- Fraction Calculator
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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.
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Perfect Square Checker CalculatorCheck instantly if a number is a perfect square. Enter any whole number to see if it equals an integer squared, plus its exact square root.
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3D Distance and Midpoint CalculatorFind the distance and midpoint between two points in 3D space. Enter (x,y,z) coordinates to compute the Euclidean distance and midpoint instantly.
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Golden Ratio CalculatorCalculate the golden ratio φ = (1+√5)/2 and split any length into golden proportions: a = L/φ and b = L − a. Free and instant.
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Remainder Theorem CalculatorFind the remainder when a polynomial P(x) is divided by (x − c) using the Remainder Theorem. Enter coefficients and c to instantly get P(c).
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pH from Concentration CalculatorConvert hydrogen ion concentration [H+] to pH and back using pH = −log10[H+] and [H+] = 10^(−pH). Also shows pOH and [OH-].
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Cross Multiplication CalculatorSolve any proportion a/b = c/x using cross multiplication. Enter three known values and instantly find the missing fourth term with steps.
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Sum of Squares of Integers CalculatorCompute the sum of squares 1² + 2² + … + n² instantly using the closed-form formula n(n+1)(2n+1)/6. Fast, exact results for any whole number n.
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Weighted Average CalculatorCalculate the weighted average (weighted mean) from values and weights using Σ(wᵢxᵢ) / Σ(wᵢ). Free, instant, and accurate for grades, finance, and stats.
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Vertical & Horizontal Asymptote CalculatorFind vertical and horizontal asymptotes of a rational function. Enter leading coefficients and degrees to get the horizontal asymptote by degree comparison.
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Rational Zero Test CalculatorApply the Rational Root Theorem: list all possible rational zeros ±p/q of a polynomial from its constant term and leading coefficient.
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Condense Logarithms CalculatorCondense logarithms into a single log. Combine a·log_b(x)+c·log_b(y)-d·log_b(z) into log_b(x^a·y^c/z^d) with step value.
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Arithmetic Series Sum from First and Last Term CalculatorFind the sum of an arithmetic series instantly using the number of terms, first term, and last term with the formula Sn = n(a1 + an)/2.
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Negative Exponent CalculatorCalculate negative exponents instantly. Enter a base and exponent to compute a⁻ⁿ = 1 / aⁿ with step-by-step results and the positive power.
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One-Step Equation CalculatorSolve one-step linear equations instantly: x + a = b, x − a = b, a·x = b, and x / a = b. Enter a and b and get x with the inverse-operation method.
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Radical Equation SolverSolve radical equations of the form √(ax+b)=c step by step. Get x = (c²−b)/a instantly, with validity checks for negative c and a=0.
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Rational Equation CalculatorSolve rational equations of the form a/(x+b) = c/(x+d). Cross-multiplies and solves for x step by step, flagging extraneous solutions.
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Sum and Product of Roots CalculatorFind the sum and product of the roots of any quadratic ax^2+bx+c=0 instantly using Vieta formulas. Sum = -b/a, product = c/a, plus discriminant.
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Find the Linear Function f(x)=mx+b from Two PointsFind the linear function f(x)=mx+b from two points. Enter (x1,y1) and (x2,y2) to compute the slope m and y-intercept b instantly.
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Modular Exponentiation CalculatorCompute a^b mod m fast with this modular exponentiation calculator. Uses square-and-multiply (fast exponentiation) for large bases, exponents and moduli.
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Evaluate a Function CalculatorEvaluate a quadratic function f(x) = ax² + bx + c at any value x = a. Enter the coefficients and the input to instantly compute f(a) with a term breakdown.
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Compound Inequality Solver CalculatorSolve compound linear inequalities of the form a < bx + c < d instantly. Get the solution set for x in interval notation, step by step.
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Ellipse Foci & Eccentricity CalculatorCalculate an ellipse linear eccentricity (focal distance c), eccentricity e, area, and perimeter from its two semi-axes a and b. Free and instant.
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Expand Logarithms CalculatorExpand logarithms using the product, quotient and power rules. Enter base, x, y and exponent to see log(xy), log(x/y) or log(x^p) rewritten and evaluated.
