Free Math Calculators
Solve common math tasks online: permutations, geometry, stats and calculus helpers. Each tool shows steps or results locally so you can check homework or quick equations without an account.
Permutation And Combination
Compute P(n,r) and C(n,r) for choosing r items from n.
OpenFactor
List all positive factors of an integer.
OpenCombination
Combinations C(n,r) = n! / (r!(n−r)!).
OpenScientific Notation
Convert a number to scientific notation a × 10^b, or expand it.
OpenPercent Error
Percent error between an experimental and a true value.
OpenZ Score
Z = (x − μ) / σ for a raw score in a normal distribution.
OpenFactorial
Compute n! for integers up to 170.
OpenRemainder
Integer division quotient and remainder (modulo).
OpenVolume Of A Sphere
V = 4/3 π r³.
OpenCovariance
Sample or population covariance of paired x and y values.
OpenAverage
Arithmetic mean of a list of numbers.
OpenArithmetic Sequence
nth term and sum of an arithmetic sequence.
OpenDistance Formula
Distance between two points in the plane.
OpenGCF
Greatest common factor of two or more integers.
OpenMean
Arithmetic mean of a data set.
OpenMidpoint
Midpoint of the segment joining two points.
OpenSig Fig
Count significant figures and round a number to n sig figs.
OpenCircumference
Circumference of a circle from radius or diameter.
OpenArea Of A Sector
Sector area = (θ/360) π r² for degrees, or (1/2) r² θ for radians.
OpenPythagorean Theorem
Find the missing side of a right triangle (a² + b² = c²).
OpenCone Volume
V = (1/3) π r² h.
OpenCBM
Cubic meters from length × width × height (and optional quantity).
OpenRectangle Area
Area and perimeter of a rectangle.
OpenSlope
Slope m = (y₂ − y₁)/(x₂ − x₁) of a line through two points.
OpenCylinder Volume
V = π r² h for a right circular cylinder.
OpenProbability
Basic probability P = favorable / possible, plus complements.
OpenVariance
Sample or population variance of a data set.
OpenSummation
Sum Σ f(k) from k = start to end (integer bounds).
OpenTrapezoid Area
Area = (a + b)/2 × h for parallel sides a, b and height h.
OpenStandard Deviation
Sample or population standard deviation.
OpenLog
Logarithm of x in base b (default natural or common).
OpenAntilog
Antilog: base^y (inverse of logarithm).
OpenStandard Form
Write a number in standard form a × 10^n (1 ≤ |a| < 10).
OpenArc Length
Arc length of a circle sector from radius and central angle.
OpenLimit
Numerical limit of f(x) as x → a (from left, right, or both).
OpenExpected Value
E[X] = Σ xᵢ pᵢ for discrete outcomes.
OpenCross Product
Cross product of two 3D vectors a × b.
OpenDerivative
Symbolic derivative dy/dx of an expression in x (via math.js).
OpenQuadratic Formula
Solve ax² + bx + c = 0.
OpenIntegral
Numerical definite integral of f(x) from a to b (trapezoidal rule).
OpenChain Rule
Differentiate nested functions: d/dx f(g(x)) = f′(g(x))·g′(x).
OpenImplicit Differentiation
Approximate dy/dx for F(x,y)=0 via −Fₓ/Fᵧ at a point.
OpenPartial Derivative
Symbolic ∂f/∂x or ∂f/∂y.
OpenDirectional Derivative
∇f · û at a point in direction ⟨a,b⟩ (2D).
OpenThird Derivative
Third derivative f\
OpenSecond Derivative
Second derivative f\
OpenNormal Line
Equation of the normal line to y=f(x) at x₀.
OpenQuotient Rule
(u/v)\
OpenProduct Rule
(uv)\
OpenDefinite Integral
Numerical ∫ₐᵇ f(x) dx.
OpenIndefinite Integral
Antiderivative for polynomials and basic forms (best-effort symbolic via math.js simplify patterns / numeri…
OpenDerivative Graph
Plot f(x) and a numerical derivative on [a,b].
OpenCurved Line Slope
Instantaneous slope f\
OpenExtreme Points
Scan [a,b] for approximate local max/min of f (critical points where f\
OpenArea Under the Curve
Approximate area between y=f(x) and the x-axis from a to b.
OpenLong Division
Divide integers and show quotient and remainder.
OpenTrapezoidal Rule
Approximate ∫ₐᵇ f(x) dx with n trapezoids.
OpenFourier Transform
Discrete Fourier Transform (DFT) of a real sample sequence.
OpenLaplace Transform
Laplace transforms for common time-domain templates.
OpenTrigonometric Substitution
Suggest a trig sub for √(a²−x²), √(a²+x²), or √(x²−a²).
OpenU Substitution
Rewrite ∫ f(g(x)) g\
OpenImproper Integral
Approximate improper integrals with a large finite cutoff.
OpenIntegration by Parts
Set up ∫ u dv = uv − ∫ v du.
OpenIntegration by Partial Fractions
Decompose (px+q)/((x-a)(x-b)) into A/(x-a)+B/(x-b).
Open
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