Mathematics Calculators & Tools
Comprehensive mathematical utilities covering arithmetic, algebra, fractions, ratios, geometry, trigonometry, calculus, statistics, linear algebra, and discrete number systems with step-by-step solutions. Aligned with secondary, high school, and undergraduate curricula (AP Calculus, IB Math, GCSE, and University STEM).
Basic Calculator
Standard arithmetic calculations with memory store, decimal precision, and history tape
Average Calculator
Calculate arithmetic mean, median, mode, range, and geometric mean from numbers
Fraction Calculator
Add, subtract, multiply, and divide fractions with common denominator steps and reduction
Fraction Simplifier
Reduce fractions to simplest irreducible form and convert improper to mixed numbers
Percentage Calculator
Calculate percentages, percentage change, markups, and discounts with steps
Ratio Calculator
Solve missing proportion terms (A:B = C:D), simplify ratios, and scale dimensions
Algebra Calculator
Evaluate polynomials, expand binomial products using FOIL, and compute power-rule derivatives
Equation Solver
Solve single-variable equations and 2x2 simultaneous linear systems via Cramer’s Rule
Linear Equation Solver
Solve linear equations ax + b = c with isolated steps and variable solutions
Quadratic Equation Solver
Calculate real and complex roots, discriminant, and parabola vertex for ax² + bx + c = 0
Factoring Calculator
Find all integer factors, factor pairs, and canonical prime factor trees with exponents
Exponent Calculator
Calculate powers, negative exponents, fractional powers, and scientific notation
Logarithm Calculator
Calculate natural logarithm ln(x), common log₁₀(x), binary log₂(x), and arbitrary base log_b(x)
Geometry Calculator
Calculate 2D areas, perimeters, 3D volumes, and surface areas across geometric shapes
Triangle Calculator
Calculate triangle area via Heron’s formula, interior angles via Law of Cosines, and perimeter
Circle Calculator
Calculate circle radius, diameter, circumference, surface area, arc length, and sector area
Area Calculator
Calculate 2D surface area for rectangles, squares, triangles, circles, trapezoids, and ellipses
Volume Calculator
Calculate 3D volume and total surface area for cubes, prisms, cylinders, spheres, and cones
Pythagorean Calculator
Solve right triangles using a² + b² = c² with exact simplified radicals and decimal values
Trigonometry Calculator
Calculate sin, cos, tan, csc, sec, cot, and inverse functions in degrees or radians
Sine Calculator
Evaluate sin(θ) for any angle with exact unit circle coordinates and radian conversions
Cosine Calculator
Evaluate cos(θ) for any angle with exact unit circle coordinates and conversions
Tangent Calculator
Evaluate tan(θ) = sin(θ)/cos(θ) with angle slopes and asymptote detection
Degree / Radian Converter
Convert angles bidirectionally between Degrees (°) and Radians (rad) with exact π multiples
Derivative Calculator
Compute polynomial and trigonometric derivatives with power rule and chain rule steps
Integral Calculator
Calculate definite and indefinite integrals with antiderivatives and area under the curve
Limit Calculator
Evaluate mathematical limits lim(x→c) with direct substitution, L’Hôpital’s rule, and one-sided limits
Statistics Calculator
Calculate sample and population variance, standard deviation, mean, and interquartile range
Mean Calculator
Calculate arithmetic mean, sum of observations, and dataset sample count with steps
Median Calculator
Find the exact middle median value of any sorted dataset, resistant to extreme outliers
Standard Deviation Calculator
Calculate sample std dev (s) and population std dev (σ) with step-by-step variance
Variance Calculator
Calculate sample variance s² and population variance σ² from squared deviations
Probability Calculator
Calculate event probabilities, permutations (nPr), combinations (nCr), and odds
Permutation Calculator (nPr)
Calculate permutations nPr where order matters using exact factorial formulas
Combination Calculator (nCr)
Calculate combinations nCr = n! / [r!(n-r)!] where order is irrelevant
Matrix Calculator
Add, multiply, invert, and transpose 2x2 and 3x3 matrices with step-by-step linear algebra
Determinant Calculator
Calculate determinants det(A) for 2x2 and 3x3 matrices using expansion by minors
Vector Calculator
Calculate 3D vector addition, dot product, cross product, magnitude, and angles
GCD Calculator (GCF / HCF)
Find Greatest Common Divisor using step-by-step Euclidean division algorithm
LCM Calculator
Calculate Least Common Multiple using the fundamental formula lcm(a, b) = |a·b| / gcd(a, b)
Prime Number Checker
Check primality up to 100 trillion, find divisors, and view prime factor trees
Prime Factorization Calculator
Decompose any positive integer into canonical prime factors with powers and tree steps
Fibonacci Calculator
Generate Fibonacci numbers Fn = Fn-1 + Fn-2 and compute golden ratio approximations
Sequence & Series Calculator
Calculate arithmetic and geometric sequence n-th terms, partial sums, and series formulas
Coordinate Geometry Calculator
Calculate 2D distance, midpoint, slope m, and line equations between points (x1, y1) and (x2, y2)
Graphing Calculator
Interactive HTML5 Canvas function plotter with Cartesian coordinate grid, zoom, and presets
Number to Words Converter
Convert numbers into formal written English words and check-writing currency formats
Roman Numeral Converter
Convert numbers bidirectionally between standard Arabic numbers (1–3999) and Roman numerals
Binary Converter
Convert base-2 binary strings into decimal, hexadecimal, octal, and ASCII text
Decimal Converter
Convert base-10 decimal numbers into binary, hexadecimal, octal, and BCD
Hex Converter
Translate hexadecimal strings into decimal, binary, octal, and ASCII text
Octal Converter
Convert base-8 octal numbers to decimal, binary, hex, and Unix chmod file permissions
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