Math Calculators & Solvers

Calculate the average percentage across multiple weighted data sets.

Convert any fraction or proper/improper ratio into an exact percentage.

Convert decimal values into clean percentage format instantly.

Calculate how long it takes an investment or population to double using Rule of 72.

Find X percent of Y or what percent X is of Y with ease.

Calculate percentage change, growth, and percent increase/decrease.

Calculate price markdowns, value depreciation, and percentage decreases.

Find the percentage difference between two non-zero positive numbers.

Compute price markups, growth rates, and positive percent changes.

Classic percentage growth calculator with step-by-step breakdown.

Calculate compound percentage of a percentage (e.g. 20% of 50%).

Calculate absolute percentage point changes between interest rates or metrics.

Compute experimental percent error relative to true accepted theoretical value.

Calculate what percentage of a day, hour, month, or year has elapsed.

Measure progress towards financial, fitness, or operational targets.

Calculate relative change and absolute difference between two metrics.

Convert elevation rise and run into grade slope percentages.

Solve linear and quadratic equations involving absolute values |x|.

Solve absolute value inequalities with interval notation step-by-step.

Combine like terms and simplify polynomial expressions effortlessly.

Compute J_v(x) and Y_v(x) Bessel functions of first and second kind.

Calculate n choose k combinations n! / (k!(n-k)!) for algebra.

Factor quadratic trinomials visually using grid box multiplication.

Transform ax² + bx + c into vertex form by completing the square.

Find the complex conjugate (a - bi) of any complex number (a + bi).

Perform addition, subtraction, multiplication, and division of complex numbers.

Find real and imaginary complex roots of polynomial equations.

Solve cubic equations ax³ + bx² + cx + d = 0 using Cardano's formula.

Determine possible number of positive and negative real polynomial roots.

Solve number diamond puzzles for factoring quadratic expressions.

Calculate direct proportion equations y = kx and variation constant k.

Calculate b² - 4ac to determine nature of roots for quadratic equations.

Solve 2x2 and 3x3 linear system of equations using elimination method.

Compute Gauss error function erf(x) and complementary error function erfc(x).

Factor quadratic polynomials ax² + bx + c into linear binomial factors.

Expand product of two binomials using First, Outer, Inner, Last method.

Calculate Gamma function Γ(z) generalizing factorials for real/complex z.

Multiply polynomials visually using generic rectangle area models.

Visualize 1D linear inequalities with open/closed rays on number line.

Solve and shade parabolas y > ax² + bx + c on coordinate plane.

Compute sinh, cosh, tanh, csch, sech, coth and their inverses.

Convert algebraic inequalities like a < x ≤ b into interval notation (a, b].

Convert set notation, number lines, and inequalities to interval syntax.

Calculate inverse variation y = k/x and proportionality constant k.

Multiply two binomial expressions with detailed step-by-step expansion.

Multiply multi-term polynomial expressions and simplify terms.

Decompose rational expressions into sum of simpler partial fractions.

Identify and factor perfect square trinomials a² ± 2ab + b².

Divide polynomials using long division with quotient and remainder.

Generate all 2ⁿ subsets of a given finite mathematical set.

Solve ax² + bx + c = 0 with exact radical solutions and step-by-step formula.

Perform 4D quaternion arithmetic (w + xi + yj + zk) and 3D rotations.

Find all potential rational roots p/q using Rational Zero Theorem.

Expand (a + b)² = a² + 2ab + b² binomial squares instantly.

Determine proper and improper subset relations between set collections.

Solve systems of linear equations using variable substitution steps.

Perform rapid synthetic division for polynomial division by (x - c).

Solve 2, 3, and 4 variable linear systems with step-by-step matrix steps.

Construct boolean truth tables for propositional logic formulas.

Compute set union (A ∪ B), intersection (A ∩ B), and relative complements.

Calculate absolute difference |x₂ - x₁| between starting and ending values.

Determine absolute distance from zero |x| for positive and negative numbers.

Add and subtract fractions with different denominators step-by-step.

Sum multiple large numbers with exact precision and running totals.

Demonstrate associative property (a+b)+c = a+(b+c) for math operations.

Calculate arithmetic mean, median, mode, and range of any number set.

Compute ceiling ⌈x⌉ rounding up to nearest integer.

Solve systems of simultaneous congruences using Chinese Remainder Theorem.

Estimate arithmetic problems easily by finding compatible friendly numbers.

Find consecutive even or odd integers satisfying sum conditions.

Solve proportion ratios a/b = c/d using cross multiplication.

Calculate exact cube root ∛x and simplified radical expressions.

Add, subtract, multiply, and divide floating point decimal numbers.

Compute single-digit digital root sum of digits iteratively.

Apply a(b + c) = ab + ac distributive expansion step-by-step.

Test if any integer is divisible by numbers 2 through 13 with explanations.

Perform long division with quotients, remainders, and visual steps.

Decompose any fraction into sum of distinct unit fractions 1/n.

Write numbers in expanded notation according to place value.

Find all positive and negative factors and factor pairs of an integer.

Compute n! factorial with exact big integer arithmetic.

Compute modular exponentiation a^(p-1) ≡ 1 (mod p) for prime p.

Divide integers rounding down to largest previous integer ⌊a/b⌋.

Compute floor ⌊x⌋ rounding real numbers down to nearest integer.

Calculate total number of outcomes for sequential independent events.

Find GCF / GCD of two or more numbers using Euclidean algorithm.

Simultaneously calculate GCF and LCM for any set of numbers.

Calculate nth root product geometric mean ⁿ√(x₁·x₂·...·xₙ).

Compare numbers and fractions with >, <, and = mathematical signs.

Calculate reciprocal average harmonic mean for ratios and rates.

Add, subtract, multiply, and divide positive and negative integers.

Find modular multiplicative inverse a⁻¹ mod m using Extended Euclidean algorithm.

Find smallest common multiple LCM of multiple integers.

Perform vertical multi-digit addition with carry indicators.

Multiply multi-digit numbers with partial product breakdown.

Perform long vertical subtraction with borrow tracking.

Generate and solve n x n magic squares with equal row/col sums.

Compute average sum divided by count with variance & standard deviation.

Calculate integer division remainder a mod n.

Multiply whole numbers, decimals, and large numbers quickly.

Find reciprocal 1/x for any non-zero real number.

Compute x such that ax ≡ 1 (mod m) for modular cryptography.

Determine power of 10 order of magnitude log₁₀(x).

Multiply numbers using partial product area expansion.

Check if a number is a perfect cube n³ and find its root.

Check if an integer is a perfect square n².

Calculate Pi approximations using Buffon's needle and Monte Carlo method.

Identify units, tens, hundreds, thousands place values for any number.

Convert standard infix math expressions to Prefix (Polish) and Postfix (RPN).

Compute b^e mod m modular exponentiation for large numbers.

Evaluate imaginary unit powers iⁿ (i, -1, -i, 1).

Decompose any number into prime factors with factor tree breakdown.

Test primality using deterministic algorithms and generate prime lists.

Find exact integer quotient and remaining fractional remainder.

Simplify nth radical roots ⁿ√x and convert to rational exponents.

Remove square roots and radicals from fraction denominators.

Convert any number or fraction into reciprocal inverse 1/x.

Check if two integers are coprime (GCF = 1).

Find exact integer division remainder step-by-step.

Factor quadratic trinomials into binomial products using reverse FOIL.

Calculate general nth root ⁿ√x for any positive real root.

Compute quadratic mean RMS √((x₁² + x₂² + ...)/n) for AC signals.

Round numbers to nearest integer, tenth, hundredth, or thousandth.

Quickly round large financial or population figures to nearest 1,000.

Convert numbers to scientific notation E-format (a × 10ᵇ).

Convert roster sets to set-builder notation {x | condition}.

Identify significant digits and perform sig fig arithmetic.

Express ∛x in simplest radical form a∛b.

Simplify square roots √x into reduced radical form a√b.

Calculate principal square root √x with exact precision.

Convert scientific numbers to standard decimal expanded notation.

Subtract proper, improper, and mixed fractions.

Subtract numbers with multi-digit precision.

Sum individual digits of any integer value.

Calculate dot product sum (a₁b₁ + a₂b₂ + ... + aₙbₙ).

Check if fraction a/b converts to terminating or repeating decimal.

Compute nth triangular number Tₙ = n(n+1)/2.

Calculate weighted average for grades, portfolios, and metrics.

Calculate average slope Δy/Δx across interval [a, b].

Interpolate 2D grid values for image processing and graphics.

Calculate hanging cable arch equation y = a·cosh(x/a).

Plot 2D points (x, y) and find distances and slope equations.

Measure vector directional similarity cos(θ) for ML and NLP.

Compute 3D vector cross product A × B perpendicular vector.

Convert between Cartesian (x, y, z) and Cylindrical (r, θ, z).

Find vector direction angle θ = arctan(y/x) in degrees/radians.

Calculate distance √((x₂-x₁)² + (y₂-y₁)²) between 2D points.

Compute 3D perpendicular distance |Ax₀ + By₀ + Cz₀ + D| / √(A²+B²+C²).

Compute scalar dot product A · B for 2D, 3D, and nD vectors.

Find unknown endpoint (x₂, y₂) given midpoint and one endpoint.

Find 3D plane equation Ax + By + Cz = D from 3 points or normal.

Calculate sphere equation (x-h)² + (y-k)² + (z-l)² = r².

Find 2D slope gradient m = Δy/Δx and incline angle.

Calculate exact point of intersection (x, y) for two 2D linear equations.

Find polygon area using Shoelace formula from vertex coordinates.

Calculate latus rectum focal chord length for parabolas, ellipses, and hyperbolas.

Calculate best fit line y = mx + b and R² correlation from scatter data.

Find unknown y value between two known data points (x₁, y₁) and (x₂, y₂).

Find slope-intercept y = mx + b from two coordinate points.

Find 3D vector equation of line where two non-parallel planes intersect.

Compute L1 taxicab distance |x₂-x₁| + |y₂-y₁|.

Find midpoint coordinates ((x₁+x₂)/2, (y₁+y₂)/2) between two points.

Analyze vertex, focus, directrix, and axis of symmetry for y = ax² + bx + c.

Find equation of parallel line passing through a given point with matching slope.

Find equation of line perpendicular (negative reciprocal slope -1/m).

Write linear equation in y - y₁ = m(x - x₁) format.

Convert Cartesian (x, y) to Polar (r, θ) coordinates.

Analyze roots, turning points, and end behavior of polynomial curves.

Divide line segment AB into ratio m:n using section formula.

Compute slope gradient m = rise / run for stairs and ramps.

Rotate 2D points around origin by angle θ using rotation matrix.

Plot (x,y) scatter points and generate trendline equation.

Calculate slope m = (y₂ - y₁) / (x₂ - x₁) between two points.

Convert standard line equation to y = mx + b format.

Convert Cartesian (x, y, z) to Spherical (r, θ, φ) coordinates.

Convert Ax + By = C into y = (-A/B)x + (C/B) form.

Calculate 3D distance √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²) in space.

Determine 2D position from angles measured from known baseline points.

Normalize vector V into unit vector u = V / |V| of magnitude 1.

Compute magnitude, angle, components, and unit vector for 2D/3D vectors.

Add multiple 2D and 3D vectors by component sum.

Calculate vector length |V| = √(v₁² + v₂² + ... + vₙ²).

Compute vector projection proj_u(v) = ((u·v)/|u|²)u.

Convert parabola equation to y = a(x - h)² + k vertex form.

Compute 3D parallelepiped volume using scalar triple product |A · (B × C)|.

Find point (0, b) where line or curve crosses vertical y-axis.

Add two or more fractions with common or different denominators.

Compare two fractions using LCD to determine which is larger.

Convert repeating and terminating decimals into simplified reduced fractions.

Divide fractions by multiplying by reciprocal with step-by-step solutions.

Generate list of equivalent fractions by scaling numerator and denominator.

All-in-one fraction engine for addition, subtraction, multiplication, and division.

Evaluate fractional powers x^(a/b) = ᵇ√(xᵃ).

Convert fractions to exact decimal numbers with repeating digits indicator.

Calculate golden ratio φ ≈ 1.6180339887 dimensions for design and geometry.

Convert improper fraction (numerator > denominator) to mixed integer number.

Find smallest common denominator LCD for adding multiple fractions.

Order a list of fractions from smallest to largest.

Reduce any fraction to its simplest lowest terms by dividing by GCD.

Perform operations with mixed numbers (whole integer + fraction).

Convert mixed numbers a b/c into improper fraction format (ac+b)/c.

Multiply fractions by multiplying numerators and denominators.

Solve unknown proportion x in ratio equation a/b = c/x.

Simplify ratios a:b and scale proportions proportionally.

Instantly reduce improper fractions to simplest terms.

Calculate unit rates (cost per ounce, miles per hour, speed).

Compute adjugate adj(A) matrix of transposed cofactors.

Find characteristic equation det(A - λI) = 0 for square matrix.

Decompose positive-definite matrix A = L·Lᵀ into lower triangular factor.

Compute matrix determinant via Laplace cofactor expansion along row/col.

Generate matrix of cofactors C_ij = (-1)^(i+j) M_ij.

Find basis and dimension of matrix column space col(A).

Compute matrix condition number κ(A) for numerical stability.

Find feasible region corner points for linear programming optimization.

Solve system of linear equations Ax = b using determinants det(A_i)/det(A).

Find modal matrix P and diagonal matrix D such that A = P D P⁻¹.

Calculate eigenvalues λ and corresponding eigenvectors v satisfying Av = λv.

Transform augmented matrix into reduced row echelon form (RREF) step-by-step.

Orthonormalize set of vectors using Gram-Schmidt process.

Compute element-wise matrix multiplication A ⊙ B.

Calculate inverse matrix A⁻¹ such that A · A⁻¹ = I.

Express vector v as linear combination c₁v₁ + c₂v₂ + ... + cₙvₙ.

Check if set of vectors are linearly independent by checking rank.

Factor matrix A = L · U into lower and upper triangular matrices.

All-in-one matrix workbench for addition, multiplication, rank, and inverse.

Add and subtract m x n matrices element-by-element.

Multiply matrix by scalar constant c · A.

Calculate det(A) for 2x2, 3x3, 4x4, and n x n square matrices.

Multiply m x n and n x p matrices with step-by-step dot products.

Compute Frobenius norm, 1-norm, ∞-norm, and 2-norm of matrix.

Calculate matrix exponentiation Aᵏ using binary exponentiation.

Determine number of linearly independent rows/columns in matrix.

Calculate sum of diagonal elements tr(A) = ∑ a_ii.

Swap matrix rows and columns Aᵀ.

Find nullspace basis null(A) solving homogeneous equation Ax = 0.

Factor real matrix A = U · P into orthogonal matrix U and positive semi-definite P.

Compute Moore-Penrose pseudoinverse A⁺ for non-square rectangular matrices.

Decompose matrix A = Q · R into orthogonal matrix Q and upper triangular R.

Convert matrix into Row Echelon Form (REF) or RREF.

Compute singular values σ_i = √(λ_i(A*A)) of matrix A.

Decompose matrix A = U Σ Vᵀ using Singular Value Decomposition.

Compute Kronecker matrix tensor product A ⊗ B.

Calculate cos⁻¹(x) in degrees and radians.

Calculate sin⁻¹(x) in degrees and radians.

Calculate tan⁻¹(x) and arctan2(y, x) 2-argument angle.

Apply cofunction identities sin(90°-θ) = cos(θ) step-by-step.

Compute csc(x) = 1/sin(x) for any angle.

Calculate cosine value for angles in degrees, radians, or turns.

Compute cot(x) = 1/tan(x) ratio.

Compute sin(2θ), cos(2θ), and tan(2θ) double angle values.

Compute sin(θ/2), cos(θ/2), and tan(θ/2) half angle values.

Compute arcsin, arccos, arctan, arccsc, arcsec, arccot simultaneously.

Solve any triangle side c² = a² + b² - 2ab·cos(C).

Solve non-right triangles using a/sin(A) = b/sin(B) = c/sin(C).

Calculate horizontal phase shift c/b for y = A·sin(bx - c) + d.

Reduce sin²(x) and cos²(x) powers to linear cosine expressions.

Interactive quiz to test right triangle SOH CAH TOA skills.

Test trig knowledge with instant feedback questions.

Compute sec(x) = 1/cos(x) for any angle.

Calculate sine ratio for any input angle.

Expand sin(A ± B), cos(A ± B), and tan(A ± B) step-by-step.

Compute tan(x) = opposite / adjacent ratio.

Verify and simplify complex trigonometric identity expressions.

Compute all 6 primary and reciprocal trig functions at once.

Solve right triangles, acute/obtuse triangles, and trig ratios.

Interactive unit circle showing exact (x, y) coordinates for special angles.

Calculate total surface area for 2D plane geometric figures.

Compute rectangle area A = length × width and perimeter P = 2(l+w).

Calculate area of lune / crescent between two intersecting circular arcs.

Calculate 2D center of mass centroid for discrete point masses.

Find geometric center centroid coordinates (x̄, ȳ) of 2D shapes.

Calculate circle chord length c = 2r·sin(θ/2) from radius and central angle.

Identify parabolas, ellipses, hyperbolas, and circles from general quadratic equations.

Calculate cross-sectional area of structural beams and pipes.

Calculate arc length L = 8r and area A = 3πr² of a rolling cycloid curve.

Calculate area A = πab, perimeter, eccentricity, and foci of ellipses.

Calculate golden rectangle dimensions using golden ratio φ ≈ 1.618.

Calculate regular hexagon area A = (3√3/2)a², perimeter, and diagonals.

Calculate surface area and boundary curve length of 3D non-orientable Möbius strip.

Calculate area moment of inertia I_x, I_y for 2D cross sections.

Calculate regular 8-sided octagon area A = 2(1+√2)a² and side lengths.

Find orthocenter intersection point of triangle altitudes.

Calculate regular 5-sided pentagon area, perimeter, and internal angles (108°).

Calculate boundary perimeter distance for arbitrary 2D polygon shapes.

Analyze 4-sided quadrilaterals: area, diagonals, and internal angles.

Interactive geometry practice quiz for calculating rectangular areas.

Calculate area A = ½·n·a·r, perimeter, and interior angles for n-gon.

Solve AB + BC = AC collinear segment length equations.

Calculate circular segment area A = ½r²(θ - sin θ).

Calculate arc length of Archimedean spiral r = a + bθ.

Compute square area A = s², perimeter P = 4s, and diagonal d = s√2.

Calculate area and perimeter of n-pointed regular star polygons.

Calculate trapezoid area A = ½(a + b)h, median, and leg lengths.

Calculate special right triangle side ratios 1 : √3 : 2.

Calculate isosceles right triangle side ratios 1 : 1 : √2.

Calculate right triangle area A = ½·a·b from legs a and b.

Find radius R = abc / (4A) of circle passing through all 3 vertices.

Classify triangles as equilateral, isosceles, scalene, acute, right, or obtuse.

Compute equilateral triangle area A = (√3/4)a² and height h = (√3/2)a.

Calculate triangle area A = √(s(s-a)(s-b)(s-c)) from 3 side lengths.

Calculate right triangle hypotenuse c = √(a² + b²).

Calculate isosceles triangle area, base angle, legs, and altitude.

Calculate triangle perimeter P = a + b + c.

Solve a² + b² = c² for any missing right triangle side.

Generate integer Pythagorean triples (3,4,5), (5,12,13), (8,15,17).

Complete right triangle solver for sides, angles, area, and perimeter.

Find unknown sides and acute angles using trig ratios.

Solve unknown side lengths using scale factor ratio of similar triangles.

Solve 30-60-90 and 45-45-90 special right triangles instantly.

Find missing third angle A + B + C = 180°.

Calculate triangle area using base/height, SAS, SSS, or ASA.

Calculate altitude height h = 2A / b for any base.

Check if 3 side lengths satisfy a + b > c triangle condition.

Calculate arc length s = r·θ (radians) or s = 2πr(θ/360°).

Calculate circle area A = πr² or A = (π/4)d² instantly.

Complete circle solver: input radius, diameter, area, or circumference.

Explore inscribed angle theorem, chord theorem, and tangent-secant theorem.

Calculate circle perimeter C = 2πr = πd.

Find radius r = C / (2π) from circumference.

Calculate net rotations when one coin rolls around another identical coin.

Convert standard (x - h)² + (y - k)² = r² to general form x² + y² + Dx + Ey + F = 0.

Calculate pie slice sector area A = ½r²θ.

Calculate half circle area A = ½πr² and perimeter P = πr + 2r.

Calculate side length s = r√2 of largest square inscribed in a circle.

Calculate height gain when adding 1 meter to string wrapping around Earth.

Find point of tangency and equation of line tangent to circle.