Hamming Distance

The Hamming distance is the number of positions at which corresponding characters differ between two equal-length strings; it only applies to equal-length comparisons.

Purpose

Measures the number of differing positions between equal-length strings, used in error detection and coding theory.

Mechanism

For equal-length strings s and t, d = Σ(s[i] ≠ t[i]). Defined only when lengths are equal. For binary strings the Hamming distance can be computed efficiently with bitwise operations (XOR + popcount).

Use cases

Error detection and error-correcting codes
Binary string similarity
Perceptual difference of image hashes
Information theory education

Examples

Input
```
karolin → kathrin
```
Output
```
3
```
3 positions differ

Common errors

Applying the Hamming distance to strings of unequal length: Use the Levenshtein distance for variable lengths

Related terms

Levenshtein Distance

The Levenshtein distance is the minimum number of single-character insertions, deletions, and substitutions needed to make two strings identical.

Jaro-Winkler Distance

The Jaro-Winkler distance is a refinement of the Jaro distance that weights common prefixes, making it better suited for matching short strings such as person names where prefixes matter.

Edit distance is the minimum number of single-character edit operations (insertion, deletion, substitution) required to transform one string into another; the Levenshtein distance is its most common form.

Related tools

Hamming Distance

Hamming Distance — pure client-side tool. Privacy-first, no server round-trip.

Hamming Weight — pure client-side tool. Privacy-first, no server round-trip.

References