Distance Between Two Points Calculator
Distance Between Two Points Calculator
Enter the coordinates of two points (x₁, y₁) and (x₂, y₂). This calculates the straight-line distance between them using the distance formula, which is really just the Pythagorean theorem applied to coordinates.
The horizontal and vertical differences between the two points form the two legs of a right triangle, and the straight-line distance between the points is that triangle's hypotenuse — which is exactly why the formula looks identical to the Pythagorean theorem underneath. This calculation shows up constantly outside pure math class too: mapping and GPS applications, physics problems involving displacement, and computer graphics all rely on the same coordinate-distance formula.
- Formula: distance = √((x₂ − x₁)² + (y₂ − y₁)²) — the square root of the sum of the squared horizontal and vertical differences.
- Based on the Pythagorean theorem: the horizontal and vertical differences between the points form the two legs of a right triangle, and the distance is the hypotenuse.
- Always non-negative: distance is a magnitude, so the result is always zero or positive, regardless of the order you enter the two points in.
Does it matter which point I label as (x₁,y₁) vs (x₂,y₂)?
No — swapping the two points gives the exact same distance, since both differences get squared before adding, which eliminates any effect of sign or ordering.
How is this related to the Pythagorean theorem?
The horizontal gap (x₂ − x₁) and vertical gap (y₂ − y₁) form the two perpendicular legs of a right triangle, and the direct distance between the points is that triangle's hypotenuse — exactly what a² + b² = c² describes.
Distance Between Two Points Calculator
Enter the coordinates of two points (x₁, y₁) and (x₂, y₂). This calculates the straight-line distance between them using the distance formula, which is really just the Pythagorean theorem applied to coordinates.
The horizontal and vertical differences between the two points form the two legs of a right triangle, and the straight-line distance between the points is that triangle's hypotenuse — which is exactly why the formula looks identical to the Pythagorean theorem underneath. This calculation shows up constantly outside pure math class too: mapping and GPS applications, physics problems involving displacement, and computer graphics all rely on the same coordinate-distance formula.
- Formula: distance = √((x₂ − x₁)² + (y₂ − y₁)²) — the square root of the sum of the squared horizontal and vertical differences.
- Based on the Pythagorean theorem: the horizontal and vertical differences between the points form the two legs of a right triangle, and the distance is the hypotenuse.
- Always non-negative: distance is a magnitude, so the result is always zero or positive, regardless of the order you enter the two points in.
Does it matter which point I label as (x₁,y₁) vs (x₂,y₂)?
No — swapping the two points gives the exact same distance, since both differences get squared before adding, which eliminates any effect of sign or ordering.
How is this related to the Pythagorean theorem?
The horizontal gap (x₂ − x₁) and vertical gap (y₂ − y₁) form the two perpendicular legs of a right triangle, and the direct distance between the points is that triangle's hypotenuse — exactly what a² + b² = c² describes.