# Algebra Calculators

A collection of calculators to solve virtually any algebra problem step-by-step. Solve equations (quadratic, polynomial, trigonometric, etc.), factor polynomials, perform synthetic division and partial fraction decomposition, discover conic sections, and many more.

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## Prime Factorization Calculator

This calculator will find the prime factorization of the given number, with steps shown.

## Mixed Number to Improper Fraction Calculator

The calculator will convert the given mixed number into an improper fraction, with steps shown.

## Improper Fraction to Mixed Number Calculator

The calculator will convert the given improper fraction into a mixed number, with steps shown.

## Decimal to Fraction Calculator

The calculator will convert decimal (simple, repeating or recurring) into fraction (and, if possible, into mixed number), with steps shown.

## Fraction to Decimal Calculator

The calculator will convert the given fraction (proper or improper) or mixed number into a decimal (possibly, repeating or recurring), with steps shown.

## Percent to Fraction Calculator

The calculator will convert percent into fraction (proper, improper, mixed number), with steps shown.

## Fraction to Percent Calculator

The calculator will convert the given fraction (proper, improper, or mixed number) into a percent, with steps shown.

## Decimal to Percent Calculator

The calculator will convert decimal into percent, with steps shown.

## Percent to Decimal Calculator

The calculator will convert percent into decimal, with steps shown.

## Fractions Calculator

The calculator will find (with steps shown) the sum, difference, product and result of the division of fractions or mixed numbers. It will also convert fraction into decimal number and into improper fraction (if possible).

## Square Root Calculator

The calculator will find the square root of the number `n` (i.e. such number `x`, that `x^2=n`) to the given precision.

## Cube Root Calculator

The calculator will find the cube root of the number `n` (i.e. such number `x`, that `x^3=n`) to the given precision.

## Greatest Common Divisor/Factor (GCD) Calculator

The calculator will find the greatest common factor/divisor (GCF) of the given positive numbers, with steps shown, using either the factoring method or the prime factorization method.

## Least Common Multiple (LCM) Calculator

The calculator will find the least (smallest) common multiple of the given positive numbers, with steps shown, using either the factoring method or the prime factorization method.

## Long Division Calculator

The calculator will divide any two numbers (positive or negative, integer or decimal), with steps shown. Enter the dividend and the divisor and get the quotient to the given precision without remainder or quotient with remainder.

## Scientific Notation Calculator

The calculator will convert the given number into scientific notation.

## Line Calculator

This calculator will find the equation of a line (in the slope-intercept, point-slope and general forms) given two points or the slope and one point, with steps shown.

## Slope Intercept Form Calculator with Two Points

The slope intercept form calculator will find the slope of the line passing through the two given points, its y-intercept and slope-intercept form of the line, with steps shown.

## Slope Calculator

The slope calculator will find the slope of the line passing through the two given points or the slope of the given line, with steps shown.

## Parallel and Perpendicular Line Calculator

The calculator will find the equation of the parallel/perpendicular line to the given line, passing through the given point, with steps shown.

For drawing lines, use the graphing calculator.

## Direct, Inverse, and Joint Variation Calculator

The calculator will find the constant of variation and other values for direct, inverse (indirect), joint, and combined variation problems, with steps shown.

## FOIL Calculator

The calculator will multiply two binomials using the FOIL method, with steps shown.

## Polynomial Calculator

The calculator will find (with steps shown) the sum, difference, product and result of the division of two polynomials (quadratic, binomial, trinomial, etc.). It will also calculate the roots of the polynomials and factor them. Both univariate and multivariate polynomials are accepted.

## Multiplying Polynomials Calculator

The calculator will multiply two polynomials (quadratic, binomial, trinomial etc.), with steps shown.

## Synthetic Division Calculator

The calculator will divide the polynomial by the binomial using synthetic division, with steps shown.

## Dividing Polynomials Calculator

The calculator will divide two polynomials (quadratic, binomial, trinomial etc.), with steps shown.

## Polynomial Long Division Calculator

The calculator will perform the long division of polynomials, with steps shown.

## Completing the Square Calculator

The calculator will try to complete the square for the given quadratic expression, ellipse, hyperbola or any polynomial expression, with steps shown.

## Quadratic Equation Calculator

The calculator will solve the quadratic equation step by step either by completing the square or using the quadratic formula. It will find both the real and the imaginary (complex) roots.

## Rational Zeros Theorem Calculator

The calculator will find all possible rational roots of the polynomial, using the Rational Zeros Theorem. After this, it will decide which possible roots are actually the roots. This is a more general case of the Integer (Integral) Root Theorem (when leading coefficient is `1` or `-1`). Steps are available.

## Factoring Polynomials Calculator

The calculator will try to factor any polynomial (binomial, trinomial, quadratic, etc.), with steps shown. The following methods are used: factoring monomials (common factor), factoring quadratics, grouping and regrouping, square of sum/difference, cube of sum/difference, difference of squares, sum/difference of cubes, Rational Zeros Theorem. The calculator accepts both univariate and multivariate polynomials.

## Descartes' Rule of Signs Calculator

The calculator will find the maximum number of positive and negative real roots of the given polynomial using the Descartes' Rule of Signs, with steps shown.

## Remainder Theorem Calculator

The calculator will calculate `f(a)` using the remainder (little Bézout's) theorem, with steps shown.

## Order of Operations Calculator

The calculator will evaluate the given expression, showing the order of operations PEMDAS.

## Arithmetic Sequence Calculator

The calculator will find the terms, common difference and sum of the first `n` terms of the arithmetic sequence from the given data, with steps shown.

## Geometric Sequence Calculator

The calculator will find the terms, common ratio, sum of the first `n` terms and, if possible, the infinite sum of the geometric sequence from the given data, with steps shown.

## Partial Fraction Decomposition Calculator

This online calculator will find the partial fraction decomposition of the rational function, with steps shown.

## Factoring Calculator

The calculator will try to factor any expression (polynomial, binomial, trinomial, quadratic, rational, irrational, exponential, trigonometric, or mix of them), with steps shown. To do this, some substitutions are first applied to convert the expression into a polynomial, and then the following techniques are used: factoring monomials (common factor), factoring quadratics, grouping and regrouping, square of sum/difference, cube of sum/difference, difference of squares, sum/difference of cubes, and Rational Zeros Theorem.

## Equation Solver

The calculator will find the roots (exact and numerical, real and complex), i.e. solve for `x`, `y` or any other variable, of any equation (linear, quadratic, polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, absolute value) on the given interval.

## System of Equations Calculator

This solver (calculator) will try to solve a system of 2, 3, 4, 5 equations of any kind, including polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, absolute value, etc. It can find both real and complex solutions. To solve a system of linear equations with steps, use the system of linear equations calculator.

## Simplify Expression Calculator

This calculator will simplify fractions, polynomial, rational, radical, exponential, logarithmic, trigonometric, and hyperbolic expressions.

## Inverse Function Calculator

The calculator will find the inverse of the given function, with steps shown. If the function is one-to-one, there will be a unique inverse.

## Parabola Calculator

This calculator will find either the equation of the parabola from the given parameters or the axis of symmetry, eccentricity, latus rectum, length of the latus rectum, focus, vertex, directrix, focal parameter, x-intercepts, y-intercepts of the entered parabola.

To graph a parabola, visit the parabola grapher (choose the "Implicit" option).

## Circle Calculator

This calculator will find either the equation of the circle from the given parameters or the center, radius, diameter, area, circumference (perimeter), eccentricity, linear eccentricity, x-intercepts, y-intercepts, domain, and range of the entered circle.

To graph a circle, visit the circle graphing calculator (choose the "Implicit" option).

## Ellipse Calculator

This calculator will find either the equation of the ellipse (standard form) from the given parameters or the center, vertices, co-vertices, foci, area, circumference (perimeter), focal parameter, eccentricity, linear eccentricity, latus rectum, length of the latus rectum, directrices, (semi)major axis length, (semi)minor axis length, x-intercepts, y-intercepts, domain, and range of the entered ellipse.

To graph an ellipse, visit the ellipse graphing calculator (choose the "Implicit" option).

## Hyperbola Calculator

This calculator will find either the equation of the hyperbola (standard form) from the given parameters or the center, vertices, co-vertices, foci, asymptotes, focal parameter, eccentricity, linear eccentricity, latus rectum, length of the latus rectum, directrices, (semi)major axis length, (semi)minor axis length, x-intercepts, and y-intercepts of the entered hyperbola.

To graph a hyperbola, visit the hyperbola graphing calculator (choose the "Implicit" option).

## Distance between Two Points Calculator

For two given points, the calculator will find the distance between them, with steps shown.

## Sine Calculator

The calculator will find the sine of the given value in radians or degrees.

The domain of the sine is `x in R`, the range is `[-1,1]`.

It is an odd function.

For graph, see graphing calculator.

## Cosine Calculator

The calculator will find the cosine of the given value in radians or degrees.

The domain of the cosine is `x in R`, the range is `[-1,1]`.

It is an even function.

For graph, see graphing calculator.

## Tangent Calculator

The calculator will find the tangent of the given value in radians or degrees.

The tangent `y=tan(x)` is such a function that `y=sin(x)/cos(x)`.

The domain of the tangent is `x != pi/2 + pi n, n in Z`, the range is `(-oo,oo)`.

It is an odd function.

For graph, see graphing calculator.

## Cotangent Calculator

The calculator will find the cotangent of the given value in radians or degrees.

The cotangent `y=cot(x)` is such a function that `y=cos(x)/sin(x)`.

The domain of the cotangent is `x != pi n, n in Z`, the range is `(-oo,oo)`.

It is an odd function.

For graph, see graphing calculator.

## Secant Calculator

The calculator will find the secant of the given value in radians or degrees.

The secant `y=sec(x)` is such a function that `y=1/cos(x)`.

The domain of the secant is `x != pi/2 + pi n, n in Z`, the range is `(-oo,-1]uu[1,oo)`.

It is an even function.

For graph, see graphing calculator.

## Cosecant Calculator

The calculator will find the cosecant of the given value in radians or degrees.

The cosecant `y=csc(x)` is such a function that `y=1/sin(x)`.

The domain of the cosecant is `x != pi n, n in Z`, the range is `(-oo,-1]uu[1,oo)`.

It is an odd function.

For graph, see graphing calculator.

## Inverse Sine Calculator

The calculator will find the inverse sine of the given value in radians and degrees.

The inverse sine `y=sin^(-1)(x)` or `y=asin(x)` or `y=arcsin(x)` is such a function that `sin(y)=x`.

The domain of the inverse sine is `[-1,1]`, the range is `[-pi/2,pi/2]`.

It is an odd function.

For graph, see graphing calculator.

## Inverse Cosine Calculator

The calculator will find the inverse cosine of the given value in radians and degrees.

The inverse cosine `y=cos^(-1)(x)` or `y=acos(x)` or `y=arccos(x)` is such a function that `cos(y)=x`.

The domain of the inverse cosine is `[-1,1]`, the range is `[0,pi]`.

It is an even function.

For graph, see graphing calculator.

## Inverse Tangent Calculator

The calculator will find the inverse tangent of the given value in radians and degrees.

The inverse tangent `y=tan^(-1)(x)` or `y=atan(x)` or `y=arctan(x)` is such a function that `tan(y)=x`.

The domain of the inverse tangent is `(-oo,oo)`, the range is `(-pi/2,pi/2)`.

It is an odd function.

For graph, see graphing calculator.

## Inverse Cotangent Calculator

The calculator will find the inverse cotangent of the given value in radians and degrees.

The inverse cotangent `y=cot^(-1)(x)` or `y=acot(x)` or `y=arccot(x)` is such a function that `cot(y)=x`.

The domain of the inverse cotangent is `(-oo,oo)`, the range is `(0,pi)`.

It is an odd function.

There are two conventional but incompatible definitions for the inverse cotangent:

- `acot(x)=pi/2-atan(x)`
- `acot(x)=atan(1/x)`

We use the first definition to make the inverse cotangent continuous at `x=0`.

For graph, see graphing calculator.

## Inverse Secant Calculator

The calculator will find the inverse secant of the given value in radians and degrees.

The inverse secant `y=sec^(-1)(x)` or `y=asec(x)` or `y=arcsec(x)` is such a function that `sec(y)=x`.

The domain of the inverse secant is `(-oo,-1]uu[1,oo)`, the range is `[0,pi/2)uu(pi/2,pi]`.

This function is neither even nor odd.

For graph, see graphing calculator.

## Inverse Cosecant Calculator

The calculator will find the inverse cosecant of the given value in radians and degrees.

The inverse secant `y=csc^(-1)(x)` or `y=acsc(x)` or `y=text(arccsc)(x)` is such a function that `csc(y)=x`.

The domain of the inverse cosecant is `(-oo,-1]uu[1,oo)`, the range is `[-pi/2,0)uu(0,pi/2]`.

This function is neither even nor odd.

For graph, see graphing calculator.

## Hyperbolic Sine Calculator

The calculator will find the hyperbolic sine of the given value.

The hyperbolic sine `y=sinh(x)` is such a function that `y=(e^x-e^(-x))/2`.

The domain of the hyperbolic sine is `(-oo,oo)`, the range is `(-oo,oo)`.

It is an odd function.

For graph, see graphing calculator.

## Hyperbolic Cosine Calculator

The calculator will find the hyperbolic cosine of the given value.

The hyperbolic cosine `y=cosh(x)` is such a function that `y=(e^x+e^(-x))/2`.

The domain of the hyperbolic cosine is `(-oo,oo)`, the range is `[1,oo)`.

It is an even function.

For graph, see graphing calculator.

## Hyperbolic Tangent Calculator

The calculator will find the hyperbolic tangent of the given value.

The hyperbolic tangent `y=tanh(x)` is such a function that `y=sinh(x)/cosh(x)=(e^x-e^(-x))/(e^x+e^(-x))`.

The domain of the hyperbolic tangent is `(-oo,oo)`, the range is `(-1,1)`.

It is an odd function.

For graph, see graphing calculator.

## Hyperbolic Cotangent Calculator

The calculator will find the hyperbolic cotangent of the given value.

The hyperbolic cotangent `y=coth(x)` is such a function that `y=cosh(x)/sinh(x)=(e^x+e^(-x))/(e^x-e^(-x))`.

The domain of the hyperbolic cotangent is `(-oo,0)uu(0,oo)`, the range is `(-oo-1)uu(1,oo)`.

It is an odd function.

For graph, see graphing calculator.

## Hyperbolic Secant Calculator

The calculator will find the hyperbolic secant of the given value.

The hyperbolic secant `y=sech(x)` is such a function that `y=1/cosh(x)=2/(e^x+e^(-x))`.

The domain of the hyperbolic secant is `(-oo,-oo)`, the range is `(0,1]`.

It is an even function.

For graph, see graphing calculator.

## Hyperbolic Cosecant Calculator

The calculator will find the hyperbolic cosecant of the given value.

The hyperbolic cosecant `y=text(csch)(x)` is such a function that `y=1/sinh(x)=2/(e^x-e^(-x))`.

The domain of the hyperbolic secant is `(-oo,0)uu(0,oo)`, the range is `(-oo,0)uu(0,oo)`.

It is an odd function.

For graph, see graphing calculator.

## Inverse Hyperbolic Sine Calculator

The calculator will find the inverse hyperbolic sine of the given value.

The inverse hyperbolic sine `y=sinh^(-1)(x)` or `y=asinh(x)` or `y=arcsinh(x)` is such a function that `sinh(y)=x`.

It can be expressed in terms of elementary functions: `y=sinh^(-1)(x)=ln(x+sqrt(x^2+1))`.

The domain of the inverse hyperbolic sine is `(-oo,oo)`, the range is `(-oo,oo)`.

It is an odd function.

For graph, see graphing calculator.

## Inverse Hyperbolic Cosine Calculator

The calculator will find the inverse hyperbolic cosine of the given value.

The inverse hyperbolic cosine `y=cosh^(-1)(x)` or `y=acosh(x)` or `y=arccosh(x)` is such a function that `cosh(y)=x`.

It can be expressed in terms of elementary functions: `y=cosh^(-1)(x)=ln(x+sqrt(x^2-1))`.

The domain of the inverse hyperbolic cosine is `[1,oo)`, the range is `[0,oo)`.

This function is neither even nor odd.

For graph, see graphing calculator.

## Inverse Hyperbolic Tangent Calculator

The calculator will find the inverse hyperbolic tangent of the given value.

The inverse hyperbolic tangent `y=tanh^(-1)(x)` or `y=atanh(x)` or `y=arctanh(x)` is such a function that `tanh(y)=x`.

It can be expressed in terms of elementary functions: `y=tanh^(-1)(x)=1/2 ln((1+x)/(1-x))`.

The domain of the inverse hyperbolic tangent is `(-1,1)`, the range is `(-oo,oo)`.

It is an odd function.

For graph, see graphing calculator.

## Inverse Hyperbolic Cotangent Calculator

The calculator will find the inverse hyperbolic cotangent of the given value.

The inverse hyperbolic cotangent `y=coth^(-1)(x)` or `y=acoth(x)` or `y=arccoth(x)` is such a function that `coth(y)=x`.

It can be expressed in terms of elementary functions: `y=coth^(-1)(x)=1/2 ln((x+1)/(x-1))`.

The domain of the inverse hyperbolic cotangent is `(-oo,-1)uu(1,oo)`, the range is `(-oo,0)uu(0,oo)`.

It is an odd function.

For graph, see graphing calculator.

## Inverse Hyperbolic Secant Calculator

The calculator will find the inverse hyperbolic secant of the given value.

The inverse hyperbolic secant `y=sech^(-1)(x)` or `y=asech(x)` or `y=arcsech(x)` is such a function that `sech(y)=x`.

It can be expressed in terms of elementary functions: `y=sech^(-1)(x)=ln(1/x+sqrt(1/x^2-1))`.

The domain of the inverse hyperbolic secant is `(0,1]`, the range is `[0,oo)`.

This function is neither even nor odd.

For graph, see graphing calculator.

## Inverse Hyperbolic Cosecant Calculator

The calculator will find the inverse hyperbolic cosecant of the given value.

The inverse hyperbolic cosecant `y=text(csch)^(-1)(x)` or `y=acsch(x)` or `y=arccsch(x)` is such a function that `text(csch)(y)=x`.

It can be expressed in terms of elementary functions: `y=text(csch)^(-1)(x)=ln(1/x+sqrt(1/x^2+1))`.

The domain of the inverse hyperbolic cosecant is `(-oo,0)uu(0,oo)`, the range is `(-oo,0)uu(0,oo)`.

It is an odd function.

For graph, see graphing calculator.

## Binomial Expansion Calculator

The calculator will find the binomial expansion of the given expression, with steps shown.

## Logarithm Calculator

The calculator will find the logarithm (natural, decimal, etc.) of the given value to the given base (e, 10, etc.).

The domain of the logarithm is `(0,oo)`, the range is `(-oo,oo)`.

It is neither an even nor an odd function.

## Inequality Calculator

This calculator will solve the linear, quadratic, polynomial, rational and absolute value inequalities. It can handle compound inequalities and systems of inequalities as well.

To graph inequalities, use the graphing calculator.

## Operations on Functions Calculator

The calculator will find the sum, difference, product, and quotient of the functions. It will also evaluate the resulting functions at the specified point, if needed.

## Composite Function Calculator

The calculator will find the composition of the functions, with steps shown. It will also evaluate the composition at the specified point, if needed.

## Evaluate Calculator

The calculator will find the value of the given expression, plugging the values of the given variables, if needed.

## Solve for X Calculator

The calculator will find the `x` (exact and numerical, real and complex) in the given equation.

## Zeros Calculator

The calculator will find zeros (exact and numerical, real and complex) of the linear, quadratic, cubic, quartic, polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, and absolute value function on the given interval.

## Simultaneous Equations Solver

This calculator will try to solve the system of 2, 3, 4, 5 simultaneous equations of any kind, including polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, absolute value, etc. It can find both real and complex solutions.

## Trigonometry Calculator

This calculator can solve trigonometric equations, simplify and evaluate expressions. It can handle trigonometric and inverse trigonometric functions.

## Complex Number Calculator

The calculator will simplify any complex expression, with steps shown. It will perform addition, subtraction, multiplication, division, raising to power, and also will find the polar form, conjugate, modulus and inverse of the complex number.

## Intercepts Calculator

The calculator will find the x- and y-intercepts of the given function, expression or equation.

## Roots of Complex Number Calculator

The calculator will find the `n`-th roots of the given complex number, using de Moivre's Formula, with steps shown.

## Cubic Equation Calculator

The calculator will find the roots of the cubic equation in both the analytic and the approximate forms.

## Quartic Equation Calculator

The calculator will find the roots of the quartic equation in both the analytic and the approximate forms.

## Exponential Function Calculator

This calculator will calculate the exponential function with the given base and exponent.

## System of Linear Equations Calculator

This calculator will solve the system of linear equations of any kind, with steps shown, using either the Gauss-Jordan Elimination method or the Cramer's Rule. To solve any system, use the system of equations calculator.

## End Behavior Calculator

This calculator will determine the end behavior of the given polynomial function, with steps shown.

## Degree and Leading Coefficient Calculator

The calculator will find the degree, leading coefficient, and leading term of the given polynomial function.