Quick answer: 2^100 = 1,267,650,600,228,229,401,496,703,205,376 exactly, a 31-digit number; an ordinary calculator would show only 1.2676506 × 10³⁰.
How it's calculated
Ordinary calculators and spreadsheets store numbers with about 15–17 significant digits, so large results are rounded. This calculator uses arbitrary-precision integers, the same method as long multiplication on paper, so every digit is exact.
Division gives the whole-number quotient and the remainder, with a = quotient × b + remainder. a mod b gives the remainder only, always between 0 and b − 1 when b is positive, which is the convention in number theory and clock arithmetic.
Powers grow fast: the number of digits of aᵇ is about b × log₁₀ a, so 2^1000 has 302 digits. Results are limited to 20,000 digits. For factorials and counting use the permutation and combination calculator; for decimals use scientific notation.
Worked examples
- Power: 2^100 = 1,267,650,600,228,229,401,496,703,205,376
- Multiplication: 123,456,789 × 987,654,321 = 121,932,631,112,635,269
- Division: 1,000,000,000,000 ÷ 7 = 142,857,142,857 R 1
Frequently asked questions
Is there a size limit?
Inputs and results can have up to 20,000 digits, which keeps the page responsive.
Can I use decimals?
No, this calculator is for whole numbers. Multiply decimals by a power of 10 first, or use the scientific calculator for approximate answers.
What is a mod b for negative numbers?
With a positive b the result is always 0 to b − 1: −7 mod 3 = 2, because −7 = −3 × 3 + 2.
How many digits does 2^100 have?
31. The full number is 1,267,650,600,228,229,401,496,703,205,376.
Why does my spreadsheet get big results wrong?
Spreadsheets only keep about 15 significant digits, so the tail end of a big result quietly turns into zeros. Here every digit is exact.
How do I check whether one big number divides another?
Use mod. If a mod b comes out as 0, b goes into a exactly.