divide and do bitwise AND, OR and XOR on hexadecimal numbers, with results in hex, decimal and binary.
- [Quadratic Formula Calculator](https://calculators.geekmidst.com/calculators/quadratic-formula-calculator.md): Solve any quadratic equation with the quadratic formula: real or complex roots, the discriminant and the vertex of the parabola.
- [Slope Calculator](https://calculators.geekmidst.com/calculators/slope-calculator.md): Find the slope between two points as a decimal and a fraction, the line’s equation y = mx + b, its angle, the distance and the midpoint.
- [Log Calculator](https://calculators.geekmidst.com/calculators/log-calculator.md): Calculate the logarithm of a number to base 10, base e, base 2 or any base you choose, with all three common logs shown together.
- [Distance Calculator](https://calculators.geekmidst.com/calculators/distance-calculator.md): Find the straight-line distance between two points from their coordinates in the plane or in space, plus the midpoint and slope.
- [Circle Calculator](https://calculators.geekmidst.com/calculators/circle-calculator.md): Enter any one of a circle’s radius, diameter, circumference or area and get the other three, using π to full precision.
- [Surface Area Calculator](https://calculators.geekmidst.com/calculators/surface-area-calculator.md): Total, lateral and base surface area of a sphere, hemisphere, cube, rectangular box, cylinder, cone or square pyramid, with the volume too.
- [Pythagorean Theorem Calculator](https://calculators.geekmidst.com/calculators/pythagorean-theorem-calculator.md): Solve a² + b² = c² for the missing side of a right triangle, with the working shown and a check for whole-number Pythagorean triples.
- [Right Triangle Calculator](https://calculators.geekmidst.com/calculators/right-triangle-calculator.md): Solve a right triangle from two legs, a leg and the hypotenuse, or a side and an angle: all three sides, both angles, area, perimeter and altitude.
- [Matrix Calculator](https://calculators.geekmidst.com/calculators/matrix-calculator.md): Find the determinant, inverse, rank, trace or transpose of a matrix, or add, subtract and multiply two matrices, with exact fractions.