Line Intersection Calculator
Define two lines — each by two points, or by a point and a bearing — and find exactly where they cross, whether that crossing falls within a given segment, and the angle between them.
Field aid, not a certified result. Verify against known control before relying on this for a legal boundary determination.
Line A
Line B
How two-line intersection is solved
Quick answer: Any two lines that aren’t parallel cross at exactly one point. Writing each line in parametric form — a starting point plus a direction — and solving the resulting pair of linear equations gives that point directly, along with how far along each line it falls.
Each line is described by a point and a direction vector: for two points, the direction is simply the vector from the first to the second; for a point and bearing, the direction is a unit vector pointing along that bearing. Setting the two parametric equations equal and solving the resulting 2×2 linear system gives a parameter for each line describing exactly where the intersection sits relative to that line’s own reference point.
That parameter is what makes the result useful beyond just coordinates: for a line defined by two points, a parameter between 0 and 1 means the intersection falls inside that segment; outside that range, the lines only cross if extended beyond one of the given points. For a line defined by a point and bearing, the parameter is simply the signed distance from that point to the intersection along the stated direction.
Common surveying uses
| Situation | How it’s set up |
|---|---|
| Two record boundary lines | Both lines by two points — check whether they actually cross within their measured segments |
| Two bearings from known control points | Both lines by point + bearing — classic bearing-bearing intersection |
| A boundary line crossing a sight line | One line by two points, the other by point + bearing |
Frequently asked questions
What does it mean if the lines are “parallel”?
It means the two lines have the same direction and never cross, no matter how far they’re extended. The calculator detects this rather than dividing by a near-zero value and returning a meaningless result.
What’s the difference between “within segment” and “beyond” in the result?
When a line is defined by two points, “within segment” means the intersection falls between those two points. “Beyond” means the lines only meet if that segment is extended past one of its endpoints.
Can I mix a two-point line with a point-and-bearing line?
Yes. Each line’s definition is independent, so you can intersect a boundary line defined by two corners with a sight line defined by a single point and bearing.
What does “coincident” mean instead of “parallel”?
Coincident lines are parallel and also pass through the same points — they’re the same line, so every point on one is also on the other, rather than there being no crossing at all.
How is the angle between the two lines calculated?
From the angle between their direction vectors, reported as the acute angle (0° to 90°) between the two lines, since a line has no single direction of its own.
Does this replace a licensed survey or boundary determination?
No. This is a calculation aid for checking and reconstructing line geometry. Any result used for a legal boundary should be verified and certified by a licensed surveyor.
