Math
1,470 math calculators: percentages, fractions, equations, geometry, trigonometry, statistics and number theory. Each one shows the method in plain words, so you get the answer and understand how it was reached, free in your browser.
Standard deviation calculator
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population standard deviation is exactly 2, while the sample one is larger because it divides by 7 instead of…
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Degrees to radians converter
180 degrees is exactly π radians, about 3.1415926536, and the converter shows both the decimal and the π form.
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Hypotenuse calculator
Legs of 3 and 4 give a hypotenuse of 5 and an area of 6, straight from the Pythagorean theorem. Give the hypotenuse and one leg instead and the missing leg…
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Arcsine calculator
The arcsine of 0.5 is 30°, or 0.5235987756 radians, always taken from the principal range between −90° and 90°.
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Trig identity verifier
Check the identities your homework relies on at 30° or any angle you choose, and see sine squared plus cosine squared come out at exactly 1 while the other four…
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Secant, cosecant & cotangent calculator
Find the three reciprocal trig values at once: at 30° the cosecant is 2 and the secant about 1.1547, shown next to sine, cosine and tangent.
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Unit circle calculator
At 30° the unit circle point is (√3/2, 1/2), and the angle is π/6 in radians. Enter any finite angle to get its cosine and sine as a point on the circle of…
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Binomial expansion calculator
(a + b)^4 expands to a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4: enter the power and see every term with its coefficient and exponents, ready to compare with your own…
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Cramer's rule calculator
If 2x + y and x + 3y both equal 5, the solution is (2, 1), with determinants 5, 10 and 5: enter the coefficients and constants and see each unknown as a ratio…
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Cubic equation solver
x³ − 6x² + 11x − 6 = 0 has the roots 3, 2 and 1: enter the four coefficients and get all three roots, real or complex, with the depressed form and discriminant…
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Discriminant calculator
Enter a, b and c and see how many real roots your quadratic has: for x² − 5x + 6 = 0, Δ = 25 − 24 = 1, so there are two distinct real roots.
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Dot product calculator
Enter two vectors of the same length and get their dot product, both lengths and the angle between them: [1, 2, 3] and [4, −5, 6] give 12 and an acute angle.
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2×2 eigenvalue calculator
Enter the four entries of a 2×2 matrix and get its eigenvalues and eigenvectors: the matrix with rows (4, 1) and (2, 3) has trace 7, determinant 10 and…
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Exponential equation solver
Find the exponent that turns a base into a value: in 2ˣ = 8 the answer is 3, shown as a decimal and in exact form, with a check that 2³ really gives 8.
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Factor quadratic calculator
Enter a, b and c and get the quadratic factored into two binomials: x² − 5x + 6 becomes (x − 2)(x − 3).
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Gaussian elimination solver
Solve n linear equations in n unknowns by row reduction: the three-equation example gives the unknowns 2, 3 and −1, with the pivots and 2 row swaps shown so you…
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Linear equation solver
Enter 2x + 3 = 11 and get x equal to 4: subtract 3 from both sides, divide by 2, then check that 2 · 4 + 3 gives 11.
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Logarithm expand & condense
Expand log(x²y/z) into 2 log x + log y − log z, or pack such a sum back into a single logarithm, with each law named step by step.
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Logarithm calculator
Find log base b of x in one step: log base 10 of 100 is 2, and the natural log of 100, 4.60517018599, appears alongside.
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Matrix addition & subtraction
Add two matrices of the same size cell by cell: for two 2 × 2 matrices with entries 1, 2, 3, 4 and 5, 6, 7, 8, the result is 6, 8, 10, 12.
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Matrix determinant calculator
Enter a square matrix and get its determinant: rows 2, 1 and 1, 3 give 5, so the matrix is invertible.
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Matrix rank calculator
Enter rows 1, 2, 3; 4, 5, 6; 7, 8, 9 and get rank 2: elimination leaves only two pivots, so the matrix is not full rank.
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Matrix trace calculator
Get the trace of a square matrix without a hand-written loop: for the rows 2 1 and 1 3 the diagonal is 2 and 3, so the trace is 5. Only the diagonal counts.
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Matrix transpose calculator
Flip a matrix over its main diagonal in one step: rows 1 2 3 and 4 5 6 become columns, giving a 3×2 result with rows 1 4, 2 5 and 3 6.
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Partial fraction decomposition
Split a rational function into simple pieces ready to integrate: 1 over (x − 1)(x − 2) becomes −1/(x − 1) + 1/(x − 2).
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Polynomial addition calculator
Combine like terms in one step: 1 + 2x + 3x² plus 3 + x² gives 4 + 2x + 4x², and subtracting instead gives −2 + 2x + 2x².
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Polynomial multiplication calculator
Expand a product of polynomials without slips: (1 + 2x) times (3 + 4x) is 3 + 10x + 8x², and the degree of the product, 2, is the sum of the degrees.
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Polynomial root finder
List the real roots of a polynomial with their multiplicities: x³ − 6x² + 11x − 6 has the roots 1, 2 and 3, each appearing once.
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Quadratic formula solver
Plug in a, b and c and get the roots straight from the formula: x² − 3x + 2 has discriminant 1 and roots 2 and 1, with the parabola's vertex at (1.5, −0.25).
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Rational root theorem
For 2x^3 - 3x^2 - 3x + 2 the possible rational roots are ±1, ±2 and ±1/2: six candidates built from divisors of the constant term over divisors of the leading…
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Remainder theorem calculator
Dividing 2 - 3x + x^2 by x − 2 leaves a remainder of 0, so 2 is a root. The calculator gets that remainder as p(r) with Horner's method, skips long division and…
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Synthetic division calculator
Dividing x^3 - 6x^2 + 11x - 6 by x - 2 gives x^2 - 4x + 3 with remainder 0, so 2 is a root and the division is exact.
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Solve a 2×2 system of linear equations
The lines 2x + y equals 5 and x + 3y equals 7 cross at (1.6, 1.8): the solver finds the single intersection of two linear equations by Cramer's rule or…
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Vector magnitude calculator
The vector (3, 4) has a magnitude of 5 and the unit vector (0.6, 0.8): enter the components in 1 to 256 dimensions and get the length, its square and the…
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Vector projection calculator
Projecting (3, 4) onto (1, 0) gives a scalar projection of 3, the vector (3, 0) and a perpendicular leftover of (0, 4).
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Vieta's formulas calculator
For x² − 3x + 2 the roots add up to 3 and multiply to 2, read straight from the coefficients with Vieta's formulas and without solving the equation.
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Combinations calculator
Find how many ways you can choose items when order does not matter: any 3 of 10 books for a weekend bag give 120 different bags, C(10,3), and the result stays…
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Integer compositions calculator
Count every ordered way to split a whole number into positive parts: 5 has 16 compositions and 4 has 8, because 1+3 and 3+1 count separately.
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Derangement calculator
Count the shuffles in which nothing stays in its original spot: 5 people drawing names for secret Santa have 44 draws where nobody gets themselves, which is !5.
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Multinomial coefficient calculator
Count the ways to split items into named groups of set sizes: 6 people placed into three labeled groups of 2 can be arranged in 90 ways, exactly 6! divided by…
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Integer partition calculator
Count the ways to write a whole number as a sum when order does not matter: 4 splits into 4, 3+1, 2+2, 2+1+1 and 1+1+1+1, so p(4) is 5, and 5 has 7.
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Pascal's triangle generator
Ask for 5 rows and get Pascal's triangle down to 1, 4, 6, 4, 1: fifteen exact numbers in which each entry is the sum of the two above it.
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Permutations calculator
Count arrangements where order matters: 3 of 5 runners can take first, second and third place in 60 ways, P(5,3), because ABC and ACB are different finishes.
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Permutations with repetition
Count ordered sequences when symbols may repeat: 5 symbols across 3 positions give 125 possibilities, 5^3, the same product rule behind codes and password…
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Stirling numbers of the second kind
Count the ways to split items into unnamed, non-empty groups: 5 people form 2 such teams in 15 ways and 3 teams in 25 ways, S(5,2) and S(5,3).
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Arc length calculator
With a radius of 10 and a 90° central angle, the arc measures 5π and the sector covers 25π square units, exactly a quarter of the circle.
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Barrel volume calculator
Estimate how much a barrel or cask holds from three measures, end radius, bulge radius and height, with V = πh/3 · (2R² + r²).
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Circle equation calculator
Turn a center and radius into the circle's standard and general equations, or go back from the general form: radius 5 at the origin gives x² + y² = 25, an area…
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Circle–line intersection
Find where a straight line crosses a circle: a circle of radius 5 at the origin and the line through (−10, 0) and (10, 0) meet at (−5, 0) and (5, 0).
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Cube calculator
Enter one measure of a cube, its edge, volume or surface area, and get all the others: an edge of 2 gives a volume of 8, a surface area of 24 and both…
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Cylinder volume calculator
Enter the radius and height of a right cylinder and get three answers at once: with radius 3 and height 5, the volume is 45π, the curved wall 30π and the full…
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Distance between two points
Type two points on a plane and get the straight-line distance between them: from (0, 0) to (3, 4) is exactly 5, with the horizontal and vertical differences…
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Ellipsoid volume calculator
Enter three semi-axes and get the ellipsoid's volume and skin area together: semi-axes 3, 2 and 1 give a volume of 8π.
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Conical frustum calculator
Give a truncated cone's two radii and its height, say 3, 4 and 5, and get the volume, slant height, side area and total surface in one go.
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Pyramid frustum calculator
Get the volume of a truncated pyramid from its two base areas and its height, so bases of 16 and 4 with a height of 6 enclose a volume of 56.
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Hemisphere calculator
Enter one radius and get a hemisphere's volume, curved dome area and total surface together: radius 1 gives a volume of two thirds of π, a dome of 2π and a…
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Heron's formula calculator
Get a triangle's area from its three sides alone, without angles or a height: sides 3, 4 and 5 give a semiperimeter of 6 and an area of 6.
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Hexagonal pyramid calculator
Get a regular hexagonal pyramid's volume and surfaces from its base edge and height, so edge 2 with height 3 gives a volume of 6√3, a lateral area of 12√3 and a…
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Hyperbola calculator
Enter a hyperbola's two semi-axes and get all its elements: semi-axes 3 and 4 give foci at ±5, vertices at ±3, an eccentricity of 5/3 and asymptote slopes of…
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Icosahedron calculator
Type one edge length and get the volume and the surface of all 20 triangular faces: an edge of 1 gives a volume of (5/12)(3+√5) and a surface of 5√3.
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