Math Calculators
Select a calculator below to perform fast, accurate calculations.
Vector Direction Angle Calculator
Find 2D direction angle θ and 3D direction cosines (cos α, cos β, cos γ).
MathResultant Vector Calculator
Calculate resultant vector magnitude ||R||, direction angle, and component form.
MathVector Component Calculator
Resolve 2D & 3D vectors into orthogonal components Vx, Vy, Vz and unit vectors.
MathRadians to Degrees Calculator
Convert radians to degrees with exact π cancellation and DMS (Deg, Min, Sec).
MathDegrees to Radians Calculator
Convert degrees to radians with exact π fraction reduction and decimal values.
MathUnit Circle Calculator
Find terminal point (x, y) coordinates and exact values for all 6 trig functions.
MathCoterminal Angle Calculator
Find positive and negative coterminal angles θ + 360°k in degrees or radians.
MathReference Angle Calculator
Find acute reference angle θ' in degrees or radians across all 4 quadrants.
MathLaw of Cosines Calculator
Solve missing sides and angles for SSS and SAS cases using the Cosine Rule.
MathLaw of Sines Calculator
Solve AAS, ASA, and SSA ambiguous triangle cases using the Sine Rule.
MathPythagorean Theorem Calculator
Solve missing sides (a, b, c) and check integer triples using a² + b² = c².
MathHypotenuse Calculator
Calculate hypotenuse c using 2 legs, a leg and angle, or area step-by-step.
MathTriangle Perimeter Calculator
Calculate triangle perimeter using 3 sides, right triangle legs, SAS, or coordinates.
MathTriangle Area Calculator
Calculate triangle area using base & height, 3 sides (Heron's), SAS, or coordinates.
MathOblique Triangle Calculator
Solve non-right triangles (SSS, SAS, AAS, ASA, SSA) step-by-step.
MathRight Triangle Calculator
Calculate missing sides, hypotenuse, angles, area, & perimeter step-by-step.
MathTrigonometric Identities Calculator
Evaluate Pythagorean, Double Angle, Half Angle, and Sum/Diff identities step-by-step.
MathArctangent Calculator
Calculate inverse tangent arctan(x) & atan2(y, x) step-by-step in degrees & radians.
MathArccosine Calculator
Calculate inverse cosine arccos(x) step-by-step in degrees & radians.
MathArcsine Calculator
Calculate inverse sine arcsin(x) step-by-step in degrees & radians.
MathTangent Calculator
Calculate tangent function tan(θ), line slope m, and inverse tangent arctan(x) step-by-step.
MathCosine Calculator
Calculate cosine function cos(θ) and inverse cosine arccos(x) step-by-step.
MathSine Calculator
Calculate sine function sin(θ) and inverse sine arcsin(x) step-by-step.
MathTrigonometry Calculator
Calculate all 6 trigonometric functions (sin, cos, tan, csc, sec, cot) for any angle step-by-step.
MathAngle Between Vectors Calculator
Calculate the angle θ between two 2D or 3D vectors step-by-step in degrees & radians.
MathVector Projection Calculator
Calculate vector projection proj_v(u) and scalar component comp_v(u) step-by-step.
MathUnit Vector Calculator
Calculate normalized unit vector v̂ = v / ||v|| for 2D and 3D vectors step-by-step.
MathVector Magnitude Calculator
Calculate vector magnitude ||v|| for 2D, 3D, and 4D vectors step-by-step.
MathCross Product Calculator
Calculate 3D vector cross product A×B step-by-step with magnitude and area.
MathDot Product Calculator
Calculate scalar dot product A·B for 2D and 3D vectors step-by-step.
MathVector Subtraction Calculator
Calculate difference vector D = A - B for 2D and 3D vectors step-by-step.
MathVector Addition Calculator
Calculate resultant vector R = A + B for 2D and 3D vectors step-by-step.
MathVector Calculator
Perform 2D and 3D vector operations: dot product, cross product, magnitude, and angle.
MathEigenvector Calculator
Calculate basis and normalized unit eigenvectors for 2x2 matrices step-by-step.
MathEigenvalue Calculator
Calculate eigenvalues and eigenvectors for 2x2 matrices step-by-step.
MathTranspose Matrix Calculator
Calculate transpose matrix Aáµ€ for 2x2 and 3x3 matrices and test matrix symmetry.
MathInverse Matrix Calculator
Calculate inverse matrix A¹ for 2x2 and 3x3 square matrices step-by-step using adjugate.
MathDeterminant Calculator
Calculate matrix determinant det(A) for 2x2 and 3x3 square matrices step-by-step.
MathMatrix Multiplication Calculator
Multiply 2x2 and 3x3 matrices step-by-step using row-by-column dot product multiplication.
MathMatrix Addition Calculator
Add and subtract 2x2 and 3x3 matrices component-wise step-by-step.
MathMatrix Calculator
Perform matrix addition, subtraction, multiplication, determinant, inverse, and transpose.
MathLong Division Calculator
Perform arithmetic long division step-by-step, find integer quotient Q, remainder R, and decimal expansion.
MathSynthetic Division Calculator
Divide polynomials P(x) by linear divisors (x - k) step-by-step, find quotient Q(x) and remainder R.
MathCompleting the Square Calculator
Convert quadratic equations ax² + bx + c = 0 into vertex form y = a(x - h)² + k step-by-step.
MathFactoring Polynomials Calculator
Factor polynomial expressions ax² + bx + c into linear binomial factors, GCF, and difference of squares.
MathPolynomial Calculator
Evaluate polynomial expressions P(x), classify degree, and calculate first derivative P'(x).
MathSystem of Equations Calculator
Solve 2x2 systems of linear equations step-by-step using Cramer's Rule determinants D, D_x, and D_y.
MathQuadratic Formula Calculator
Solve quadratic equations ax² + bx + c = 0 step-by-step using discriminant Δ = b² - 4ac.
MathLinear Equation Calculator
Calculate linear equations from two points, slope m, y-intercept b, and standard form Ax + By = C.
MathAlgebra Calculator
Solve linear algebraic equations (ax + b = c) step-by-step for variable x and verify solutions.
MathSimplifying Radicals Calculator
Simplify radical expressions c&supn;√x into a&supn;√b form using prime factor power decomposition.
MathNth Root Calculator
Calculate principal nth roots (&supn;√x) for any degree index n, fractional exponents, and power inverses.
MathCube Root Calculator
Calculate cube roots (&neib;x) for positive/negative numbers, simplify cube radicals, and check perfect cubes.
MathSquare Root Calculator
Calculate principal square roots (√x), simplify radicals into a√b form, and check perfect squares.
MathLog Base 2 Calculator
Calculate binary logarithms log2(x), computer bit depth requirements, and powers of 2.
MathNatural Log Calculator
Calculate natural logarithms ln(x) with Euler's base e (≈ 2.71828) and exponential inverses.
MathLogarithm Calculator
Calculate logarithms log_b(x) for any base, natural log (ln x), common log, and change of base.
MathScientific Notation Calculator
Convert decimals to scientific notation (a × 10^b), E-notation, and engineering notation.
MathExponent Calculator
Calculate power of numbers (b^x), negative exponents, fractional roots, and scientific notation.
MathFactorial Calculator
Calculate n! with BigInt precision, trailing zeros count, digit length, and Stirling approximation.
MathCombination Calculator
Calculate combinations C(n, r) where order does not matter, with repetition, and Pascal symmetry.
MathPermutation Calculator
Calculate permutations P(n, r) where order matters, with replacement, and circular seating.
MathProbability Calculator
Calculate event probabilities P(A), complements P(not A), independent combined events, and odds.
MathSample Size Calculator
Calculate required survey sample size (n) with confidence levels, margin of error, and population correction.
MathVariance Calculator
Calculate sample variance (s²), population variance (σ²), and standard deviations.
MathStandard Deviation Calculator
Calculate sample SD (s), population SD (σ), sample variance (s²), and population variance (σ²).
MathRange Calculator
Calculate statistical range (R = Max − Min), maximum, minimum, and mid-range for datasets.
MathMode Calculator
Find the most frequent number or value, classify unimodal/bimodal distributions, and view frequency tallies.
MathMedian Calculator
Find the exact middle number of any dataset (odd or even sample sizes) with sorted order.
MathMean Calculator
Calculate arithmetic mean (xÌ„ = ˆ‘x/n), sum, sample count, geometric mean, and range.
MathInverse Proportion Calculator
Calculate inverse variation (y = k/x), constant product (k = x·y), and worker-time rates.
MathDirect Proportion Calculator
Calculate direct variation (y = kx), constant of proportionality (k = y/x), and scale quantities.
MathProportion Calculator
Solve direct (A/B = C/D) and inverse (A·B = C·D) proportion equations with step-by-step proofs.
MathAspect Ratio Calculator
Resize images and videos proportionally without distortion (16:9, 4:3, 1:1, 9:16).
MathGolden Ratio Calculator
Calculate Golden Ratio (Phi Φ ‰ˆ 1.618034) dimensions for UI layouts, design, and architecture.
MathEquivalent Ratios Calculator
Generate sets of equivalent ratios or test ratio equivalence with cross-multiplication proofs.
MathSimplifying Ratios Calculator
Simplify 2-part, 3-part, and multi-part ratios to lowest integer terms with multi-term GCD.
MathRatio Calculator
Simplify ratios to lowest terms, solve proportions (A:B = C:D), and calculate unit ratios.
MathReducing Fractions Calculator
Reduce proper and improper fractions to lowest terms with step factor division chains.
MathSimplifying Fractions Calculator
Reduce proper and improper fractions to lowest terms with GCD division steps.
MathDividing Fractions Calculator
Divide proper fractions, improper fractions, and mixed numbers using Keep-Change-Flip.
MathMultiplying Fractions Calculator
Multiply proper fractions, improper fractions, and mixed numbers with cross-cancellation steps.
MathSubtracting Fractions Calculator
Subtract proper fractions, improper fractions, and mixed numbers with step-by-step LCD work.
MathAdding Fractions Calculator
Add fractions with like and unlike denominators, mixed numbers, and improper fractions.
MathOrdering Fractions Calculator
Order multiple fractions from least to greatest or greatest to least with LCD steps.
MathComparing Fractions Calculator
Compare two fractions or mixed numbers with cross-multiplication proofs and LCD fractions.
MathEquivalent Fractions Calculator
Generate equivalent fractions and check fraction equivalence with cross-multiplication proofs.
MathPercent to Fraction Calculator
Convert percentages to simplified fractions, mixed numbers, and decimals.
MathFraction to Percent Calculator
Convert proper, improper, and mixed fractions to percentages.
MathDecimal to Fraction Calculator
Convert terminating and repeating decimals to simplified fractions and mixed numbers.
MathFraction to Decimal Calculator
Convert proper, improper, and mixed fractions to exact decimal values.
MathImproper Fraction Calculator
Convert improper fractions to mixed numbers and mixed numbers to improper fractions.
MathMixed Number Calculator
Add, subtract, multiply, and divide mixed numbers with automatic improper fraction conversion.
MathFraction Simplifier
Simplify fractions to lowest terms using Greatest Common Divisor (GCD) and prime factor breakdown.
MathFraction Calculator
Add, subtract, multiply, and divide proper, improper, and mixed fractions.
MathPercentage Change Calculator
Calculate percentage change from an original old value to a new final value.
MathPercentage Difference Calculator
Calculate direction-neutral percentage difference and midpoint discrepancy between two numbers.
MathPercentage Decrease Calculator
Calculate percentage decrease and relative reduction between two numbers.
MathPercentage Increase Calculator
Calculate percentage increase and relative growth between two numbers.
MathPercentage Calculator
Calculate percentages, percentage changes, and percentage differences easily.