CRC Calculator

What is a CRC?

A cyclic redundancy check (CRC) is a short checksum computed from a block of data. The sender calculates it and sends it along with the data; the receiver repeats the calculation and compares. If the two values differ, the data was damaged on the way and can be re-sent. CRCs are fast to compute in hardware and software, and they are very good at catching the kinds of errors that real communication channels and storage devices produce, such as bursts of flipped bits.

A CRC is named after the length of its result. A CRC-8 has 8 bits (two hex digits), a CRC-16 has 16 bits and a CRC-32 has 32 bits. The longer the check value, the smaller the chance that damaged data slips through unnoticed: roughly 1 in 256, 1 in 65,536 and 1 in 4.3 billion for random corruption. Even the one-bit parity bit is a (very weak) CRC.

A CRC protects against accidents, not attackers. It is trivial to change a file and adjust it so that its CRC stays the same, so never use it to prove that data is authentic. For that, use a cryptographic hash such as SHA-256.

How to use the CRC calculator

1. Choose the CRC algorithm: CRC-8, CRC-16 or CRC-32 (the default).
2. Type or paste your text into the String box.
3. Press Calculate. The checksum appears as a hexadecimal number starting with 0x.

Example: the text 123456 gives 0x70930F27 with CRC-32, 0xA141 with CRC-16 and 0xC3 with CRC-8.

What is checksummed. The calculator works on the UTF-8 bytes of the text exactly as you typed it. Nothing is trimmed, normalised or added, and the result is written in upper-case hexadecimal.

• Every character counts. Spaces, tabs and capital letters change the bytes, and so usually the checksum (CRC-8 is the exception, see below).
• UTF-8 encoding. A plain ASCII character is one byte, é is two (c3 a9), 日 is three (e6 97 a5) and an emoji such as 😀 is four (f0 9f 98 80).
• Line breaks are kept as they arrive. A browser text box stores each line break as a single line-feed character (LF, byte 0a), and text pasted with Windows CR LF line endings normally arrives as LF too. The calculator does not convert it to anything else. CRC-32 sees the byte 0a, CRC-16 sees its spelling 0a, and CRC-8 counts it as a non-digit.

To checksum a file that uses Windows CR LF line endings, run a command-line tool on the file itself. This page can only checksum text the way a browser text box holds it.

How a CRC is calculated

A CRC treats the message as one very long binary number, divides it by a fixed generator polynomial using arithmetic without carries, and keeps the remainder. Without carries, addition and subtraction are the same operation, an exclusive OR (XOR), which is why CRC circuits are built from shift registers and XOR gates.

CRC = (message × 2^n) mod G(x)n is the CRC width in bits; the division is carry-less (XOR) division.

Worked example with a 3-bit CRC. Take the message 10110011 and the generator 1011 (the polynomial x³ + x + 1). Append three zeros to the message to make room for the remainder, giving 10110011000. Then repeatedly line the generator up under the leftmost 1 and XOR:

No 1 bit is left in the first eight positions, so the division is finished. The remainder, 101, is the 3-bit CRC. The sender transmits 10110011 followed by 101; a receiver that divides the whole thing by 1011 gets a remainder of zero if nothing was damaged.

Real CRCs add a few conventions on top of this division: a non-zero starting value, optional reversal of the bit order of each byte and of the result, and a final XOR. Each combination of polynomial and conventions is a different, named variant.

Which variants this calculator uses

CRC is a family, not a single algorithm, and two tools can both say "CRC-32" and give different numbers. This calculator follows these definitions:

• CRC-32 uses the polynomial 0x04C11DB7, starts from 0xFFFFFFFF, does not reflect any bits and XORs the result with 0xFFFFFFFF. This is the algorithm called CRC-32/BZIP2, and the four bytes of the answer are written in the opposite order (the "crc32" hash of the PHP programming language works this way). It is not the CRC-32 used by zip, gzip, PNG and Ethernet.
• CRC-16 is CRC-16/XMODEM (polynomial 0x1021, starting value 0) applied to the hexadecimal spelling of the input's UTF-8 bytes, in lower case with two characters per byte. The text ab is first written as 6162, and the checksum covers those four characters.
• CRC-8 uses the polynomial 0x4D with starting value and final XOR 0xFF and reflected bits (CRC-8/KOOP). Each UTF-8 byte of the input is first reduced to its digit value: the characters 0 to 9 count as 0 to 9, and every other byte (letters, spaces, line breaks, each byte of an accented letter) counts as 0. As a result the CRC-8 of a text without digits depends only on its length in bytes.

Because of these differences, compare the results of this calculator with other tools only when they use exactly the same variant. If you need the checksum that a zip file or PNG image stores, use a tool that implements the standard CRC-32 (also called CRC-32/ISO-HDLC).

Where CRCs are used

• Network frames (Ethernet, Wi-Fi) and storage formats (zip, gzip, PNG) include a CRC-32 so that corrupted data is detected.
• Short CRCs such as CRC-8 and CRC-16 appear in sensor buses, serial protocols, barcodes and memory cards, where space is tight.
• Firmware and configuration blocks often end with a CRC so that a device can refuse to run damaged data.

In all of these the receiver divides the data it got by the same polynomial and compares the result, as described above. For a fingerprint that must also resist deliberate tampering, see the MD5 generator and its caveats, or prefer SHA-256.