Big Number Calculator
Exact arithmetic on integers up to 10,000 digits: add, subtract, multiply, divide with remainder, and raise to powers. No rounding, no precision loss — every digit of every result is correct, computed entirely in your browser.
Big-integer arithmetic
Example: 2 ^ 128 has 39 digits.
The precision cliff at 2⁵³
Double-precision floating point — what most calculators and programming languages use for numbers — represents integers exactly only up to 9,007,199,254,740,992 (2⁵³). One past that, gaps appear: a float cannot tell 9,007,199,254,740,993 from its neighbor. Multiply it by 2 in floating point and you get a rounded answer; this calculator returns the exact 18,014,398,509,481,986. The example is computed at build time by the same engine that runs the calculator above.
What exact big-integer math is for
Cryptography lives here — RSA keys, Diffie–Hellman groups, and hash arithmetic all involve integers hundreds of digits long. So do combinatorics (factorials and binomial coefficients overflow floats almost immediately), number theory, precise financial ledgers counted in smallest units, and checking the output of arbitrary-precision code. For instance, 2¹²⁸ — the size of the IPv6 address space and of an AES-128 key space — is exactly:
340,282,366,920,938,463,463,374,607,431,768,211,456
— 39 digits, every one of them significant.
Integer division, explicitly
Dividing integers exactly generally produces a fraction, which an integer calculator cannot
represent. Instead, division here returns the truncated quotient and the remainder separately
— the same convention as the / and % operators in most programming languages
— so no precision is silently discarded.
Frequently asked questions
Why do ordinary calculators give wrong answers for big integers?
Most calculators (and JavaScript numbers, and spreadsheet cells) store values as 64-bit floating point, which is only exact up to 2^53 = 9,007,199,254,740,992. Beyond that, integers get silently rounded to the nearest representable value. This calculator uses arbitrary-precision integers, so every digit is exact.
What happens when I divide?
Division is integer division with an explicit remainder — 100 ÷ 7 gives quotient 14, remainder 2 — because a fraction cannot be represented exactly as an integer. Quotient × divisor + remainder always reconstructs the original value.
How big can the numbers get?
Operands and results are capped at 10,000 digits, and exponents at 100,000 (subject to the same result cap). That comfortably covers cryptographic sizes — RSA-2048 moduli are 617 digits.
Can I enter decimals or commas?
No — this is an integer calculator, and commas are rejected rather than guessed at. Paste raw digit strings, optionally with a leading minus sign. Results are displayed with thousands separators for readability, but copied without them.
Values are processed locally in your browser and never transmitted. Arithmetic is implemented as tested, typed BigInt functions — see the methodology page.