Number Theory & Statistics Calculators

Paste a list of numbers to get the mean, with the sum divided by the count written out and the median and spread alongside for comparison.

Paste a list of numbers and choose σ or s to get the standard deviation, with the variance it came from and a count of how many values sit within one σ of the mean.

Paste a list of numbers to get the median, with the sorted list highlighting the middle value — or the two middle values whose average is the answer.

Enter a whole number to find out whether it is prime, with the factor found when it is composite, the prime factorisation, and the nearest primes on either side.

Enter a term index to get that Fibonacci number exactly — to all its digits — with the neighbouring terms, the digit count and the ratio approaching the golden ratio.

Enter a number or an expression such as |3 − 7| to get its distance from zero, with the sign of the input and the opposite value shown.

Paste a list of numbers to get the mean, with the sum divided by the count written out and the median and spread alongside for comparison.

Enter one value and weight per line to get Σ(value × weight) ÷ Σweight, with each row's share and contribution listed and the unweighted mean beside it.

Paste a list of numbers to get the median, with the sorted list highlighting the middle value — or the two middle values whose average is the answer.

Paste a list of numbers to find the value or values that appear most often, with the highest frequency reported and the no-mode case stated plainly.

Paste a list of numbers to get the first, second and third quartiles together, with the five-number summary and the split rule used stated on the page.

Paste a list of numbers and a percentile from 0 to 100 to get the value at that position, with the two sorted values it interpolates between shown.

Paste a list of numbers and a value to get its percentile rank, with the counts of values below and equal to it shown so the percentage is checkable.

Paste a list of numbers to get the range, with the maximum and minimum identified and the interquartile range shown alongside for comparison.

Paste a list of numbers to get the midrange, (max + min) ÷ 2, with the two extreme values named and the mean and median beside it.

Paste a list of numbers to get the mean absolute deviation, with every value's distance from the mean listed so the average can be checked by eye.

Paste a list of numbers and choose population (σ²) or sample (s²) variance to get the result with the sum of squared deviations and the divisor spelled out.

Paste a list of numbers and choose σ or s to get the standard deviation, with the variance it came from and a count of how many values sit within one σ of the mean.

Enter a value with its mean and standard deviation — or paste a whole dataset and score one entry against it — to get the z-score and what it means in words.

Paste a list of numbers to get the interquartile range with the quartiles it came from, the fences it defines, and how many values sit inside the middle half.

Paste a list of numbers to flag every value outside the 1.5 × IQR fences, with the fences, the quartiles and how far each flagged value sits from the mean.

Enter a whole number to find out whether it is prime, with the factor found when it is composite, the prime factorisation, and the nearest primes on either side.

Generate primes up to a limit with the sieve of Eratosthenes, or take the first N primes, and get the count, sum and largest value with the full list.

Enter an upper limit to get π(N), the number of primes at or below it, with the density, the N ÷ ln(N) estimate and the full list of primes counted.

Enter a number and a divisor to get a yes-or-no divisibility answer with the quotient, the remainder and the equation written out, plus the digit rules to check by eye.

Enter a whole number to get every factor in ascending order, each a × b pair, the divisor count and the prime factorization with the repeats collected as powers.

Enter a number and a count to get n, 2n, 3n, … with the nth multiple highlighted as n × k, and the list named as the arithmetic sequence it is.

Enter two numbers and a count to get the least common multiple and the first common multiples — the multiples of the LCM, generated rather than tested.

Enter a number to get its classification from the aliquot sum — the sum of its proper divisors — written out, with the known perfect numbers listed alongside.

Enter a starting number to get the step count, the peak value and the whole chain — even numbers halve, odd numbers triple and add one, until 1.

Enter a number to get the sum-of-digit-squares chain — happy numbers reach 1, and every other number falls into the same eight-value loop.

Enter a number to get its digital root with each pass written out, plus the casting-out-nines congruence 1 + (n − 1) mod 9 that gives the same answer in one step.

Pick an arithmetic or geometric sequence, give it a start, a step and a length, and get the listed terms with the nth term and the sum.

Enter the first term, the common difference and the length to get the nth term and the sum of the first n terms, with both formulas shown with your numbers substituted.

Enter the first term, the common ratio and the length to get the nth term and the sum of the first n terms, with the substituted formula and the behaviour of the ratio described.

Enter a term index to get that Fibonacci number exactly — to all its digits — with the neighbouring terms, the digit count and the ratio approaching the golden ratio.

Enter a number of rows to get the triangular number T(n) = n(n + 1) ÷ 2 drawn as dots, or enter a number to test whether it is triangular and which T(n) it is.

Enter a term index to get that Lucas number exactly — to all its digits — with the neighbouring terms, the digit count and the ratio approaching the golden ratio.

Enter a number or an expression such as |3 − 7| to get its distance from zero, with the sign of the input and the opposite value shown.

Paste a list of numbers to get the mean, with the sum divided by the count written out and the median and spread alongside for comparison.

Enter one value and weight per line to get Σ(value × weight) ÷ Σweight, with each row's share and contribution listed and the unweighted mean beside it.

Paste a list of numbers to get the median, with the sorted list highlighting the middle value — or the two middle values whose average is the answer.

Paste a list of numbers to find the value or values that appear most often, with the highest frequency reported and the no-mode case stated plainly.

Paste a list of numbers to get the range, with the maximum and minimum identified and the interquartile range shown alongside for comparison.

Paste a list of numbers to get the midrange, (max + min) ÷ 2, with the two extreme values named and the mean and median beside it.

Paste a list of numbers to get the mean absolute deviation, with every value's distance from the mean listed so the average can be checked by eye.

Paste a list of numbers and choose population (σ²) or sample (s²) variance to get the result with the sum of squared deviations and the divisor spelled out.

Paste a list of numbers and choose σ or s to get the standard deviation, with the variance it came from and a count of how many values sit within one σ of the mean.

Enter a value with its mean and standard deviation — or paste a whole dataset and score one entry against it — to get the z-score and what it means in words.

Paste a list of numbers and a percentile from 0 to 100 to get the value at that position, with the two sorted values it interpolates between shown.

Paste a list of numbers and a value to get its percentile rank, with the counts of values below and equal to it shown so the percentage is checkable.

Paste a list of numbers to get the first, second and third quartiles together, with the five-number summary and the split rule used stated on the page.

Paste a list of numbers to get the interquartile range with the quartiles it came from, the fences it defines, and how many values sit inside the middle half.

Paste a list of numbers to flag every value outside the 1.5 × IQR fences, with the fences, the quartiles and how far each flagged value sits from the mean.

Enter a whole number to find out whether it is prime, with the factor found when it is composite, the prime factorisation, and the nearest primes on either side.

Generate primes up to a limit with the sieve of Eratosthenes, or take the first N primes, and get the count, sum and largest value with the full list.

Enter an upper limit to get π(N), the number of primes at or below it, with the density, the N ÷ ln(N) estimate and the full list of primes counted.

Enter a number and a divisor to get a yes-or-no divisibility answer with the quotient, the remainder and the equation written out, plus the digit rules to check by eye.

Enter a whole number to get every factor in ascending order, each a × b pair, the divisor count and the prime factorization with the repeats collected as powers.

Enter a number and a count to get n, 2n, 3n, … with the nth multiple highlighted as n × k, and the list named as the arithmetic sequence it is.

Enter two numbers and a count to get the least common multiple and the first common multiples — the multiples of the LCM, generated rather than tested.

Enter a number to get its classification from the aliquot sum — the sum of its proper divisors — written out, with the known perfect numbers listed alongside.

Enter a starting number to get the step count, the peak value and the whole chain — even numbers halve, odd numbers triple and add one, until 1.

Enter a number to get the sum-of-digit-squares chain — happy numbers reach 1, and every other number falls into the same eight-value loop.

Enter a number to get its digital root with each pass written out, plus the casting-out-nines congruence 1 + (n − 1) mod 9 that gives the same answer in one step.

Pick an arithmetic or geometric sequence, give it a start, a step and a length, and get the listed terms with the nth term and the sum.

Enter the first term, the common difference and the length to get the nth term and the sum of the first n terms, with both formulas shown with your numbers substituted.

Enter the first term, the common ratio and the length to get the nth term and the sum of the first n terms, with the substituted formula and the behaviour of the ratio described.

Enter a term index to get that Fibonacci number exactly — to all its digits — with the neighbouring terms, the digit count and the ratio approaching the golden ratio.

Enter a number of rows to get the triangular number T(n) = n(n + 1) ÷ 2 drawn as dots, or enter a number to test whether it is triangular and which T(n) it is.

Enter a term index to get that Lucas number exactly — to all its digits — with the neighbouring terms, the digit count and the ratio approaching the golden ratio.