Algebra Calculator

Algebra calculators handle the building blocks of algebra and number theory — greatest common factor and least common multiple, averages, sequences, and special number series. Popular tools include the GCF Calculator, LCM Calculator, LCD Calculator, Average Calculator, and Quadratic Sequence nth-Term Calculator.

Choose a tool below for an instant, step-shown answer, or open the Trending tab to see what students are working on this week. Everything is free and works on any device.

  • Average Calculator
    Enter numbers separated by commas to get the average, sum, count, median, geometric mean, minimum, maximum, and range—instant results.
  • Double-Exponential (DE) Quadrature: Integral over (-∞, ∞)
    Numerically integrate any f(x) over the whole real line (-∞, ∞) using Double-Exponential (tanh-sinh / Takahasi-Mori) quadrature. Set precision in significant digits.
  • Polynomial from Roots Calculator
    Build and expand a polynomial P(x) from its real roots. Enter zeros and a leading coefficient to get the full expanded form, degree, and constant term.
  • Cranes and Tortoises Problem Calculator
    Solve the classic cranes-and-tortoises (tsurukamezan) word problem. Enter total heads and total legs to find how many cranes and tortoises there are.
  • GCF Calculator
    Calculate the Greatest Common Factor (GCF) with this easy-to-use GCF calculator. Input your numbers and quickly find the largest factor shared by all. Simplify fractions and solve math problems efficiently.
  • LCM Calculator
    Calculate the Least Common Multiple (LCM) with this LCM calculator. Input numbers separated by commas to find the smallest positive integer divisible by all given numbers.
  • Quadratic Function Analyzer Calculator
    Analyze any quadratic ax²+bx+c: find the vertex, axis of symmetry, real roots, discriminant, and y-intercept instantly with steps.
  • Inverse Variation Calculator
    Free inverse variation calculator. Enter a known x and y to find the constant k = xy, then solve y = k/x for any new x value instantly.
  • Completing the Square: Circle Equation Calculator
    Convert a general circle equation x²+y²+Dx+Ey+F=0 to standard form. Find the center and radius instantly by completing the square.
  • LCD Calculator
    Find the least common denominator for multiple fractions. Enter fractions, mixed numbers, or integers separated by commas to get the LCD.
  • Linear Equation from a Table of Values Calculator
    Find the linear equation y = mx + b from two points in a table of values. Computes slope and y-intercept instantly with steps.
  • Fourth Root Calculator
    Calculate the fourth root of any non-negative number (y = x^(1/4)) instantly. Free, accurate, with formula, worked example and FAQ.
  • Numerical Integration over (a, b) — Double-Exponential (Tanh-Sinh) Method
    Compute the definite integral of f(x) on a finite interval [a, b] with Double-Exponential (Tanh-Sinh) quadrature — robust even for endpoint singularities like 1/sqrt(x).
  • Prime Number Primality Checker
    Check if a number is prime or composite. Lists all factors, the previous prime and next prime using a fast trial-division primality test.
  • Absolute Value Graph Vertex Calculator
    Free combination (nCr) calculator. Find how many ways to choose r items from n where order does not matter, using C(n,r) = n!/(r!(n-r)!).
  • Function End Behavior Calculator
    Convert a line from slope-intercept form y = mx + b into standard form Ax + By = C instantly. Enter slope and y-intercept to get A, B, and C.
  • Rationalize the Numerator Calculator
    Find the distance between two points (x₁,y₁) and (x₂,y₂) using the distance formula d = √((x₂−x₁)² + (y₂−y₁)²). Fast and exact.
  • Add and Subtract Rational Expressions Calculator
    Add or subtract two fractions a/b ± c/d, get the combined fraction, simplify it by the greatest common factor, and see the decimal value instantly.
  • Zeros of a Function Calculator — Quadratic & Linear f(x)
    Find the zeros (roots) of a quadratic function f(x)=ax²+bx+c. Solves f(x)=0 with the quadratic formula and reports real or complex roots.
  • Proportion Calculator
    Enter any three of A, B, C, and D to complete A:B = C:D and instantly calculate the missing term. Fast, accurate proportion results.
  • Scientific Notation Calculator
    Convert any number to scientific notation (m × 10^e) instantly. Get the mantissa and exponent for very large or very small numbers.
  • Absolute Value Calculator
    Find the absolute value of any number instantly. Enter a positive, negative, or decimal value and get |x| with a clear worked explanation.
  • Simplifying Radicals Calculator
    Simplify any square root into the form a√b. Enter a number to get the simplified radical, coefficient, radicand, and decimal value instantly.
  • Absolute Value Inequalities Calculator
    Solve absolute value inequalities of the form |ax+b| < c, ≤, >, or ≥ c. Get the exact solution interval, boundary points, and step-by-step logic.

Frequently asked questions

What can I calculate with these algebra tools?

Factors and multiples (GCF, LCM, LCD), means and averages, arithmetic and quadratic sequences, nth-term formulas, and figurate numbers such as triangular numbers.

Do they show the working, not just the answer?

Yes — most display the steps and formula so you can check your own work and learn the method.

Are they free and mobile-friendly?

Yes — free, no sign-up, and fully usable on phones and tablets.

How accurate are the results?

They apply standard algebraic methods and are tested against known values; for exact fractions or symbolic results, check the tool matches the form your assignment requires.

Which algebra calculators are most popular?

This page lists them by usage; the Trending tab shows what's rising this week.

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