Distance Metric Explorer

Compare two small numeric vectors, true token sets or bitstrings. Results update locally as you type; only applicable metrics are shown. Definitions reveals their formulas. Example restores the current tab’s inputs. CSV contains the parsed inputs, unrounded results and any undefined-cosine reason.

Vectors: 1–32 decimal components, separated by spaces, commas or semicolons; decimal point and scientific notation are accepted. A comma separates components, it is not a decimal mark. Equal dimensions are required. Nonzero magnitudes 1e−300–1e300; 8,000 characters per input. Euclidean is straight-line distance; Manhattan sums absolute component differences. Distances use input units and grow with scale, not a similarity percentage. Hamming counts unequal component values using exact numeric equality, without a tolerance.

Sets: whitespace/comma/semicolon-separated tokens, at most 500 before removing duplicates; empty input is the empty set. Tokens are NFC-normalized and case-sensitive, punctuation within a token is retained. Order and repetitions have no effect. Jaccard is intersection/union (two empty sets: similarity 1). Set cosine uses binary presence vectors, not word frequencies. For {a,b} and {b,c}, Jaccard is 1/3 and cosine 1/2. For lexical text or images use Similarity Search.

Bits: 1–128 zeroes/ones, whitespace ignored, equal lengths. Hamming counts differing positions; similarity is 1−count/length. Euclidean equals √Hamming and Manhattan equals Hamming. Jaccard compares positions of ones, ignoring shared zeroes; all-zero pairs have Jaccard similarity 1. Cosine uses the bit vectors. 100/010 gives Hamming 2, similarity 1/3, Jaccard 0.

Cosine measures direction, independent of positive scale: similarity −1 to 1, distance 1−similarity (0 to 2). Opposite signed vectors give similarity −1 and distance 2; orthogonal nonzero vectors similarity 0 and distance 1; an empty set or zero vector has no defined direction and shows a dash. Cosine distance is not a metric satisfying the triangle inequality in general. A dash in the similarity column for Euclidean/Manhattan means no arbitrary conversion is invented. Finite floating-point arithmetic and eight significant display digits; CSV retains full precision. This compares coordinates/tokens, not semantic meaning.