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.
Number of divisors calculator
12 has 6 divisors: it factors as 2² × 3, so the count is (2+1) × (1+1) = 6. Enter any positive whole number and get its number of divisors together with the…
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Sum of divisors calculator
The divisors of 12 add up to 28: 1 + 2 + 3 + 4 + 6 + 12. Enter any positive whole number up to one trillion and get this exact sum with the prime factors used…
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Euler's totient φ(n)
Euler's totient of 36 is 12: that many numbers from 1 to 36 share no prime factor with 36. Enter any positive integer up to one trillion and get the exact count…
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Extended Euclidean calculator
For 240 and 46 the greatest common divisor is 2, and 240 × (−9) + 46 × 47 = 2. Enter two integers to get their divisor, the two Bézout coefficients and the…
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Factorial prime factorization
10! factors as 2⁸ × 3⁴ × 5² × 7, and you get that list without ever computing the full product. Enter n from 0 to 100000 and see every prime up to n with its…
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Happy number checker
19 is happy: 1² + 9² gives 82, then 68, then 100, then 1, in four steps. Enter any positive integer to see whether it reaches 1 or falls into the endless…
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Jacobi symbol calculator
The Jacobi symbol (5/13) is −1, which tells you 5 is not a square modulo 13. Enter any integer and any odd positive denominator to get −1, 0 or +1 through…
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Legendre symbol (a/p)
The Legendre symbol (2/7) is 1, so 2 is a square modulo 7: 3 times 3 is 9, which leaves 2. Enter any integer and odd prime to get 1, −1 or 0 with a…
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Mersenne number checker
Enter an exponent and get the full value of 2^p − 1 with a prime verdict: 7 gives 127, a Mersenne prime, while 11 gives 2047, which is 23 × 89.
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Modular exponentiation calculator
Raise a number to a power and keep only the remainder: 2 to the 10th modulo 1000 is 24, and 3 to the 5th modulo 13 is 9.
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Modular multiplicative inverse
Find the number that undoes a multiplication modulo m: the inverse of 3 modulo 11 is 4, because 3 times 4 leaves the remainder 1.
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Next prime after n
Find the smallest prime strictly greater than any whole number: after 10 comes 11, a gap of 1, and after the prime 7 comes 11, not 7 itself.
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Pandigital number checker
Check whether a number uses every digit of its base exactly once: 1023456789 is pandigital in base 10, while a number made only of the digits 1 to 9 is not…
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Previous prime finder
Finds the largest prime strictly below your number: for 10 the primes below are 2, 3, 5 and 7, so the answer is 7.
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Prime counting function π(n)
Counts how many primes are less than or equal to n: π(10) is 4, because the primes are 2, 3, 5 and 7.
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Quadratic residue checker
Tells you whether a number has a square root modulo m, and lists every root: 2 is a square modulo 7, because 3 squared is 9, which leaves 2, and the roots are 3…
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Radix converter
Rewrites a whole number from any base between 2 and 36 into another: hexadecimal FF is 255 in decimal.
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Factorial trailing zeros
100! ends in 24 zeros: 100 holds 20 fives and 4 twenty-fives, and 20 + 4 = 24. Enter a non-negative whole number to get the count of trailing zeros of its…
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Twin prime checker
3 and 5 are both prime and differ by two, so they form a twin prime pair, just like 11 and 13. Enter a number to check it against the one two places above, or…
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Birthday paradox calculator
In a group of just 23 people, the chance that two share a birthday is already about 50 percent, even with 365 days in the year.
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Coin flip probability
Ten fair flips land exactly five heads with probability 0.24609375, because 252 of the 1024 possible sequences have five heads.
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Conditional probability calculator
With P(A) of 0.5, P(B) of 0.4 and a joint probability of 0.2, P(A given B) is 0.5 and the events are independent; lower the joint to 0.1 and the result drops to…
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Dice sum probability
With two six-sided dice, 7 comes up 6 ways out of 36, a 1 in 6 chance, while 2 and 12 each have just 1 in 36.
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Dice roll probability
Rolling exactly 7 with two six-sided dice happens in 6 of 36 outcomes, a 1/6 chance. Pick the number of dice, the sides and your target, then choose exact or…
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Expected value calculator
A fair die with faces 1 to 6 has an expected value of 3.5: the long-run average of many rolls, though no single roll shows it.
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Geometric distribution calculator
If each try succeeds with probability 0.25, the first success lands exactly on the third try with probability 0.140625, and you should expect 4 tries on…
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Hypergeometric probability
Drawing 5 cards from a 52-card deck with 4 aces gives exactly 2 aces in close to 4 percent of hands: 6 times 17296 of the 2598960 possible hands.
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Odds to probability converter
Odds of 1 to 4 mean a probability of 0.2, or 20 percent, and 25 percent turns back into odds of 1 to 3.
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Poisson probability calculator
If tickets arrive at an average of 2.5 per hour, exactly 3 in an hour happens a little over one time in five, and 3 or fewer about three times in four.
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Poker hand odds
A flush that is not a straight shows up in 5108 of the 2598960 possible five-card hands, odds of 648463 to 1277 against.
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Coefficient of variation calculator
The values 2, 4, 4, 4, 5, 5, 7 and 9 have a mean of 5 and a population standard deviation of 2, so their coefficient of variation is 0.4, or 40 percent.
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Five-number summary calculator
For 1, 3, 5, 7, 9, 11 and 13 you get a minimum of 1, Q1 of 3, a median of 7, Q3 of 11 and a maximum of 13: the five landmarks of a box plot, with no normal…
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Geometric mean calculator
Average numbers that multiply rather than add: the geometric mean of 2, 8 and 32 is 8, against an arithmetic mean of 14.
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Harmonic mean calculator
Average rates the right way: the harmonic mean of 1, 2 and 4 is 12/7, below their ordinary average, because it averages the reciprocals and then turns the…
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Linear regression calculator
See how well a straight line explains your data: x of 1 to 5 with y of 2, 4, 5, 4 and 5 gives slope 0.6, intercept 2.2 and an R-squared of 0.6, with every…
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Mean median mode calculator
For 1, 2, 2, 3 and 4 you get a mean of 2.4, a median of 2, a mode of 2 and a range of 3, all from one list and shown with the count, sum, minimum and maximum.
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Quartile and IQR calculator
For the numbers 1 to 9, Q1 is 2.5, the median is 5 and Q3 is 7.5, so the IQR is 5 and the outlier fences sit at −5 and 15.
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Skewness and kurtosis calculator
The sample 1, 2, 3, 4, 5, 12 has a mean of 4.5 and a variance of 15.5, leans to the right and has heavier tails than a normal curve.
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Variance calculator
Calculate both kinds of variance at once: for 2, 4, 4, 4, 5, 5, 7 and 9 the mean is 5, the population variance is 4 and the sample variance divides the same 32…
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Weighted average calculator
Combine numbers that do not count equally: for a grade where the midterm and the final are worth 40% each and homework 20%, enter weights of 0.4, 0.4 and 0.2.
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Z-score calculator
See how unusual a value is: a test score of 85 against a mean of 70 and a standard deviation of 10 has a z-score of 1.5, within two standard deviations.
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Amplitude, period & phase shift calculator
For 3 sin(2x), the amplitude is 3 and the period is π. Enter the coefficients A, B, C and D of any sine function to get its amplitude, period, phase shift and…
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Angle of elevation calculator
A target 50 units higher at a horizontal distance of 100 sits at an angle of elevation of 26.565051177078°.
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Coterminal angle calculator
Type 45° and you get 45° as the positive coterminal angle and −315° as the negative one, both within a single turn of the original ray.
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Degrees minutes seconds converter
45° 30′ 36″ is exactly 45.51 decimal degrees, and the same tool splits a decimal angle back into degrees, minutes and seconds.
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Double-angle calculator
For an angle of 30°, the doubled angle is 60°: sin(2x) is 0.8660254038, cos(2x) is 0.5 and tan(2x) is 1.7320508076.
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Arccosine calculator
The arccosine of 0.5 is 60°, or 1.047197551197 radians, and both come back together so you never have to switch calculator modes.
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Arctangent calculator
The arctangent of 1 is 45°, or 0.7853981634 radians: a slope that rises as much as it runs. Give two components instead and you get the full-plane heading with…
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Law of cosines angle finder
Turn three side lengths into all three angles: sides 3, 4 and 5 give exactly 90° opposite the longest side and two acute angles at the other corners.
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Law of sines calculator
Finish a whole triangle from sparse data: angle A of 40°, side a of 7 and angle B of 60° give a third angle of 80° plus both missing sides.
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Polar to rectangular converter
Turn a distance and a direction into x and y on the plane: a radius of 5 at 45° lands on the same value on both axes, 5 ÷ √2. Angles go in degrees or radians.
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Reference angle calculator
Reduce any angle to the acute angle your tables need: 225° lies in quadrant III and has a reference angle of 45°.
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Right triangle trig solver
Get every side and angle from one angle and one length: a 30° angle with an opposite side of 5 gives a hypotenuse of 10 and a second acute angle of 60°, plus…
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Sine cosine tangent calculator
One angle gives you all six trig functions at once, so 30° returns a sine of 0.5 and a cosecant of 2, with cosine, tangent, secant and cotangent beside them.
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Sine wave calculator
Know the height of a sine wave at any point: with amplitude 2 and period 1, a quarter of the way along the wave reaches 2, its peak.
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Sum and difference angle calculator
Combine two angles without guessing: 30° and 45° give a sum of 75° and a difference of −15°, each with its sine, cosine and tangent.
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Exact trig values calculator
The sine of 30° is exactly 1/2 and its cosine is √3/2. Enter a special angle in degrees or radians and get exact radical values with decimals, the quadrant and…
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Bearing and heading calculator
From (0, 0) to (1, 1) the bearing is 45°, northeast. Enter the x and y coordinates of a start and a target on a flat grid and get the direction measured…
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Triangular number calculator
The 5th triangular number is 15 and the 10th is 55. Enter a position to get n(n+1)/2, enter any whole number to learn whether it is triangular and where it sits…
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Harshad number checker
18 is a Harshad number: its digits add up to 9, and 18 divided by 9 is exactly 2. Enter any positive integer to see its digits, their sum and whether that sum…
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