Euclidean Distance
Calculate the 2D Euclidean distance between two points A(x1,y1) and B(x2,y2) using the formula d = sqrt((x2-x1)^2+(y2-y1)^2). Free online distance calculator for coordinate geometry and vector analysis.
About This Calculator
The Euclidean Distance Calculator computes the straight-line distance between two points in the 2D plane using the Pythagorean distance formula. Given points A(x1,y1) and B(x2,y2), the distance d = sqrt((x2-x1)^2 + (y2-y1)^2).
Named after the ancient Greek mathematician Euclid, this is the most commonly used distance metric in mathematics, physics, engineering, and computer science. It is fundamental to geometry, vector calculations, and is the basis for more complex distance measures in machine learning and data analysis.
Frequently Asked Questions
What is Euclidean distance?
Euclidean distance is the straight-line distance between two points in Euclidean space. In 2D, it is calculated as d = sqrt((x2-x1)^2 + (y2-y1)^2), which is essentially the Pythagorean theorem applied to coordinate differences.
How is Euclidean distance used in real life?
Euclidean distance is used in GPS navigation, computer graphics, machine learning (k-nearest neighbors, clustering), physics (displacement calculations), robotics (path planning), and geolocation services.
Is this calculator free?
Yes, all calculators on Calculy are completely free to use.