Hamming Distance Calculator

Count differing bits between two equal binary strings.

What it does

Hamming distance measures how many bits flip between two equal strings. Error codes use it to tell how many flips they can spot or fix. Larger distance means easier separation.

The tool above takes two binary strings and returns distance, similarity, and length. The defaults 1010 and 1001 match the worked example, so the page opens showing distance 2. Type new strings to update all three results.

Counting is positional: compare first with first, second with second, and tally mismatches. Here positions three and four differ, so distance is 2 over length 4 for 50.0 percent same.

Use this for code theory, barcodes, and DNA k-mers in binary form. For hex bytes with XOR totals use a checksum tool instead.

This page shows the method, one full hand checked example at 1010 vs 1001, a reference table, and practice checks that run through the tool.

How to use

1. Type first string with 0 and 1 only.
2. Type second string with equal length.
3. Keep each 1 to 64 bits.
4. Read Distance as mismatch count.
5. Read Similarity as same percent.
6. Pad shorter codes before comparing.

Formula

distance

Differing positions.

length

Shared string length.

similarity

Same share in percent.

Equal length required. Spaces and dashes strip first. Non binary stops with a message.

Worked example

Reference table

Limits

• Equal length binary only, 1 to 64 bits.
• Counts substitutions, not inserts or deletes.
• No code correction here, only distance.
• Text needs binary encode first.

Common mistakes

• Comparing different lengths without padding.
• Counting matches instead of mismatches.
• Pasting spaces that change length. This tool strips them first.
• Using hex without binary convert.
• Reading similarity as distance.

Try it yourself

Quick checks. Answers sit tucked under each question.

Questions

Sources

• Wikipedia: Hamming distance
• Wikipedia: Exclusive or

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