Distance Calculator
Calculate distance between two points.
Two Points
Point 1
Point 2
Points:
(0, 0) and (3, 4)
Distance Result
Distance
5.0000
units
Horizontal Difference (Δx)
3.00
Vertical Difference (Δy)
4.00
Formula:
d = √[(3 - 0)² + (4 - 0)²]
d = √[(3)² + (4)²]
d = 5.0000
About This Calculator
The Distance Calculator helps you calculate the distance between two points in a 2D coordinate system using the distance formula. This is the straight-line (Euclidean) distance between the two points.
Simply enter the coordinates of two points (x₁, y₁) and (x₂, y₂), and the calculator will compute the distance using the Pythagorean theorem. This is useful in geometry, navigation, and coordinate geometry problems.
Formula & Calculation Method
Distance Formula:
Distance Formula (2D):
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
where:
(x₁, y₁) = coordinates of first point
(x₂, y₂) = coordinates of second point
d = distance between points
Derived from:
Pythagorean Theorem: c² = a² + b²
The distance formula is derived from the Pythagorean theorem. The horizontal difference (dx) and vertical difference (dy) form the legs of a right triangle, with the distance as the hypotenuse.
How to Use This Calculator
- Enter Point 1: Input the x and y coordinates of the first point.
- Enter Point 2: Input the x and y coordinates of the second point.
- View Results: See the calculated distance and coordinate differences.
- Interpret: The distance is the straight-line distance between the two points.
Frequently Asked Questions
What is the distance formula?
The distance formula is d = √[(x₂ - x₁)² + (y₂ - y₁)²], which calculates the straight-line distance between two points in a coordinate system. It is derived from the Pythagorean theorem.
Can I use this for 3D coordinates?
This calculator is for 2D coordinates. For 3D, the formula extends to d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²], adding the z-coordinate difference.
What units does the distance use?
The distance uses the same units as the coordinates. If coordinates are in meters, distance is in meters. If coordinates are in feet, distance is in feet. Ensure both points use the same coordinate system and units.
How is this related to the Pythagorean theorem?
The distance formula is essentially the Pythagorean theorem applied to coordinate geometry. The horizontal difference (dx) and vertical difference (dy) are the legs of a right triangle, and the distance is the hypotenuse.
Expert Reviewed
This calculator was reviewed by NumCalculators Editorial Team, Multi-disciplinary Expert Team