Algebra Calculator

  • Vertical Asymptote Calculator
    Find the vertical asymptotes of a rational function. Enter the denominator coefficients (a, b, c) and get every x = value where the function is undefined.
  • Factor by Grouping Calculator
    Factor by grouping calculator: enter a, b, x, y to factor ax+ay+bx+by into (a+b)(x+y) and verify the expanded value instantly.
  • Horizontal Asymptote Calculator
    Find the horizontal asymptote of a rational function by comparing numerator and denominator degrees. Returns y=0, the leading-coefficient ratio, or none.
  • Solve and Graph Inequalities Calculator
    Solve linear inequalities ax + b ≤ c (and <, ≥, >) instantly. Get the boundary value, direction, and interval notation for the number line.
  • Long Division Calculator
    Free long division calculator: enter a dividend and divisor to get the quotient, remainder, and decimal result instantly using a = b·q + r.
  • Solve for y Calculator
    Solve for y in a linear equation Ax + By = C. Enter A, B, C and x to instantly isolate y, plus get the slope and y-intercept. Free online tool.
  • Multi-Step Equation Calculator
    Solve linear equations of the form ax + b = cx + d for x. Enter the four coefficients and get the exact step-by-step solution instantly.
  • Round to n Significant Figures Calculator
    Round any number to a chosen number of significant figures and view its scientific-notation form (mantissa and exponent). Free, instant, and accurate.
  • 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.
  • Average Speed Calculator (Two Trips)
    Calculate average speed across two trips using total distance divided by total time. Enter distances and times to get the true overall speed.
  • Simplify Fraction Calculator
    Simplify any fraction to its lowest terms using the greatest common factor (GCF). Get the reduced fraction, GCF, decimal value, and mixed number instantly.
  • Parallel or Perpendicular Lines Checker
    Check if two lines are parallel, perpendicular, or neither by comparing their slopes. Enter m₁ and m₂ to get an instant answer with the product.
  • Average of Two Numbers (Midpoint Value) Calculator
    Find the average (midpoint) of two numbers instantly with average = (a + b) / 2. Also shows the amplitude (half-range) between the values.
  • Minimum/Maximum Value of a Quadratic Calculator
    Find the vertex and the minimum or maximum value of a quadratic ax²+bx+c. Computes x* = −b/(2a) and the extreme value c − b²/(4a) instantly.
  • Standard to Vertex Form Calculator
    Convert a quadratic from standard form ax²+bx+c to vertex form a(x−h)²+k by completing the square. Shows h, k, the vertex, and steps.
  • Partial Fraction Decomposition Calculator
    Decompose (px+q)/((x−a)(x−b)) into A/(x−a)+B/(x−b). Enter p, q and the two distinct roots a, b to get the coefficients A and B instantly.
  • Exponential to Logarithmic Form Converter
    Convert an exponential equation b^x = y into logarithmic form log_b(y) = x instantly. Enter the base and exponent to see both forms and the value.
  • Completing the Square / Vertex Calculator
    Find the vertex, minimum or maximum of a quadratic ax^2 + bx + c. Computes vertex x = -b/(2a) and the extreme value c - b^2/(4a) instantly.
  • Equation of a Line from Slope and a Point Calculator
    Find the equation of a line from a slope and one point. Enter m, x1, and y1 to get the slope-intercept form y = mx + b instantly.
  • Sum of First n Natural Numbers Calculator
    Add up the first n natural numbers instantly with the formula S = n(n+1)/2. Enter n and get the total, term count, and average. Free and fast.
  • Reciprocal Calculator
    Find the reciprocal of any number or fraction instantly. Flip a/b to b/a or compute 1/x with both fraction and decimal results shown.
  • Percent to Fraction in Simplest Form Calculator
    Convert any percent to a fraction in simplest (lowest) form. Enter a percentage and get the reduced fraction, unreduced form, and decimal value instantly.
  • Binomial Coefficient Calculator (n choose k)
    Compute the binomial coefficient C(n,k) = n!/(k!(n−k)!) — the number of ways to choose k items from n. Fast, accurate "n choose k" calculator.
  • Prime or Composite Number Calculator
    Check instantly whether any whole number is prime or composite. Find the smallest factor and an example factorization with this free prime checker.

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