2D Distance Calculator
Calculate the distance between two points in a 2D plane using the Euclidean distance formula. Free online calculator with instant results and step-by-step explanation.
Point A (x₁, y₁)
Point B (x₂, y₂)
About This Calculator
The 2D Distance Calculator computes the straight-line distance between two points in a two-dimensional coordinate system. This calculation is fundamental in geometry, physics, computer graphics, and navigation.
The calculation uses the Euclidean distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2), which is derived from the Pythagorean theorem. The result represents the length of the shortest path between the two points.
- Point A (x1, y1): The coordinates of the first point.
- Point B (x2, y2): The coordinates of the second point.
- Distance: The Euclidean distance between the two points in the same units as the input coordinates.
Frequently Asked Questions
How do you calculate 2D distance between two points?
The 2D distance between two points (x1, y1) and (x2, y2) is calculated using the Euclidean distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). Simply subtract the x-coordinates, subtract the y-coordinates, square both results, add them together, and take the square root.
What is the formula for Euclidean distance in 2D?
The Euclidean distance formula for 2D space is d = sqrt((x2 - x1)^2 + (y2 - y1)^2). This formula is derived from the Pythagorean theorem, treating the horizontal and vertical differences as the legs of a right triangle with the distance as the hypotenuse.
What is 2D distance used for?
2D distance calculations are used in computer graphics for collision detection, in GPS navigation for map distances, in geometry for finding lengths, in machine learning for k-nearest neighbors algorithms, in robotics for path planning, and in game development for measuring distances between objects on a 2D plane.
What is the distance between (0,0) and (3,4)?
Using the formula d = sqrt((3-0)^2 + (4-0)^2) = sqrt(9 + 16) = sqrt25 = 5. So the distance between (0,0) and (3,4) is 5 units. This is a classic example because 3-4-5 forms a Pythagorean triple.
Is 2D distance always positive?
Yes, distance is always a non-negative value. The Euclidean distance formula produces zero when both points are identical and a positive value for any two distinct points. This is because squares of real numbers are always non-negative and the square root of a non-negative number is also non-negative.
What is the difference between 2D and 3D distance?
2D distance uses two coordinates (x, y) and the formula d = sqrt((x2-x1)^2 + (y2-y1)^2). 3D distance adds a third dimension z with the formula d = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2). The 2D formula is a special case of the 3D formula where z2 = z1.