• Euler's Totient Function Calculator
    Compute Euler's totient φ(n) — the count of integers from 1 to n coprime to n — using prime factorization. Free, instant, with worked steps.
  • Slope-Intercept Form from a Point and Slope
    Find the slope-intercept equation y = mx + b from a known slope and one point. Computes the y-intercept b instantly with steps and examples.
  • Simplify Exponents Calculator
    Simplify exponent expressions using the product, quotient, and power rules. Enter a base and two exponents to get the simplified power and its value.
  • Complete the Pattern: Next Number in Sequence Calculator
    Find the next number in a sequence. Automatically detects arithmetic or geometric patterns and predicts the next terms using the common difference or ratio.
  • Find the Vertex from Standard Form Calculator
    Find the vertex (h, k) of a parabola from standard form ax^2 + bx + c. Enter a, b, c to get the turning point and axis of symmetry instantly.
  • X-Intercept Calculator
    Find the x-intercept of a line from its slope-intercept equation y = mx + b. Set y = 0 and solve x = −b/m with worked steps.
  • Factor Out the GCF from a Polynomial Calculator
    Factor out the greatest common factor (GCF) from any polynomial. Enter the terms and get the fully factored form with steps. Free and instant.
  • 3D Vector Cross Product Calculator
    Compute the cross product of two 3D vectors a × b instantly. Get each component (x, y, z) plus the magnitude of the resulting perpendicular vector.
  • Number Base Converter Calculator
    Convert numbers between binary, octal, decimal, and hexadecimal. Free base converter using place value and repeated division with worked steps.
  • De Moivre's Theorem Calculator
    Apply De Moivre's theorem to raise a complex number in polar form (r∠θ) to a power n. Get modulus, angle, and rectangular a+bi form instantly.
  • Arithmetic Sequence Calculator
    Compute the nth term (aₙ) and the sum (Sₙ) of an arithmetic sequence from the first term, common difference, and term position.
  • Original Value Before Percent Change Calculator
    Find the original value before a percent increase or decrease. Enter the final value and percent change to reverse-calculate the starting amount instantly.
  • Find X and Y Intercepts of a Line
    Find the x-intercept and y-intercept of a line in standard form Ax + By = C. Enter A, B, and C to get both intercepts and the slope instantly.
  • Nature of Roots Calculator
    Find the discriminant of a quadratic equation and determine the nature of its roots — two real, one repeated, or two complex conjugate roots.
  • Slope-Intercept from Standard Form Calculator
    Convert a linear equation Ax + By = C into slope-intercept form y = mx + b. Instantly find the slope m = -A/B and y-intercept b = C/B.
  • Equivalent Ratios Calculator
    Generate equivalent ratios by scaling a:b with a multiplier, and check if two ratios a:b and c:d are equal using cross multiplication.
  • X and Y Intercepts of a Line Calculator
    Find the x-intercept and y-intercept of a line from its equation ax + by + c = 0. Enter coefficients a, b, c to get both intercepts instantly.
  • Percent Grade (Slope) Calculator
    Calculate percent grade and slope from two points. Enter X/Y coordinates to get rise/run, slope ratio, grade percentage, and angle of incline.
  • Solve Quadratic by Factoring Calculator
    Solve any quadratic equation ax²+bx+c=0 by factoring. Get both roots, the discriminant, and step-by-step factor logic instantly.
  • Part of a Whole Calculator
    Find the part, whole, or percent in any part-of-a-whole problem. Solve part = percent/100 × whole instantly with this free percentage ratio calculator.
  • Percent Proportion Calculator
    Solve percent word problems with the proportion part/whole = percent/100. Find the missing part, whole, or percent instantly with full steps.
  • Markup & Markdown Calculator
    Calculate the final price after a percent markup or markdown. Enter an original price and percentage to see the new price and the dollar change instantly.
  • Evaluate an Algebraic Expression Calculator
    Evaluate the algebraic expression a·x² + b·x + c·y + d by substituting your values for x and y. See each term and the simplified result instantly.
  • Solve for x: Variables on Both Sides Calculator
    Solve linear equations of the form ax + b = cx + d. Enter the coefficients and constants to find x instantly, with full steps shown.