Precalculus Calculators

Precalculus

Precalculus is the bridge between algebra and calculus — the toolkit you build before tackling derivatives and integrals. These solvers cover the recurring topics: counting, complex numbers, polynomial manipulation and exponential equations.

A precalculus course gathers the pieces of algebra and trigonometry that calculus assumes you already know. The topics look unrelated at first — combinations and complex numbers, the binomial theorem and polynomial division — but they all return throughout calculus, so the time spent here pays off later.

Counting: permutations and combinations

nPr counts ordered arrangements; nCr counts unordered selections. Both come from the factorial n! and underpin the binomial coefficients.

The binomial theorem

Expand (a + b)ⁿ as a sum of binomial-coefficient terms. The same coefficients appear in Pascal's triangle and in counting subsets.

Complex numbers

A complex number a + bi extends arithmetic to include the square root of −1. The calculator adds, subtracts, multiplies and divides them using the conjugate trick.

Polynomial long division and exponentials

Long division splits a polynomial into a quotient plus a remainder, mirroring integer long division. Exponential equations bring the unknown out of the exponent with a logarithm.

All solvers

Permutations & Combinations Compute nPr, nCr and the factorial. Binomial Expansion Expand (ax + b)ⁿ with the binomial theorem. Complex Number Calculator Add, subtract, multiply or divide complex numbers. Polynomial Long Division Divide one polynomial by another for quotient and remainder. Exponential Equation Solver Solve a·bˣ = c for the exponent x. Function Inverse Calculator Find f⁻¹(x) for linear, exponential, logarithmic, radical and linear-fractional functions. Function Composition Calculator Compute (f ∘ g)(x) symbolically, plus an optional value at x = a. Domain & Range Calculator Find domain restrictions and the range of a function of x. Circle Calculator Equation, expanded form, diameter, circumference and area of a circle. Parabola Properties Vertex, axis, focus, directrix and intercepts of y = ax² + bx + c. Ellipse Properties Vertices, foci, eccentricity and area of an ellipse from (h, k, a, b). Hyperbola Properties Vertices, foci, asymptotes and eccentricity of a hyperbola.

Frequently asked questions

Why is precalculus needed before calculus?

Calculus assumes fluency with functions, polynomials, trigonometry and the binomial theorem — precalculus is where those become automatic.

What does nCr mean?

It is the number of ways to choose r items from n without regard to order, equal to n! divided by r! and (n − r)!.

Can the binomial tool handle negative or fractional exponents?

It handles whole-number exponents. Negative or fractional exponents give an infinite series, which is a calculus topic.