Distance between two points (2D or 3D)
Enter the coordinates of the two points: the page gives the length of the segment joining them.
Result
5Distance AB
- d = √(3² + 4²) = √25 = 5
- Change in x (x₂ − x₁)
- 3
- Change in y (y₂ − y₁)
- 4
- Midpoint
- (2.5, 4)
Inputs
- Dimension
- Plane (2D)
- x of point A
- 1
- y of point A
- 2
- x of point B
- 4
- y of point B
- 6
How it is calculated
Compute the changes Δx = x₂ − x₁, Δy = y₂ − y₁ (and Δz in 3D).
Result
Distance AB
- Change in x (x₂ − x₁)
- 3
- Change in y (y₂ − y₁)
- 4
- Midpoint
- (2.5, 4)
How it is calculated
- Compute the changes Δx = x₂ − x₁, Δy = y₂ − y₁ (and Δz in 3D).
- Distance = √(Δx² + Δy² + Δz²): this is Pythagoras’ theorem.
- Midpoint = average of the two points’ coordinates.
Example
A(1, 2) and B(4, 6): Δx = 3, Δy = 4, d = √(9 + 16) = √25 = 5. Midpoint (2.5, 4).
Good to know
- This is the straight-line distance in an orthonormal grid, not a road trip.
- For two cities on Earth you need a distance on the sphere (latitude, longitude), not this formula.
- Both points must use the same unit.
Frequently asked questions
What is this tool used for?
Enter the coordinates of the two points: the page gives the length of the segment joining them.
How is the result calculated?
Compute the changes Δx = x₂ − x₁, Δy = y₂ − y₁ (and Δz in 3D).
What should I check before using the result?
This is the straight-line distance in an orthonormal grid, not a road trip.