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.
Continued fraction convergents
Enter the partial quotients 3, 7, 15, 1 and you get the convergents 3/1, 22/7, 333/106 and 355/113, each a closer fraction for π.
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Deficient number checker
15 is deficient: its proper divisors 1, 3 and 5 add up to 9, which is less than 15. Enter any positive integer to get the exact divisor sum and a plain yes or…
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Pell equation solver
Get the smallest positive solution of x² − Dy² = 1 for a non-square D: for 2 it is x 3 and y 2, and for 61 it jumps to x 1766319049 and y 226153980, exact to…
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Proper divisors list
Lists every positive divisor of n except n itself, in ascending order with a count: for 12 you get 1, 2, 3, 4 and 6, five in all.
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Sum of totatives
The numbers up to 10 that share no factor with 10 are 1, 3, 7 and 9, and they add up to 20. Enter a positive whole number to get that sum, its totient and its…
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Engel Expansion Calculator for Positive Fractions
4/13 has the Engel denominators 4, 5, 7 and 13, which give 1/4 + 1/20 + 1/140 + 1/1820. Enter a positive fraction and get the exact expansion with no decimal…
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Frobenius number for two coins
Coins of 4 and 7 can pay every amount above 17, but never 17 itself: this calculator finds that largest impossible amount for any two coprime values and counts…
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Gaussian integer multiplication calculator
Multiply two Gaussian integers exactly: (3 + 2i)(1 − 4i) gives 11 − 10i. The calculator expands the product, replaces i² with −1 and returns the real and…
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Odd parts partition count
Count the ways to write a number as a sum of odd parts: 10 has 10 such partitions, and by Euler's theorem that is also how many ways it splits into distinct…
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Pythagorean triple generator
Builds a Pythagorean triple from two whole numbers m greater than n with Euclid's formula: choosing 2 for m and 1 for n gives the 3-4-5 triangle.
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Sum of two squares checker
65 is a sum of two squares, 1² + 8², while 3 and 7 never are. Enter a whole number to get a yes or no, one working pair and the prime factors behind Fermat's…
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Taxicab number representations as sums of two positive cubes
1729 can be written as 1³ + 12³ and as 9³ + 10³, so it has two representations. Enter a whole number to see every pair of positive cubes that adds up to it, or…
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Woodall number generator
The fifth Woodall number is 5 × 2⁵ − 1 = 159, a number with 3 digits. Enter a positive position to get its exact Woodall number and digit count, even when the…
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Integer compositions count
The number 5 can be written as an ordered sum in 16 ways, because the count of compositions is always 2^(n-1).
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Digitadition generators
101 has two generators, 91 and 100, because 91 + 10 and 100 + 1 both equal 101. Enter a positive whole number to list every generator in ascending order, or…
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Moran number checker
Check whether a number divided by its digit sum gives a prime: 18 has digit sum 9, 18 divided by 9 is 2, and 2 is prime, so 18 is a Moran number.
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Pernicious number checker
Count the ones in a number's binary form and see whether that count is prime: 13 is 1101 in binary, with 3 ones, so it is pernicious.
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Prime quadruplet finder
Lists every group of four primes shaped p, p + 2, p + 6, p + 8 up to your limit: the first is 5, 7, 11, 13, and a group only counts once its largest member…
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Right-Truncatable Prime Checker
Checks whether a prime stays prime as you remove its last digit again and again: 3797 gives 379, 37 and 3, all prime, so it passes.
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Strobogrammatic number checker
619 turned upside down still reads 619, so it is strobogrammatic, while 10 fails because the turn reverses its digits.
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Wilson prime checker
5 is a Wilson prime: 4! + 1 = 25, which 5² divides exactly, leaving remainder 0. Enter a prime to see the exact remainder and whether this rare condition holds…
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Digit frequency counter
In 100234001 the digit zero appears 4 times, one appears 2 times and two, three and four once each.
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Product of digits calculator
The digits of 234 multiply to 24, because 2 × 3 × 4 = 24. Enter zero or any positive whole number and get the product of its digits in a single pass, with every…
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Extravagant number checker
Four is extravagant because its factorization, 2², takes two digits while 4 takes only one. Enter any whole number from 2 up and see both digit counts side by…
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Golomb sequence calculator
Get any term of Golomb’s sequence: the 10th term is 5 and the 20th is 8. The sequence 1, 2, 2, 3, 3, 4, 4, 4… lists each value as many times as its own term…
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Gray code decoder
Paste a Gray code reading and get the number it stands for: 0111 decodes to binary 0101, which is 5.
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Palindrome bases finder
See every base in which a number reads the same both ways: up to base 16, 10 is a palindrome in bases 3, 4 and 9, written 101, 22 and 11, and in every base from…
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Super-prime checker
11 is the fifth prime and 5 is prime, so 11 is a super-prime; 7 is the fourth prime, and 4 is not.
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Ulam sequence calculator
The first ten Ulam numbers are 1, 2, 3, 4, 6, 8, 11, 13, 16 and 18, so the tenth is 18. Enter how many terms you need to get the ordered list and its last…
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Line intercept form calculator
Enter where the line crosses each axis and get every form of its equation: intercepts 6 and 3 give the slope −0.5, x/6 + y/3 = 1 and the standard form x + 2y =…
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Discriminant and root type calculator
Know how many real solutions a quadratic has before solving it: for x² − 5x + 6 the discriminant is 25 − 24 = 1, which is positive, so there are two distinct…
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Quadratic y-intercept calculator
Get the y-intercept of a parabola instantly: for f(x) = 2x² − 3x + 5, putting in zero for x leaves the constant, so the curve crosses the y-axis at (0, 5).
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Standard form of a line calculator
2x + 4y = 6 and x + 2y = 3 are the same line; standard form keeps only the second, with whole-number coefficients, no common factor and a positive leading term.
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Height of a square pyramid
A square pyramid with a base side of 6 and a volume of 144 stands 12 tall: enter those two values and get the perpendicular height in the matching unit.
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Height of a cone calculator
A cone holding about 37.7 with a base radius of 3 stands 4 tall: enter the volume and the radius to get the perpendicular height of a right circular cone, the…
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Legendre formula calculator
The prime 5 appears 24 times in the factorial of 100: 100 divided by 5 gives 20, 20 divided by 5 gives 4, and 20 plus 4 makes 24.
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Reduced binary quadratic forms
Lists the reduced primitive positive-definite forms ax² + bxy + cy² for a negative discriminant; −23 gives three forms, [1, 1, 6], [2, −1, 3] and [2, 1, 3], so…
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Tetranacci number calculator
Starting from 0, 0, 0 and 1 and adding the last four terms each time, position 10 holds 56. Enter a position to get its exact tetranacci number, with every…
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Absolute Value Greater-Than Inequality Solver
|2x − 6| > 4 holds when x < 1 or x > 5, written (−∞, 1) ∪ (5, ∞): the values lie outside a central range.
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Augmented matrix solver
Type the augmented matrix [A|b] and learn whether the system has one solution, infinitely many or none; the classic three-equation example returns the solution…
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Cubic discriminant calculator
x³ − 6x² + 11x − 6 has discriminant 4, so it has three distinct real roots: enter the four coefficients and get the discriminant, its sign and how many…
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Descartes rule of signs calculator
x² − 3x + 2 has 2 sign changes, so it has 2 or 0 positive real roots and no negative ones: enter the coefficients from the highest power down and get every…
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Direct variation calculator
Give one known pair and get the constant of variation with its equation: when x is 4 and y is 12, k is 3, so y equals 3x and an x of 7 gives a y of 21.
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Horner method calculator
Evaluate 2x³ − 6x² + 2x − 1 at x equals 3 and get 5, with every intermediate step (2, 0, 2, 5) shown so you can compare it with a handwritten Horner table.
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Quadratic maximum-minimum calculator
Find the turning point of a parabola in one step: f(x) = x² − 6x + 5 has its minimum value −4 at x equal to 3, because a is positive and the graph opens upward.
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Quartic equation from roots calculator
Give four roots and get the quartic back: roots 1, 2, 3 and 4 expand to x^4 - 10x^3 + 35x^2 - 50x + 24 = 0.
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Height of a cylinder calculator
A cylinder holding about 62.83 with a base radius of 2 is 5 tall: enter the volume and the radius to get the height of a right circular cylinder, worked out as…
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Heptagon calculator
A side of 5 is all a regular heptagon needs: it gives a perimeter of 35, an area of about 90.847811 and interior angles of 128.571429° each.
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Compound inequality solver
−2x + 4 < 8 and 3x − 1 ≤ 11 together give (−2, 4]: enter both inequalities, say whether both must hold or either one is enough, and get the combined interval…
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Factor trinomial calculator
Enter three whole-number coefficients and get the trinomial factored exactly: 6x² + 5x + 1 becomes (2x + 1)(3x + 1).
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Vertical shift of a function calculator
Add a constant to a function and see the graph move: shifting x² − 4x + 3 by 5 gives g(x) = (x² − 4x + 3) + 5, five units up, and the point (2, −1) lands at (2…
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Polynomial LCM calculator
Get the smallest polynomial both inputs divide: x² − 3x + 2 and x² − 1 share x − 1, so their least common multiple is x³ − 2x² − x + 2, of degree 3.
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Simplify rational expression calculator
(x^2 - 1)/(x - 1) simplifies to x + 1, yet the value 1 stays excluded because it made the original denominator zero.
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Rational function x-intercepts calculator
The graph of (x - 1)/(x^2 - 4) crosses the x-axis only at (1, 0). The calculator finds every real zero of the numerator and drops those that also zero the…
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System of linear inequalities calculator
x + y ≤ 6 with x ≥ 0 and y ≥ 0 shades a triangle with corners (0, 0), (6, 0) and (0, 6). The calculator lists every boundary line and corner point and says…
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Hexagonal pyramid surface area
A hexagonal pyramid with a base side of 2 and a slant height of 3 has a total surface of about 28.392: 18 for the six triangular faces, the rest for the…
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Hilbert's hotel paradox
With three guests in rooms 1 to 3 and two new arrivals, everyone moves up two rooms and rooms 1 and 2 open up.
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Complex Reciprocal Calculator
The reciprocal of 3 + 4i is 0.12 − 0.16i, because its squared modulus is 25: enter the real and imaginary parts and get 1/z in rectangular form, ready for…
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Complex to polar form calculator
−3 + 4i has modulus 5 and argument 126.869897645844°: enter the real and imaginary parts, pick radians or degrees, and get r, θ and the trigonometric form ready…
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Exponential growth calculator
See where steady percentage growth leads: 1000 growing 5% per period for 10 periods reaches 1628.89462678, with the factor of 1.05 per period and the…
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