Do exact arithmetic on numbers with hundreds or thousands of digits, with no rounding to 15 digits.
Most calculators, spreadsheets and programming languages store numbers as floating-point values that are only exact to about 15 or 16 digits. Past that point the trailing digits are rounded away, so 2100 shows up as 1.2676506002282294 × 1030 instead of the full 1,267,650,600,228,229,401,496,703,205,376. This calculator works with every digit, so what you see is the true value, however long it is. That matters for number theory homework, checking code that uses big integers, puzzles, and anywhere an answer that is off in the last digits is simply wrong.
The factorial of 25 is 25 × 24 × 23 × … × 1, and it is 15,511,210,043,330,985,984,000,000, a 26-digit number. Enter 25 and press X!. By 52! you reach 68 digits, which is the number of ways to arrange a shuffled deck of cards, so any properly shuffled deck is almost certainly in an order that has never existed before. If you want to count the ways of picking or arranging some items out of a larger set instead, the Permutation and Combination Calculator uses the same exact arithmetic.
Adding, subtracting, multiplying and raising whole numbers to a power always gives a finite, exact answer, and whole-number results are always shown in full. Division and square roots often go on forever (1 ÷ 7 = 0.142857…), so any result with decimals is cut off, not rounded, after the number of decimal places in the precision box. With the default of 20, 1 ÷ 7 gives 0.14285714285714285714. Negative numbers and decimals are fine for the basic operations, and the exponent must be a whole number. For very large or very small answers the line under the result also gives the number in scientific notation, which is easier to compare at a glance.
Three of the buttons work only with whole numbers. X mod Y is the remainder after dividing X by Y, which is how clocks and calendars wrap around and how a check digit is computed. GCD is the greatest common divisor, the largest number that divides both X and Y, and LCM is the least common multiple, the smallest number both divide into. For example GCD(48, 180) = 12 and LCM(4, 6) = 12. If you also need the actual list of factors, the GCF Calculator, LCM Calculator and Factor Calculator show the working step by step for smaller numbers.
Public-key encryption relies on multiplying two primes that each have hundreds of digits, and recovering them from the product is what makes the code hard to break. Large Mersenne numbers like 2127 − 1 = 170,141,183,460,469,231,731,687,303,715,884,105,727 are used to hunt for record primes. Even everyday things get big quickly: a 10-character password drawn from 94 symbols has 9410 possible combinations, a number with 20 digits. You can try that with the power button, and the Password Generator makes passwords with that much variety.
For everyday sums, an ordinary calculator is fine. When the digits are what you care about, use this one. When the size is what you care about and a few significant digits will do, the Scientific Notation Calculator is lighter, and for ordinary powers and roots the Exponent Calculator and Root Calculator are quicker.
Each input can have up to 60,000 digits, and results of up to about 150,000 digits are shown for powers. Factorials work up to 20,000.
A normal calculator rounds to about 15 digits. This one keeps every digit of whole-number results, so only the last digits differ.
No. They are cut off after the number of decimal places in the precision box, so 100 ÷ 7 with a precision of 5 is 14.28571.
X mod Y is the remainder when X is divided by Y. For example 100 mod 7 is 2, because 7 goes into 100 fourteen times with 2 left over.
Yes, for adding, subtracting, multiplying, dividing, powers with a whole-number exponent, and squares. MOD, GCD, LCM and factorials need whole numbers.
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