Line Intersection Calculator
Find the 2D coordinate where two lines intersect from two coordinate points on each line. Check whether the intersection also lies inside both finite segments.
Coordinate convention: X = Easting and Y = Northing. All four points must use the same coordinate system and unit.
How to use this calculator
Quick example: A(0,0)–B(10,10) and C(0,10)–D(10,0) intersect at (5,5).
1. Enter line coordinates
2. Intersection results
Enter two valid points for each line.
Export results
Calculation method
The calculator uses the vector form P = A + t(B − A) and P = C + u(D − C). A non-zero cross product produces one intersection. Values 0 ≤ t ≤ 1 and 0 ≤ u ≤ 1 mean the point is inside both finite segments.
Parallel lines have no unique intersection. Collinear lines have infinitely many points in common, so a single coordinate cannot be reported without another constraint.
Frequently asked questions
Does the calculator use infinite lines or finite segments?
You can choose either mode. Infinite-line mode reports the geometric intersection even when it falls beyond a segment endpoint.
What do the t and u parameters mean?
They show the relative position of the intersection along A–B and C–D. Zero is the first point and one is the second point.
What happens if the lines are parallel?
The calculator reports that there is no unique intersection and distinguishes parallel from collinear lines.
Can I use local grid coordinates?
Yes. Use any consistent projected or local coordinate system; do not mix coordinate systems or units.
Does it work with latitude and longitude?
For small local work, first convert geographic coordinates to a suitable projected coordinate system. This calculator performs planar geometry.
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