Minkowski Distance Calculator
Calculate the Minkowski distance (generalized Lp norm) between two vectors.
Inputs
Comma-separated values
Comma-separated values
Minkowski Distance
4.326749
Dimensions
3
Step by step
Sum of |aᵢ − bᵢ|^3
Σ|aᵢ − bᵢ|^3
= 81.0000
p-th root
81.0000^(1/3)
= 4.326749
How it works
Minkowski distance generalizes both Euclidean (p=2) and Manhattan (p=1) distances using a configurable p parameter. Higher p values give more weight to the largest single-dimension difference, while lower p values spread weight more evenly across dimensions.
Formula
Minkowski Distance
d(a, b) = (sum(|a_i - b_i|^p))^(1/p)
- p
- Order of the norm (1=Manhattan, 2=Euclidean)
Frequently Asked Questions
What values of p are most common?
p=1 (Manhattan), p=2 (Euclidean), and p=∞ (Chebyshev, max absolute difference) are the most commonly used. Fractional p values between 0 and 1 are sometimes used in high-dimensional data.
How does p affect the distance behavior?
As p increases, the metric becomes more sensitive to the single largest coordinate difference. In the limit (p→∞), Minkowski distance equals the maximum absolute difference across all dimensions.