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.
Tukey HSD post-hoc
Find out which group means differ after an ANOVA: for groups averaging 2, 6 and 4, Tukey's test flags all three pairs as different at the 0.05 level.
Free · Runs in your browser
Half-angle calculator
Enter a full angle of 90° and get a half-angle of 45° with sine and cosine of 0.707106781187 and a tangent of 1.
Free · Runs in your browser
Rectangular to polar converter
Turn a point on the plane into distance and direction: the point (3, 4) lies 5 units from the origin, with its angle in quadrant I.
Free · Runs in your browser
Midline of a sinusoidal function
Get the line a sine or cosine wave swings around: a vertical shift of 3 puts the midline at height 3, and with an amplitude of 2 the wave peaks at 5 and bottoms…
Free · Runs in your browser
Complete the square calculator
x² + 6x + 5 becomes (x + 3)² − 4, with its vertex at (−3, −4): enter the three coefficients and get the vertex form, the turning point and the axis of symmetry…
Free · Runs in your browser
Cross product calculator
(2, 3, 4) × (5, 6, 7) is (−3, 6, −3), and the parallelogram they span has area √54: enter two vectors in space and get the perpendicular vector and that area.
Free · Runs in your browser
Exponent rules calculator
Turn a chain of powers with one base into a single power: 2³ · 2⁵ becomes 2⁸, which is 256. Choose multiply, divide or power of a power and the right exponent…
Free · Runs in your browser
Linear inequality solver
Type 2x + 3 < 11 and get x < 4, also written as the interval (−∞, 4). When the coefficient of x is negative, the inequality sign is reversed for you and the…
Free · Runs in your browser
Matrix inverse calculator
Enter rows 4, 7 and 2, 6 to get the inverse with rows 0.6, −0.7 and −0.2, 0.4, plus the determinant 10.
Free · Runs in your browser
Matrix multiplication calculator
Multiply a 2 × 3 matrix by a 3 × 2 matrix and get a 2 × 2 product: rows 1, 2, 3 and 4, 5, 6 times rows 7, 8; 9, 10; 11, 12 give 58, 64 and 139, 154.
Free · Runs in your browser
Polynomial long division calculator
Check a polynomial long division in seconds: x² − 3x + 2 divided by x − 1 gives the quotient x − 2 with remainder 0, so x − 1 is a factor.
Free · Runs in your browser
Polynomial GCD calculator
Find the factor two polynomials share: x² − 3x + 2 and x − 1 have greatest common divisor x − 1, found in 1 Euclidean step and always scaled to lead with 1.
Free · Runs in your browser
Reduced row echelon form calculator
Row-reduce a matrix all the way: a 3 × 4 system becomes three pivots equal to 1, zeros above and below each one, and a last column of -8, 1 and -2, with rank 3.
Free · Runs in your browser
3×3 system of equations solver
Three equations, three unknowns, one answer: the textbook system x + y + z equal to 6, 2y + 5z equal to −4 and one more equation gives 5, 3 and −2.
Free · Runs in your browser
Combinations with repetition
Count selections where each type can repeat and order does not matter: 3 picks from 5 types give 35, which is C(7, 3), the same stars-and-bars count used for…
Free · Runs in your browser
Handshake problem calculator
Find how many handshakes happen when everyone in a group greets everyone else once: 5 people make 10 handshakes and 4 make 6, and a total such as 10 turns back…
Free · Runs in your browser
Monotone lattice paths on an a×b grid
Count the routes across a grid that only move right or up: reaching the point 2 across and 3 up takes one of 10 paths, C(5, 2), while a 2 by 2 square has 6.
Free · Runs in your browser
Unsigned Stirling numbers of the first kind
Count the arrangements of n items that break into exactly k cycles: 5 items in 2 cycles give 50, 4 items in 2 cycles give 11, and 3 items in one cycle give 2.
Free · Runs in your browser
Chord length calculator
Get the straight length of a chord from the radius and either the central angle or the distance to the centre: a radius of 5 and an angle of 60° give a chord of…
Free · Runs in your browser
Circle through three points
Enter three points and get the only circle through all of them: (0, 0), (4, 0) and (0, 3) give a center at (2, 1.5) and a radius of 2.5.
Free · Runs in your browser
Cone volume calculator
Enter the base radius and height of a cone and get its volume, slant height and surface areas: radius 3 and height 4 give a slant height of exactly 5 and a…
Free · Runs in your browser
Dodecahedron calculator
Enter one edge of a regular dodecahedron and get its volume and full surface: an edge of 1 gives a volume of about 7.663 and a surface of about 20.646, covering…
Free · Runs in your browser
Ellipse calculator
Enter the two semi-axes of an ellipse and get every key measure at once: semi-axes of 5 and 3 give an area of about 47.12, a perimeter of about 25.5269988628…
Free · Runs in your browser
Line intersection calculator
The lines y equals 2x + 1 and y equals −x + 4 cross at the point (1, 3). Enter two lines in slope-intercept or standard form and get their meeting point, or a…
Free · Runs in your browser
Pipe volume calculator
A pipe 10 units long with radii 2 and 3 holds 125.6637061436 cubic units inside, and its wall uses 157.0796326795 of material.
Free · Runs in your browser
Polygon area calculator
Paste the corners of a polygon in order and get its area: the rectangle (0, 0), (4, 0), (4, 3), (0, 3) gives 12, and the sign of the area tells you whether you…
Free · Runs in your browser
Prism surface area calculator
Enter the base perimeter, base area and height of a right prism and get its lateral and total surface: 20, 24 and 5 give a lateral area of 100 and a total of…
Free · Runs in your browser
Pyramid volume calculator
Enter the height and the base of a pyramid and get its volume: a square base of side 6 and a height of 4 give 48, with a slant height of 5 and a total surface…
Free · Runs in your browser
Rhombus calculator
Enter the two diagonals of a rhombus, or one side and an angle, and get the rest: diagonals of 6 and 8 give a side of 5, an area of 24 and a perimeter of 20.
Free · Runs in your browser
Slope calculator
Enter two points and get the slope of the line through them: from (1, 2) to (4, 8) the rise is 6 and the run is 3, so the slope is 2 and the line climbs at…
Free · Runs in your browser
Spherical segment calculator
Cut a sphere with two parallel planes and get the slice between them: on a sphere of radius 5, cuts at heights 1 and 4 give a segment 3 high, plus its volume…
Free · Runs in your browser
Square pyramid volume
Solve a square pyramid from just its base edge and vertical height. An edge of 6 and a height of 4 give a volume of 48, a slant height of 5 and a total surface…
Free · Runs in your browser
Torus volume calculator
Size a ring-shaped solid such as an O-ring, a toroidal vessel or a doughnut box from two radii: a tube radius of 1 around a centre radius of 3 gives a volume of…
Free · Runs in your browser
45-45-90 triangle calculator
Give one leg or the hypotenuse and get every other measure: a leg of 5 means a hypotenuse of 5 times √2 and an area of 12.5.
Free · Runs in your browser
Circumcenter calculator
Find the point equally far from three vertices and the circle through them: for (0, 0), (4, 0) and (0, 3) the circumcenter is (2, 1.5) and the radius 2.5.
Free · Runs in your browser
SSA triangle calculator
Two sides and an angle that is not between them can give two different triangles: with a of 10, b of 16 and A of 30°, the third side is 19.8564064606 or…
Free · Runs in your browser
Geometric sequence calculator
With a first term of 2 and a ratio of 3, the 5th term is 162 and the first five terms add up to 242.
Free · Runs in your browser
Pell number calculator
P10 is 2378: each Pell number is twice the previous one plus the one before, starting 0, 1, 2, 5, 12, 29.
Free · Runs in your browser
Perfect square checker
Find out whether a whole number is a perfect square, or get the n-th square: 49 is a square with root 7, and square number 7 is 49.
Free · Runs in your browser
Sum of first n cubes
Add up 1³ + 2³ + … + n³ exactly for any whole number n: the first 10 cubes sum to 3025, which is 55 squared, the square of the 10th triangular number.
Free · Runs in your browser
Superfactorial calculator
Multiply the first n factorials exactly: the superfactorial of 5 is 1! × 2! × 3! × 4! × 5!, which is 34560, shown in full with its number of digits for any n…
Free · Runs in your browser
Telescoping series sum
The first 10 terms of 1/(k(k+1)) add up to exactly 10/11. Enter how many terms you want and get the partial sum as a reduced fraction and a decimal, worked out…
Free · Runs in your browser
Tetrahedral number calculator
The 5th tetrahedral number is 35, the balls in a triangular pyramid five layers high. Enter a position from 1 to 378,076 and get its exact value from…
Free · Runs in your browser
Abundant number checker
The proper divisors of 12 are 1, 2, 3, 4 and 6, which add up to 16, so 12 is abundant by 4. Enter any positive whole number to see its divisor sum, the excess…
Free · Runs in your browser
Carmichael function calculator
λ(15) is 4: any number coprime to 15, raised to the 4th power, leaves remainder 1 when divided by 15, while Euler's φ(15) is 8.
Free · Runs in your browser
Chinese remainder theorem solver
Solve simultaneous congruences in one step: x ≡ 2 mod 3, x ≡ 3 mod 5 and x ≡ 2 mod 7 give x ≡ 23 mod 105.
Free · Runs in your browser
Collatz conjecture calculator
Start at 7 and the 3n+1 rule takes 16 steps to reach 1, climbing as high as 52 on the way. Enter any positive whole number to see its full path, step count and…
Free · Runs in your browser
Coprime checker
8 and 15 are coprime: their greatest common divisor is 1. Enter any two integers, negatives and zero included, and get the exact common divisor plus a clear yes…
Free · Runs in your browser
Kaprekar number checker
45 is a Kaprekar number: 45 squared is 2025, and 20 plus 25 gives 45 again. Enter any positive integer to test every way of splitting its square and see the…
Free · Runs in your browser
Nth prime calculator
Find the prime at any position in the list of primes: the 10th prime is 29, counting 2 as the first.
Free · Runs in your browser
Prime factorization calculator
Breaks a whole number into prime powers: 360 is 2³ × 3² × 5, with each prime shown next to its exponent.
Free · Runs in your browser
Primitive root calculator
Finds the smallest primitive root of a prime: modulo 7 it is 3, whose powers run through all six nonzero remainders, while the powers of 2 repeat after three.
Free · Runs in your browser
Smith number checker
Tells you whether a composite number's digits add up to the same total as the digits of its prime factors: 22 is a Smith number, since 2 + 2 equals 2 + 1 + 1…
Free · Runs in your browser
Bayes theorem calculator
With a prior of 0.01, a sensitivity of 0.99 and a false-positive rate of 0.05, a positive result leaves about a 1 in 6 chance that the hypothesis is true.
Free · Runs in your browser
Binomial probability calculator
In 10 trials with a success chance of 0.5, exactly 5 successes happen close to one time in four, and 5 or fewer a little over 60 percent of the time.
Free · Runs in your browser
Lottery odds calculator
In a 6-from-49 game, matching exactly 3 numbers covers 246820 of the 13983816 possible draws, while the jackpot is a single one of them.
Free · Runs in your browser
Negative binomial calculator
With a success chance of 0.4 per trial, the third success lands exactly on trial 8 just over 10 percent of the time, and on average it arrives at trial 7.5.
Free · Runs in your browser
Correlation coefficient calculator
The values 1 to 5 paired with 2, 4, 6, 8 and 10 give a Pearson r of exactly 1, a perfect positive straight-line link; reverse the second list and r becomes −1.
Free · Runs in your browser
Mean absolute deviation calculator
For 2, 4, 4, 4, 5, 5, 7 and 9 the mean is 5 and the mean absolute deviation is 1.5: the distances from the mean add up to 12, and 12 divided by 8 values is 1.5.
Free · Runs in your browser
Percentile calculator
In the list 7, 15, 36, 39, 40, 41 the 50th percentile is 37.5, halfway between 36 and 39. Paste your numbers, pick k from 0 to 100 and get the interpolated…
Free · Runs in your browser