Calculators » CRC-16 Calculator | CRC16 Formula, Polynomial & Examples

CRC-16 Calculator | CRC16 Formula, Polynomial & Examples

crc-16 crc16 calculator formula calculator

A CRC-16 calculator is a reliable tool used to compute 16-bit Cyclic Redundancy Check (CRC-16) values for verifying data integrity in digital communication, embedded systems, and networking protocols. CRC-16 algorithms are widely used in standards such as MODBUS, CCITT, X-25, USB, CAN, and IBM/ANSI, making accurate CRC calculation essential for software developers, hardware engineers and protocol designers.

This online CRC-16 calculator allows you to generate CRC values using custom input data, generator polynomials, initial values, reflection options (RefIn/RefOut), and XOR output settings. Along with instant calculation, the page also explains the CRC-16 formula.

CRC16 checksum Calculator

Inputs

Outputs

EXAMPLE-1 : CRC-16/CCITT-FALSE

INPUTS:

  • hexInput = “12345678”
  • polynomial = 0x1021
  • Init = 0xFFFF
  • xorOut = 0x0000
  • RefIN = 0 (i.e. FALSE)
  • RefIN = 0 (i.e. FALSE)

OUTPUT:

  • CRC Checksum(Hex) = 0x30EC

EXAMPLE-2 : CRC-16/IBM (ANSI)

INPUTS:

  • hexInput = “12345678”
  • polynomial = 0x8005
  • Init = 0x0000
  • xorOut = 0x0000
  • RefIN = 1 (i.e. TRUE)
  • RefIN = 1 (i.e. TRUE)

OUTPUT:

  • CRC Checksum(Hex) = 0x347B

CRC-16 Formula

The polynomials are different for CRC-16 CCITT and IBM variants of CRC Type as mentioned in the table below.

CRC-16 Calculation Formula

CRC TypePolynomialHex value
CRC-16/IBMX^16 + X^15 + X^2 + 10x8005
CRC-16/CCITTX^16 + X^12 + X^5 + 10x1021

Why Reflection (RefIn & RefOut) is used ?

CRC algorithms were historically implemented in LSB first shift registers in hardware.

When data enters least significant bit (LSB) first, the CRC math must be adapted. Instead of redesigning the polynomial math, designers:

  • RefIn : Reverse bits of each input byte before CRC processing

  • RefOut : Reverse bits of final CRC value

This produces the same mathematical result, but matches LSB first hardware behavior.

Summary: Use this CRC-16 calculator and formula guide to quickly validate checksums, troubleshoot communication errors and gain a deeper understanding of how CRC-16 protects data in real world systems.

References for further study

  1. Ross N. Williams, A Painless Guide to CRC Error Detection Algorithms
  2. ITU-T Recommendation V.41 — CRC-16-CCITT specification
  3. ISO/IEC 13239 — HDLC CRC definitions