About the Big Number Calculator
A big number calculator handles arithmetic that overflows ordinary numeric limits — large powers and factorials whose results run to dozens or hundreds of digits. These appear in combinatorics, probability, cryptography, and any counting problem where the possibilities multiply.
The formula
n! = n · (n − 1) · … · 2 · 1 and aᵇA factorial multiplies every integer from 1 up to n and counts the number of ways n distinct items can be ordered. A power multiplies the base by itself b times.
How to use this calculator
- 1Enter your Number A. The field starts at
100, which you can overwrite. - 2Enter your Number B (exponent or factorial input). The field starts at
5, which you can overwrite. - 3Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Number A | 100 |
| Number B (exponent or factorial input) | 5 |
Result
A^B = 100^5 = 10,000,000,000
log₁₀(A^B) ≈ 10.0000
100! ≈ ~10^156.6
A × B = 500
A ÷ B = 20.000000
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
Factorials grow faster than almost anything else in elementary mathematics. 10! is 3.6 million, 20! exceeds 2 quintillion, and 70! is beyond the range of standard double-precision floating point entirely. This is why brute-force approaches to ordering problems become impossible so quickly: a travelling salesman visiting 20 cities has 20! possible routes.
Standard computer numbers cannot represent these exactly. A 64-bit float carries about 15 to 17 significant digits, so beyond that results are approximations expressed in scientific notation — the magnitude is right but the trailing digits are not. Exact arithmetic on such numbers requires arbitrary-precision libraries, which is what cryptographic software uses.
Things worth knowing
- Factorials are defined only for non-negative integers, with 0! = 1 by convention.
- For very large factorials, Stirling's approximation gives a usable estimate without computing the full product.
- Results beyond about 15 significant digits are approximate. Treat the exponent as reliable and the tail as indicative.
- When comparing enormous numbers, compare their logarithms — the difference of logs is far easier to interpret.
- Cryptography relies on the fact that multiplying two large primes is easy while factoring the product is not.
Frequently asked questions
What is a factorial used for?+
Counting arrangements. 5! = 120 is the number of ways to order five distinct items, and factorials form the basis of permutation and combination formulas throughout probability.
Why is 0! equal to 1?+
Because there is exactly one way to arrange nothing — the empty arrangement. Defining it as 1 also keeps the recursive rule n! = n · (n−1)! consistent and makes combination formulas work at the boundaries.
How large can these calculations go?+
Standard double-precision arithmetic overflows around 1.8 × 10³⁰⁸, roughly 170 factorial. Beyond that you need arbitrary-precision libraries, and results here are shown in scientific notation once exact representation is lost.
Why are results shown in scientific notation?+
Because writing out a hundred-digit number is unreadable and the precision is not there anyway. Scientific notation shows the leading significant digits and the magnitude, which is what actually conveys the size.