About the Big Number Calculator
This big number calculator does exact arithmetic on numbers far larger (or more precise) than an ordinary calculator or spreadsheet can handle. Normal calculators keep about 15–16 significant digits, so 2^100 or 30! come back rounded in scientific notation. Here every digit is kept: enter numbers with hundreds or thousands of digits and get the full result.
It supports addition, subtraction, multiplication, division to any number of decimal places, whole-number powers, remainders (mod), factorials, the greatest common divisor and square roots. Decimals are exact too, so 0.1 + 0.2 is exactly 0.3 rather than 0.30000000000000004.
Use it for number theory and cryptography exercises, checking combinatorics answers, verifying financial calculations that need exact decimal results, or simply exploring how big numbers grow. Inputs can include commas, spaces or scientific notation like 6.022e23. Results are limited to about 20,000 digits so the page stays responsive.
How to use the big number calculator
- 1Type or paste Number A — commas, spaces and e-notation are allowed.
- 2Choose the operation.
- 3Enter Number B (not needed for factorial or square root).
- 4For division or square roots, set how many decimal places you want.
- 5Copy the exact result, or read the scientific-notation summary.
Formula and method
Ordinary calculators use 64-bit floating point, which keeps only about 15–17 significant digits and cannot represent most decimals (like 0.1) exactly. This tool stores each number as an arbitrary-length integer plus a count of decimal places, so addition, subtraction and multiplication are exact: numbers are aligned to the same scale and combined digit for digit.
Division and square roots usually produce endless decimals, so they are calculated to the number of decimal places you choose and rounded half-up at the last digit. Square roots use Newton’s integer method, factorials multiply 1 × 2 × … × A exactly, and the GCD uses the Euclidean algorithm.
- a
- All the significant digits as one exact integer
- s
- Number of digits after the decimal point
Worked examples
Multiply two 30-digit numbers
123456789012345678901234567890 × 987654321098765432109876543210 has 60 digits. A normal calculator would show only about 1.2193263113702 × 10^59; here every digit is exact, and the scientific line rounds to 16 significant digits (1.219326311370218 × 10^59).
2 to the power of 100
2^100 = 1,267,650,600,228,229,401,496,703,205,376, a 31-digit number. The scientific-notation line rounds it to 16 significant digits: 1.267650600228229 × 10^30.
Exact decimal addition 0.1 + 0.2
Because the digits are stored exactly, 0.1 + 0.2 is exactly 0.3 — unlike binary floating point, which gives 0.30000000000000004.
1 ÷ 7 to 30 decimal places
The repeating block 142857 continues forever; the result is cut to 30 decimals and the last digit rounded (the next digit is 1, so no round-up).
25 factorial
25! = 1 × 2 × … × 25 = 15,511,210,043,330,985,984,000,000, which has 26 digits and ends in six zeros (from the six factors of 5 paired with 2s).
Square root of 2 to 30 decimal places
√2 = 1.414213562373095048801688724210 to 30 places; the final 0 is dropped from the display. The value comes from Newton’s method on exact integers, so every digit shown is correct.
Frequently asked questions
Why does my normal calculator round big numbers?+
Most calculators and spreadsheets use IEEE 754 double-precision numbers, which keep only 15–17 significant digits. Beyond that, digits are lost and results appear in scientific notation. Excel, for instance, turns any digit past the 15th into 0.
How big can the numbers be?+
Inputs and results can have up to about 20,000 digits, and factorials go up to 5000!. That is far more than any physical quantity needs, while keeping the calculation fast enough to run instantly in your browser.
Why is 0.1 + 0.2 not 0.3 in some software?+
In binary floating point, 0.1 and 0.2 cannot be stored exactly, so their sum is 0.30000000000000004. This calculator stores decimals as exact integers with a decimal scale, so the sum is exactly 0.3.
How does division work with infinite decimals?+
A division such as 1 ÷ 3 never ends, so it is calculated to the number of decimal places you set (up to 1,000) and the final digit is rounded half-up. Any trailing zeros are removed from the displayed result.
Can I use negative numbers and decimals?+
Yes. Add, subtract, multiply, divide, mod and whole-number powers all accept negative numbers and decimals. Factorial and GCD need whole numbers, and square roots need a non-negative A.