Hamming Distance Calculator

Compare two equal-length strings or binary codes and count how many positions differ, plus the normalized distance and percent similarity.

Quick Facts

Formula
Count positions i where A[i] ≠ B[i]
Only defined for two sequences of equal length n.

Your Results

Calculated
Hamming distance
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Positions that differ
Sequence length
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Characters compared (n)
Normalized distance
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Distance ÷ length (0-1)
Similarity
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Matching positions, as %

Ready

Enter two equal-length sequences, then press Calculate.

About the Hamming Distance

The Hamming distance between two strings of equal length is the number of positions at which the corresponding characters differ. Named after Richard Hamming, who introduced it in his 1950 paper on error-detecting and error-correcting codes, it is a core tool in coding theory, cryptography, bioinformatics, and information theory whenever you need a simple count of "how many spots are different" between two same-length sequences.

The formula

For two sequences A and B, each of length n, the Hamming distance d(A, B) is defined as:

d(A, B) = number of positions i (1 to n) where A[i] ≠ B[i]

Two related figures follow directly from that count. The normalized Hamming distance divides the raw distance by the length, d(A, B) / n, giving a value from 0 (identical) to 1 (every position differs) that lets you compare sequences of different lengths on the same scale. The percent similarity is simply (1 − normalized distance) × 100, the share of positions that match.

A worked example

Compare the seven-character binary strings 1011101 and 1001001:

  • Position 1: 1 vs 1 — match
  • Position 2: 0 vs 0 — match
  • Position 3: 1 vs 0 — differs
  • Position 4: 1 vs 1 — match
  • Position 5: 1 vs 0 — differs
  • Position 6: 0 vs 0 — match
  • Position 7: 1 vs 1 — match

Two of the seven positions differ, so the Hamming distance is 2, the normalized distance is 2/7 ≈ 0.2857, and the similarity is about 71.4%.

Why sequences must be the same length

Hamming distance compares characters position by position, so it is only defined when both sequences have identical length. If your two inputs have different lengths, there is no valid pairing — pad the shorter one (with zeros, spaces, or a placeholder character) or trim the longer one so both are equal length before comparing, or use a different metric such as edit (Levenshtein) distance, which is designed for strings of unequal length.

Where it is used

In telecommunications and storage, Hamming distance determines how many bit errors a code can detect or correct — a code with minimum distance d can detect up to d − 1 errors and correct up to ⌊(d − 1) / 2⌋ errors. In genetics, it counts point differences between equal-length DNA or protein sequences. In cryptography and information retrieval, it measures how similar two fixed-length hashes or fingerprints are.

Frequently Asked Questions

What is Hamming distance?
Hamming distance is the number of positions at which two strings of equal length differ. For sequences A and B of length n, it counts the indices i where A[i] does not equal B[i]. Richard Hamming introduced it in 1950 for detecting and correcting errors in transmitted data.
Why do the two sequences need to be the same length?
Hamming distance compares characters at matching positions, so it only makes sense when both sequences are the same length. If the lengths differ, pad, trim, or otherwise align them to equal length before comparing — or use a metric like edit distance that handles unequal lengths.
What is normalized Hamming distance?
Normalized Hamming distance is the raw distance divided by the sequence length n, producing a value between 0 and 1 that is comparable across sequences of different lengths. Multiplying by 100 gives a percent difference; one minus that value gives a percent similarity.
Is this the same as edit distance (Levenshtein distance)?
No. Hamming distance only counts substitutions at matching positions and requires equal-length strings. Edit distance (Levenshtein distance) also allows insertions and deletions and works on strings of different lengths, making it a more general but more expensive metric to compute.

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