Distance Calculator
Calculate distance between points in 2D and 3D coordinate systems. Free, fast, accurate — no signup, mobile-friendly, wo
Distance Type
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
📐 Formula
Distance Results
Distance
coordinate units
Midpoint
Angle
📋 Step-by-Step Solution
How it works
A distance calculator finds the straight-line distance between two points on a plane using the Pythagorean theorem applied to their coordinate differences. For travel, the related relationship distance = speed × time applies.
Distance between two points
d = √[ (x₂ − x₁)² + (y₂ − y₁)² ]
- (x₁, y₁)
- first point
- (x₂, y₂)
- second point
Worked example
- Point A (1, 2)
- Point B (4, 6)
- Δx = 3, Δy = 4
- d = √(3² + 4²) = √25
Distance = 5 units.
Good to know
- It's the Pythagorean theorem with the coordinate differences as the legs.
- For points on Earth, the great-circle (haversine) distance accounts for curvature.
- For travel time, rearrange distance = speed × time.
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Frequently Asked Questions
How do I calculate the distance between two points?
Use the distance formula, which comes from the Pythagorean theorem: d = √((x₂−x₁)² + (y₂−y₁)²). The horizontal and vertical separations form the legs of a right triangle, and the distance is the hypotenuse.
How does the formula extend to 3D?
Add the third coordinate inside the square root: d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²). The same pattern continues to any number of dimensions, which is how distance is computed in physics and machine learning alike.
Can I use this for locations on Earth?
Not directly — latitude and longitude lie on a sphere, so straight-line coordinate math understates real separation. Great-circle distance via the haversine formula is the standard for geographic points; the planar formula is only acceptable over very short distances.
What units does the result use?
Whatever units the coordinates are in: meters in, meters out. Just ensure both axes use the same unit — mixing feet on one axis with meters on the other produces a meaningless result.