Adding and Subtracting Polynomials CalculatorAdd or subtract two polynomials of any degree, combining like terms automatically with the resulting degree and term count.Adjoint Matrix CalculatorFind the adjugate (classical adjoint) of a 2x2 or 3x3 matrix: the transpose of its cofactor matrix, used in the inverse formula A-inv = adj(A) / det(A).Arc Length & Sector Area CalculatorCalculate arc length, sector area, chord, and segment area from radius and central angleAspect Ratio CalculatorSimplify any width by height to its lowest aspect ratio, or resize while preserving the ratioAssociative Property CalculatorVerify the associative property of addition and multiplication by computing both groupings for any three numbers.Average CalculatorAverage calculator: find the arithmetic mean, median, and mode of any list of numbers with instant statistics resultsBase Arithmetic CalculatorAdd, subtract, multiply, and divide numbers in binary, octal, decimal, or hexadecimalBig Number CalculatorArbitrary-precision arithmetic - add, multiply, power, and factorial of very large integersBig-O Operation Count CalculatorCompare operation counts across common Big-O complexity classes for a given input size, from constant time up to factorial timeCartesian to Polar CalculatorConvert a 2D point (x, y) to polar coordinates (r, theta), where r is the distance from origin and theta = atan2(y, x). Both radians and degrees supplied.Centroid of a Triangle CalculatorFind the centroid of a triangle from its three vertices: the average of the vertices, which is the center of mass and the intersection of the three medians.Circle CalculatorFind the area, circumference, diameter, or radius of a circle from any single known measurement with step-by-step formulas. Free.Circumcenter CalculatorFind the circumcenter of a triangle from three vertices: the point equidistant from all three, which is the center of the circle through the vertices.Circumscribed Circle CalculatorFind the circumscribed circle of a triangle: center (circumcenter) and radius R = abc / (4K), where K is the triangle area.Cofactor Matrix CalculatorFind the cofactor matrix of a 2x2 or 3x3 matrix. Each entry is the signed minor: the determinant of the submatrix remaining after deleting row i and column j.Collatz Sequence CalculatorRun the Collatz sequence from any starting integer and find the number of steps to reach one and the highest value reachedComplex Number CalculatorAdd, subtract, multiply, and divide complex numbers, with modulus, argument, and polar formComplex Root CalculatorFind all n-th roots of a complex number w = a + bi using De Moivre's formula. Returns the n distinct roots in rectangular and polar form.Concrete CalculatorCalculate concrete volume in cubic yards and bags needed for slabs, footings, columns, or steps. Includes waste factor and cost estimate. Free.Condition Number CalculatorCompute the condition number kappa(A) = norm(A) times norm(A inverse) for a 2x2 or 3x3 matrix - measures how sensitive Ax = b is to small input changes.Cone CalculatorCalculate the volume, slant height, and total surface area of a right circular cone from its radius and heightContinued Fraction CalculatorExpand any number into its continued fraction and recover best rational approximations (convergents)Cramer's Rule CalculatorSolve a 2x2 or 3x3 linear system Ax = b using Cramer's rule: x_k = det(A_k) / det(A), where A_k replaces column k of A with b.Cylindrical Coordinates CalculatorConvert between 3D Cartesian (x, y, z) and cylindrical (r, theta, z) coordinates. Useful for problems with rotational symmetry around the z-axis.Dating Theory Calculator (37% Rule)Apply the 37% rule (optimal stopping / secretary problem): how many candidates to evaluate and reject before committing.Decimal to Fraction CalculatorConvert decimals, including repeating decimals, to exact fractions in lowest terms and backDescriptive Statistics CalculatorCalculate mean, median, mode, standard deviation, variance, quartiles, and range for any data set. Free, instant statistics tool.Diagonalize Matrix CalculatorDecompose a 2x2 matrix A as P D P inverse, where D is diagonal of eigenvalues and P has eigenvectors as columns.Digital Root CalculatorFind the digital root of any integer by summing its digits repeatedly until one digit remains. Uses the shortcut 1 + ((n-1) mod 9) for instant results.Distance Between Two Points CalculatorCalculate 2D or 3D distance and midpoint between coordinates using the distance formulaDistance from Point to Plane CalculatorCompute the perpendicular distance from a 3D point (x, y, z) to a plane ax + by + cz + d = 0, plus the signed distance and the foot of the perpendicular.Eigenvalue and Eigenvector CalculatorFind eigenvalues and unit eigenvectors of a 2x2 or 3x3 matrix using the characteristic polynomial det(A - λI) = 0.Elimination Method CalculatorSolve a 2-variable linear system ax + by = c by eliminating one variable. Returns the elimination factor, intermediate equation, and the final x and y.Ellipse CalculatorCalculate the area, circumference, and eccentricity of an ellipse from its two semi-axesExponent CalculatorRaise any base to a power - negative, fractional, and zero exponents - with expanded formExponential Growth CalculatorCalculate final value, growth rate, time, or initial value for exponential growth or decay with discrete or continuous models.Factorial CalculatorCompute n! with the expanded product, trailing-zero count, and digit length for n up to 170Factoring Trinomials CalculatorFactor a quadratic trinomial ax^2 + bx + c into linear factors over integers when possible, or report the discriminant and roots.Fence CalculatorCalculate posts, rails, pickets, and concrete bags needed to build a wood or vinyl fence from total length and spacing. Free results.Fibonacci CalculatorCompute the n-th Fibonacci number F_n where F_0 = 0, F_1 = 1, F_n = F_{n-1} + F_{n-2}. Uses BigInt for exact answers up to n = 200.Flooring CalculatorCalculate total flooring needed including waste factor for any room shape. Supports hardwood, laminate, tile, and carpet. Free results.Fraction CalculatorFraction calculator: add, subtract, multiply, or divide fractions with step-by-step fraction math and automatic simplificationGalileo's Paradox of InfinityExplore Galileo's paradox: natural numbers and perfect squares map one-to-one, yet squares seem rarer. See how infinite sets challenge everyday intuition.Gauss-Jordan Elimination CalculatorSolve a 2x2 or 3x3 linear system by reducing the augmented matrix [A|b] to reduced row echelon form (RREF) with partial pivoting.Harmonic Number CalculatorCompute the n-th harmonic number H_n = 1 + 1/2 + 1/3 + ... + 1/n and compare to the asymptotic ln(n) + gamma + 1/(2n) - 1/(12n^2) formula.Heron's Formula CalculatorCalculate the area and perimeter of a triangle from its three side lengths using Heron's formulaHilbert's Hotel Paradox CalculatorStep through Hilbert's hotel paradox: a fully booked infinite hotel can still fit one more guest, a busload, or infinitely many new guests. Free online tool.Inscribed Angle CalculatorApply the inscribed angle theorem: an inscribed angle equals half the central angle on the same arc. Convert between central, inscribed, and arc angle measures.Integration by Completing the Square CalculatorIntegrate 1 / (ax^2 + bx + c) by completing the square. Returns the completed-square form and the antiderivative (arctan or natural log).Latus Rectum CalculatorCompute the length of the latus rectum for a parabola, ellipse, or hyperbola from its standard parameters - the focal chord perpendicular to the major axis.Law of Cosines CalculatorSolve a triangle from two sides and the included angle using the law of cosines, with the third side, area, and remaining anglesLCM & GCD CalculatorFind the Least Common Multiple and Greatest Common Divisor of two or more integers using the Euclidean algorithm with step-by-step work shownLinear Combination CalculatorCompute the linear combination c1·v1 + c2·v2 + ... of up to four vectors with the resulting vector and its magnitude.Linear Interpolation CalculatorInterpolate or extrapolate any value between or beyond two known data points on a straight line using linear interpolation. Free.Logarithm CalculatorCalculate natural logarithm, log base 10, log base 2, or any custom base logarithm for any positive number. Free, instant results.Long Division CalculatorDivide with a full step-by-step long-division worklog, remainder, and decimal resultLottery Odds CalculatorCalculate your exact odds of winning any lottery jackpot from ticket numbers and range, and compare to real-life probability events. Free.Matrix CalculatorAdd, subtract, and multiply 2x2 or 3x3 matrices, find the determinant, and compute the inverse matrix. Free, instant matrix calculator.Matrix Inverse CalculatorInvert a 2×2, 3×3, or 4×4 matrix with determinant, adjugate, and step-by-step Gauss–Jordan outputMatrix Norm CalculatorCompute the Frobenius, 1, infinity, and max norms of a 2x2 or 3x3 matrix - measures of matrix size used in numerical analysis and machine learning.Matrix Power CalculatorCompute A to the power n by repeated multiplication for a 2x2 or 3x3 square matrix with non-negative integer exponent.Matrix Rank CalculatorFind the rank of a 2x2, 3x3, or 4x4 matrix via row echelon form. Rank equals the number of pivots and the dimension of the row and column spaces.Mixed & Improper Fraction CalculatorConvert mixed numbers to improper fractions and back, reduced, with step-by-step workModular Inverse CalculatorFind the modular multiplicative inverse of any integer modulo n using the extended Euclidean algorithm. Free, instant math tool.Modulo CalculatorFind a mod n with quotient and remainder, including correct handling of negative numbersMultiplying Binomials CalculatorMultiply two binomials (ax + b)(cx + d) using the FOIL method and get the expanded trinomial with step-by-step product terms.Multiplying Polynomials CalculatorMultiply two polynomials of any degree by entering space-separated coefficients (highest degree first) and get the expanded product.Newton's Method CalculatorFind a root of a function iteratively with Newton–Raphson and watch the convergence per stepNumerical Integration CalculatorApproximate a definite integral with the trapezoidal, midpoint, and Simpson rules and compare errorOrthocenter CalculatorFind the orthocenter of a triangle from three vertices: the intersection point of the three altitudes (perpendiculars from each vertex to the opposite side).Parallel Line CalculatorFind the equation of the line parallel to y = mx + b that passes through a given point (x, y). The new line has the same slope, different intercept.Partial Fraction Decomposition CalculatorDecompose a proper rational function (cx + d) / (ax^2 + bx + c) into partial fractions when the denominator factors over the reals.Percent Error CalculatorCalculate percent error between a measured or experimental value and the actual or theoretical true value, with signed and absolute error. Free.Percentage CalculatorFree percentage calculator: find what percent X is of Y, percentage change, percentage increase or decrease, and reverse percentagePerfect Cube CalculatorCheck whether an integer is a perfect cube and find its integer cube root. Works on positive and negative numbers using BigInt arithmetic.Perfect Square CalculatorCheck whether a non-negative integer is a perfect square and find its integer square root. Uses BigInt for exact answers on arbitrarily large numbers.Perfect Square Trinomial CalculatorCheck whether ax^2 + bx + c is a perfect square trinomial and return its (px + q)^2 factored form, or report what is needed.Permutations & Combinations CalculatorCalculate P(n,r) permutations and C(n,r) combinations for any n and r values, with step-by-step factorial formulas. Free, instant.Perpendicular Line CalculatorFind the equation of the line perpendicular to y = mx + b that passes through a given point (x, y). The new slope is the negative reciprocal of m.Polar to Cartesian CalculatorConvert polar coordinates (r, theta) to 2D Cartesian (x, y) using x = r times cos(theta) and y = r times sin(theta). Accepts degrees or radians.Polygon Area CalculatorFind the area of a regular polygon, or any irregular polygon from its vertex coordinatesPolynomial Roots CalculatorFind the real and complex roots of quadratic, cubic, and quartic polynomials with step-by-step solutions. Free, instant math tool.Pool Volume CalculatorCalculate pool volume in gallons and liters for rectangular, oval, or round poolsPopulation & Sample Standard Deviation CalculatorCalculate population standard deviation, sample standard deviation, and variance from any data set with mean and sum of squares. Free.Power Mod CalculatorCompute a^b mod m for arbitrarily large integers using fast modular exponentiation (binary method) - the backbone of RSA and modular arithmetic.Prime Number CheckerCheck if a number is prime, find its prime factorization, or generate all prime numbers up to N using the Sieve of Eratosthenes. Free.Probability CalculatorCalculate event probability using the classical formula, plus combinations C(n,r) and permutations P(n,r) for any scenarioProgrammer Base Converter with ASCIIConvert between binary, octal, decimal, and hex with 0b/0o/0x prefix support and ASCII character outputPseudoinverse CalculatorCompute the Moore-Penrose pseudoinverse of a 2x2 or 3x2 full-rank matrix, used for least-squares solutions when A is not square or not invertible.Pythagorean Theorem CalculatorSolve a right triangle - find a missing side, the angles, perimeter, and area from a² + b² = c²Pythagorean Triples CalculatorGenerate Pythagorean triples via Euclid's formula (m^2-n^2, 2mn, m^2+n^2), or check if three integers satisfy a^2 + b^2 = c^2. Identifies primitive triples.Quadratic Formula CalculatorSolve ax² + bx + c = 0 and find real or complex roots using the quadratic formula, with discriminant analysis and vertex coordinatesQuaternion CalculatorAdd, subtract, multiply, conjugate, or invert quaternions of the form w + xi + yj + zk - the algebra used for 3D rotations and computer graphics.Quick Base Converter (Bin/Oct/Dec/Hex)Instantly convert a whole number between binary, octal, decimal, and hexadecimalRatio CalculatorSimplify ratios to lowest terms, solve proportion equations for a missing value, and scale ratios up or down to any target quantityRecurrence Sequence CalculatorGenerate terms of a linear recurrence such as Fibonacci or Lucas from your own coefficientsRoman Numeral ConverterConvert between Arabic numbers and Roman numerals instantly - supports numbers from 1 to 3,999 with standard and modern notationRoom Paint & Cost CalculatorEstimate gallons of paint and total cost for a room from its dimensions, doors, windows, and number of coatsRotation CalculatorRotate a 2D point (x, y) counter-clockwise by an angle around a chosen center (cx, cy). Uses the standard rotation matrix.Rounding & Significant Figures CalculatorRound to significant figures, decimal places, or nearest unit, and count the sig figsRow Echelon Form CalculatorReduce a 2x2 or 3x3 matrix to row echelon form (REF) by forward elimination with partial pivoting. The REF has zeros below each leading entry.Scientific CalculatorFull-featured scientific calculator with trigonometry, logarithms, exponents, factorial, and memoryScientific Notation CalculatorConvert numbers to and from scientific notation, find the coefficient and exponent, and see the full expanded form. Ideal for chemistry, physics, and astronomy.Sequence CalculatorGenerate arithmetic or geometric sequences, find the nth term, and calculate the partial sum for any starting values. Free, instant.Set Operations CalculatorCompute union, intersection, difference, symmetric difference, and subset checks for two setsSimilar Triangles CalculatorCheck whether two triangles are similar by comparing the ratios of corresponding sides (SSS similarity). Returns the scale factor when similar.Slope CalculatorFind the slope between two points plus the line equation, angle, midpoint, and distanceSpeed Distance Time CalculatorSolve for speed, distance, or time when you know any two of the three values, with unit conversions between mph, km/h, and m/s. Free.Sphere CalculatorCalculate the volume, surface area, and diameter of a sphere from any radius input. Includes unit conversions. Free, instant results.Spherical Coordinates CalculatorConvert between 3D Cartesian (x, y, z) and spherical (rho, theta, phi) using ISO physics convention where phi is the polar angle measured from the z-axis.Square Root & Nth Root CalculatorFind the square root or any nth root, with simplified radical form and perfect-power detectionSubstitution Method CalculatorSolve a 2-variable linear system by isolating x from the first equation and substituting into the second. Shows isolated form, substitution, and final solution.Surface Area CalculatorCalculate total and lateral surface area of cubes, spheres, cylinders, cones, and pyramidsSurface Area to Volume Ratio CalculatorCompute the surface-area-to-volume ratio (SA/V) for spheres, cubes, cylinders, and rectangular boxes.Synthetic Division CalculatorDivide a polynomial by (x - r) using synthetic division. Returns the quotient coefficients and remainder, equal to p(r) by the remainder theorem. Free tool.System of Equations CalculatorSolve a 2x2 or 3x3 system of linear equations using Gaussian elimination with partial pivoting. Detects singular (no unique solution) systems.Torus CalculatorCalculate the volume and surface area of a torus from its major radius and minor tube radiusTriangle CalculatorCalculate area, perimeter, all angles, and missing sides for any triangle using SSS, SAS, AAS, or ASA inputs. Free, instant results.Triangle Congruence CalculatorCheck whether two triangles are congruent by SSS. They are congruent when all three corresponding side lengths match. Free online tool, instant results.Triangle Inequality Theorem CalculatorTest whether three lengths can form a triangle. The triangle inequality requires the sum of any two sides to be strictly greater than the third.Triangular Numbers CalculatorCompute the n-th triangular number T_n = n(n+1)/2, or check whether a given integer is triangular and find its index.Triangulation CalculatorLocate an unknown point from a known baseline and two angles measured to it (classical surveying triangulation).Trigonometry CalculatorCalculate all six trigonometric functions (sin, cos, tan, csc, sec, cot) and their inverses in degrees or radians. Free, instant.Truth Table GeneratorBuild the full truth table for a Boolean expression with AND, OR, NOT, XOR, and implicationVector CalculatorCompute 2D or 3D vector magnitude, sum, dot and cross product, angle, and unit vectorVolume of Solids CalculatorCalculate the volume of a cube, sphere, cylinder, cone, pyramid, or prism with the formula shownWallpaper CalculatorCalculate how many rolls of wallpaper you need - enter wall dimensions, roll width, and pattern repeat length, then subtract doors and windows.
About Math Calculators
Math calculators turn the formulas you half-remember from school into one-click answers you can trust. Our collection covers the everyday workhorses (fractions, percentages, ratios, averages) alongside the heavier algebra and geometry tools you actually need at work: quadratic equations, matrix arithmetic up to 3×3, sequences, logarithms in any base, and full trigonometric functions in both degrees and radians. Every calculator follows the standard order of operations (PEMDAS/BODMAS) and uses IEEE 754 double-precision floating point, so results match what you'd get from a TI-84 or a desktop scientific calculator to roughly 15 significant digits.
Geometry is one of the busiest sections. The triangle calculator solves any triangle from three known parts using the Law of Sines and Law of Cosines, returning area via Heron's formula and reporting whether the configuration is the ambiguous SSA case. The circle calculator works in both directions (radius from area, area from circumference, sector and arc lengths) and the pool, aquarium, and tank-volume tools apply the same primitives to real-world cylinders, ellipsoids, and bow-front shapes. For statistics-adjacent work, the standard deviation and descriptive statistics calculators distinguish between population (σ, divide by N) and sample (s, divide by N−1) estimators. That is the difference that quietly breaks a lot of homework answers.
Algebra and number theory get equal attention. The quadratic formula returns both real and complex roots and shows the discriminant. The LCM/GCD calculator uses the Euclidean algorithm so it handles large integers fast. The number base converter moves cleanly between binary, octal, decimal, and hexadecimal, which is the bridge most people need into the networking and engineering tools elsewhere on the site. Permutations and combinations cover the counting problems behind everything from card hands to A/B test design.
Most users land here while doing something else: sizing a paint job, prepping for the SAT, double-checking a spreadsheet formula, helping a kid with homework, or working out how much concrete a footing needs. The calculators are designed to give the answer first and the working underneath, so you can copy a number into a quote or a worksheet and still see the steps if you need to defend it. Inputs accept fractions, mixed numbers, and scientific notation interchangeably, and every result page links to the closely related tools so you don't get stuck switching between calculators for one project.
When to Use a Math Calculator
- Solving algebra, geometry, or trig problems where you need step-by-step working, not just an answer
- Converting between number bases (binary, hex, decimal) for programming or networking tasks
- Computing descriptive statistics (mean, median, standard deviation) from a list of values
- Sizing real-world projects: pool volume, paint coverage, fence posts, concrete footings
- Checking spreadsheet formulas, homework, or estimates against an independent calculation
- Working with large integers (LCM/GCD, primes, factorials) where mental math breaks down
Frequently Asked Questions
What is the difference between sample and population standard deviation?
Population standard deviation (σ) divides the squared deviations by N and is used when your data covers the entire group of interest. Sample standard deviation (s) divides by N−1 (Bessel's correction) and is the right choice when you're estimating the variability of a larger population from a sample. Most real-world surveys and experiments use the sample formula.
Do these calculators show the steps or just the final answer?
Both. Each calculator prints the result first so you can copy it, then expands the worked solution underneath: formulas substituted with your numbers, intermediate values, and a final answer with units where applicable.
Can I enter fractions, decimals, and scientific notation in the same calculator?
Yes. Inputs like 3/4, 0.75, and 7.5e-1 are all accepted and parsed to the same internal value. Results can be toggled between decimal, fraction, and scientific notation on most pages.
How precise are the results?
Calculations use IEEE 754 double-precision floats, which give roughly 15-17 significant decimal digits, more than enough for engineering, finance, and science work. Where rounding matters (currency, building materials), the calculator rounds in the conventional direction for that domain.
Are these calculators free to use without signing up?
Yes. Every calculator on AllCalculators is free, requires no login, and runs entirely in your browser. None of your inputs are sent to a server.