CRC Calculator

W. Wesley Peterson published the foundational CRC paper, "Cyclic Codes for Error Detection", in 1961 while at the University of Hawaii. His key insight: treating the message and divisor as polynomials in GF(2) (binary arithmetic mod 2) produces a checksum with beautifully predictable error-detection properties — in particular, any burst error shorter than the CRC length is guaranteed to be caught, plus all single-bit errors, all odd-count errors, and a high fraction of random errors.

Hardware implementation is trivially cheap: a shift register with XOR gate taps at positions corresponding to the polynomial coefficients. Early telecom equipment implemented CRC in dedicated logic; modern systems use either table-lookup (fast on CPUs) or dedicated hardware (built into every Ethernet PHY). The Intel pclmulqdq instruction added to x86 in 2008 reduces even software CRC-32 to a handful of cycles.

Polynomial standardization settled a few common variants: CRC-8 (0x07) for short packets like I²C and 1-Wire; CRC-16-CCITT (0x1021) for XMODEM, X.25, and Bluetooth; CRC-16-IBM (0x8005) for USB and Modbus; CRC-32 (0x04C11DB7) for Ethernet, ZIP, PNG, and most storage checksums. Each polynomial was selected to maximize error detection over expected burst lengths while remaining hardware-efficient. New applications still typically pick one of these standard polynomials rather than design custom ones.

Enter hex data (with or without 0x prefix, and optional whitespace) and pick a CRC variant. The tool performs bitwise polynomial division and returns the CRC in hex and decimal, along with the polynomial and input length.

Important detail: full CRC specifications include initial value, XOR-out, bit reflection (input and output), and polynomial — this calculator uses the standard defaults for each variant. If your target system uses non-standard parameters (some embedded protocols reflect differently or use unusual init values), verify against a known-good reference implementation for that system. All math runs client-side; no data leaves your browser.