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➗ MathFree
Fraction to Lowest Terms Calculator
Reduce any fraction to its simplest form in one step: 42/56 becomes 3/4, because both numbers divide by 14.
F
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➗ MathFree
Luhn algorithm validator
Find out at once whether a digit string passes the Luhn mod-10 check: 79927398713 does. It catches any single mistyped digit and most swaps of neighbouring…
B
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➗ MathFree
Magic square generator
Build an odd-order magic square in which every row, column and main diagonal has the same sum: the 3×3 square adds up to 15 and the 5×5 to 65.
S
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➗ MathFree
Power calculator
Raise a base to an exponent and get one finite number: 2 to the 10th is 1024 and 9 to the power one-half is 3.
A
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➗ MathFree
Matrix calculator
Add, subtract or multiply two matrices of up to fifty rows and fifty columns: adding the 2×2 matrices 1, 2, 3, 4 and 5, 6, 7, 8 gives 6, 8, 10, 12.
P
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➗ MathFree
Matrix norm calculator
Sum up a matrix in one number: for the rows 1, −2, 3 and 4, 0, −1, the infinity norm is 6 and the one norm is 5.
F
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➗ MathFree
Mayan numeral converter
Turn a whole number into Mayan dots and bars: 429 becomes one dot in the four-hundreds row, one dot in the twenties row and a bar with four dots for the units.
B
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➗ MathFree
Midsegment of a triangle calculator
Halve the side parallel to a triangle's midsegment and you have the midsegment itself: a parallel side of 18 units gives a midsegment of 9.
F
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➗ MathFree
Minutes to decimal degrees calculator
Turn the minutes part of an angle into decimal degrees by dividing by 60: 30 minutes is 0.5 degree and 15 minutes is 0.25.
B
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➗ MathFree
Mixed Number to Improper Fraction Calculator
Turn a mixed number into an improper fraction by multiplying the whole part by the denominator and adding the numerator, so 3 and 2/5 becomes 17/5.
F
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➗ MathFree
Integer palindrome checker
Check whether a whole number reads the same both ways: 121 and 3443 do, 10 and 123 do not. You also see the digits and their reverse, so the verdict can be…
S
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➗ MathFree
Missing side of a right triangle
Find the third side of a right triangle from the two you know: legs of 3 and 4 give a hypotenuse of 5, and a hypotenuse of 13 with a leg of 5 gives 12.
P
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➗ MathFree
Mixed number converter
Rewrite an improper fraction as a whole number plus a leftover: 11/4 becomes 2 3/4, and the leftover is reduced, so 10/4 gives 2 1/2.
A
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➗ MathFree
Modulo order of operations calculator
Evaluate an expression with +, −, ×, ÷ and the % remainder in the standard order: 2 + 3 * 4 % 5 is 4, because 3 * 4 % 5 is worked out first, left to right.
S
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➗ MathFree
Multiplicative inverse calculator
Get the reciprocal of any non-zero number: 4 inverts to 0.25 and −8 to −0.125. The two are multiplied back next to the answer, so you can see the product is…
A
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➗ MathFree
Multiplicative inverse modulo n
Find the number that undoes multiplication by an integer modulo n: the inverse of 3 modulo 11 is 4, because 3 × 4 = 12 leaves remainder 1.
P
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➗ MathFree
Multiplying fractions
Multiply two fractions and get the product already in lowest terms: 2/3 times 3/4 is 6/12, which cancels by 6 to 1/2.
S
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➗ MathFree
Multiplying radicals calculator
Multiply two roots and get the product in simplest form: √8 times √2 is 4. Roots with different indices are first brought to a common index, then every perfect…
P
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➗ MathFree
Natural log calculator
Find the natural logarithm of any positive number: ln 1 is 0, ln e is 1 and ln 10 is about 2.30258509299.
A
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➗ MathFree
Oblique triangle calculator
With sides 8 and 6 and a 40° angle between them, the calculator finds the third side and the other two angles and reports an obtuse triangle.
S
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➗ MathFree
Obtuse triangle checker
Sides 3, 4 and 6 form an obtuse triangle, because 3² + 4² = 25 is less than 6² = 36. Enter any three side lengths to get a yes or no with that comparison, no…
A
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➗ MathFree
Bitwise OR calculator
5 OR 3 gives 7: in binary, 101 and 11 line up from the right and every column holding a 1 keeps it, giving 111.
P
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➗ MathFree
Pentagon calculator
A regular pentagon with sides of 2 has a perimeter of 10 and an area of about 6.8819. Enter the side length to get both measures together with the formula…
S
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➗ MathFree
Percentage change calculator
From 80 to 100 is a rise of 25 %: the difference of 20 divided by the old value of 80, times 100. Enter an old and a new value to get the signed percent change…
A
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➗ MathFree
Percentage difference calculator
10 and 6 differ by 50 %: their gap of 4 is half of their average, 8. Enter two values to get the percentage difference measured against their mean, with neither…
P
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➗ MathFree
Percent of time calculator
15 minutes into a 60-minute meeting, 25 % of the time is gone. Enter the time elapsed and the total duration in the same unit to get the share used, the time…
A
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➗ MathFree
Percentage of a percentage calculator
20% of 50% is 10%, because (20 × 50) / 100 = 10. Enter two percentages to get the compound rate they form together, for a cut of a discount, a tax on a taxable…
S
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➗ MathFree
Perfect square trinomial
x² + 6x + 9 is a perfect square, (x + 3)², because 6² equals 4 × 1 × 9. Enter the three coefficients to learn whether ax² + bx + c is the square of a binomial…
P
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➗ MathFree
Rectangle perimeter from area and one side
A rectangle of area 24 with one side of 6 has its other side at 4 and a perimeter of 20. Enter the area and the side you know to get the missing side and the…
S
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➗ MathFree
Perimeter of a sector
A sector with radius 5 and a 90° angle has a perimeter of 10 + 5π/2: two radii of 5 plus a quarter-circle arc.
A
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➗ MathFree
Triangle perimeter from vertices
The triangle with corners (0, 0), (3, 0) and (0, 4) has sides 3, 5 and 4 and a perimeter of 12. Enter the coordinates of three points to get each side and the…
P
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➗ MathFree
Perimeter of a rectangle
A rectangle 8 long and 5 wide has a perimeter of 26, twice the sum of its sides. Enter the length and the width to get the distance all the way round, ready for…
S
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➗ MathFree
Phase shift calculator
In y = sin(2x + 1) the graph moves half a unit to the left, because the phase shift is −C/B = −1/2.
A
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➗ MathFree
Polar decomposition calculator
The matrix with rows (2, 1) and (0, 3) splits into a rotation U and a symmetric stretch P, so that A = U P.
S
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➗ MathFree
Polar form of a complex number
3 + 4i has a magnitude of 5 and an angle of about 0.927 radians, so its polar form is 5∠0.927. Enter the real and imaginary parts to get the magnitude, the…
P
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➗ MathFree
Polygon angle
Type the number of sides and get both angles of a regular polygon at once: a pentagon has interior angles of 108° and exterior angles of 72°.
A
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➗ MathFree
Polynomial division calculator
Divide one polynomial by another and get the quotient and the remainder: x² − 3x + 2 divided by x − 1 gives x − 2 with a remainder of 0.
P
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➗ MathFree
Polynomial graphing calculator
Enter the coefficients and an x-range and get evenly spaced points ready to draw: x² from −2 to 2 with five points gives (−2, 4), (−1, 1), (0, 0), (1, 1) and…
S
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➗ MathFree
Power modulo calculator
Get the remainder of a huge power without ever computing the power: 2 to the 10th mod 1000 leaves 24, and 3 to the 5th mod 13 leaves 9.
A
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➗ MathFree
Power of a power calculator
Collapse a nested power into a single one: (2^3)^4 is 2 to the 12th, which is 4096, because the two exponents multiply.
S
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➗ MathFree
Power-reducing identities calculator
Rewrite sin² or cos² of an angle as a first-power cosine of the double angle and get the number: sin² of 30 degrees is 0.25, because the cosine of 60 degrees is…
P
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➗ MathFree
Prisoner's dilemma calculator
Score one round of the prisoner's dilemma: pick cooperate or defect for each player and get both scores.
A
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➗ MathFree
Pyramid angle calculator
Give the base side and height of a square pyramid and get the angle its slant edges make with the base: a side of 6 and a height of 4 give just over 43 degrees…
S
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➗ MathFree
Pythagorean triples
List every primitive Pythagorean triple up to the hypotenuse you choose: up to 25 there are four, 3-4-5, 5-12-13, 8-15-17 and 7-24-25, each with the legs in…
P
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➗ MathFree
QR decomposition
Factor a real matrix into Q with orthonormal columns and an upper-triangular R using Gram-Schmidt: the matrix with rows 3, 1 and 0, 2 is already triangular, so…
A
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➗ MathFree
Quarter circle perimeter
Get the full boundary of a quarter circle from its radius, the curved arc plus the two straight radii: a radius of 7 gives a perimeter of 24.995574287564, with…
S
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➗ MathFree
Quaternion calculator
Enter the four parts of a quaternion and get its norm and conjugate together: for 1 + 2i + 3j + 4k the conjugate is 1 − 2i − 3j − 4k and the norm is the square…
P
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➗ MathFree
Simplify radical
Rewrite a square root in simplest radical form: √12 becomes 2√3 and √50 becomes 5√2, with the number that comes out and the part that stays under the root shown…
S
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➗ MathFree
Radius of a circle
Get the radius of a circle from the distance around it: a circumference of 2π gives a radius of 1 and a diameter of 2, and one of 10π gives a radius of 5.
A
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➗ MathFree
Sphere radius calculator
Recover the radius of a sphere from its volume, surface area or diameter: a volume of thirty-six π, about 113.097335529233, gives a radius of 3 and a diameter…
P
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➗ MathFree
Ratio of 2 numbers calculator
Compare two numbers as a ratio in lowest terms and as a decimal: 8 to 12 reduces to 2:3, with a greatest common divisor of 4 and a quotient of 0.666666666667.
P
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➗ MathFree
Rational exponents calculator
Evaluate a power with a fractional exponent: 8 to the 2/3 is 4, because the cube root of 8 is 2 and 2 squared is 4.
S
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➗ MathFree
Rationalize denominator calculator
Clear the square root from the bottom of a fraction: 1/√8 becomes √2/4, with the square factor pulled out and the result reduced, and 6/√9 simplifies all the…
A
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➗ MathFree
Reciprocal calculator
Get the reciprocal of any non-zero number, one divided by it: the reciprocal of 4 is 0.25, of two thirds is three halves, and of minus four is minus one…
S
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➗ MathFree
Rectangle diagonal angle calculator
A 4 by 3 rectangle has a diagonal of 5 that meets the length at arctan(3/4) and the width at arctan(4/3), two angles that always add up to 90°.
A
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➗ MathFree
Rectangular prism volume
A box 3 by 4 by 5 holds 60 cubic units. Enter the three edges and get the volume as length times width times height, in the cubic version of your unit.
P
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➗ MathFree
Rectangular to polar
The point (3, 4) sits 5 units from the origin at an angle of about 53.13°. Enter any x and y and get the radius and the angle in degrees, in the right quadrant…
S
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➗ MathFree
Regular polygon perimeter
A regular hexagon with sides of 2 has a perimeter of 12, because every side is equal and the total is simply the number of sides times their length.
A
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➗ MathFree
Relatively prime checker
8 and 15 are relatively prime because their only common divisor is 1, even though neither number is prime.
P
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➗ MathFree
Right circular cone
A cone with radius 3 and height 4 has a slant height of exactly 5 and a volume of 37.6991118431 cubic units.
A
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2
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3
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Receive a signed webhook the moment it's ready, or fetch a signed link. A failed task is never charged.
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The full API — 7800+ capabilities — billed only for what you run, from $0.002 per call. No monthly fee.
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