Line-Plane Intersection
Where a line meets a plane in 3D
About this calculator
The Line-Plane Intersection Calculator finds where a line P(t) = P₀ + t·d meets a plane ax + by + cz = e. Substituting the line into the plane gives t = (e − n·P₀)/(n·d), from which it reports the intersection point, the parameter t, and the dot product n·d. When n·d = 0 it distinguishes a line strictly parallel to the plane from one lying inside it, and it rejects zero direction or normal vectors, which don't define a line or plane.
How to use the Line-Plane Intersection calculator
- Enter the measurements you know into the input fields.
- Read the computed properties — they update instantly as you type.
- Compare the diagram with your figure to confirm the setup is right.
- Copy the page URL to share the exact calculation.
Common examples
- Line through (0, 0, 0) with direction (0, 0, 1) meets plane z = 5 → point (0, 0, 5) at t = 5
- Line (1, 2, 0) + t(1, 1, 1) meets x + y + z = 9 → intersection (3, 4, 2) at t = 2
- Line through (0, 0, 1) with direction (1, 0, 0) and plane z = 5 → parallel, no intersection (n·d = 0)
- Line through (0, 0, 5) with direction (1, 0, 0) and plane z = 5 → coincident: the line lies in the plane
Frequently asked questions
How does the Line-Plane Intersection calculator work?
Enter the known measurements of your figure and the calculator applies the standard geometric formulas to find the remaining properties, alongside a diagram that reflects your numbers. All values are computed with high-precision arithmetic.
When would I use the Line-Plane Intersection calculator?
It helps with geometry homework, technical drawing, construction and DIY layout, and any situation where you know some measurements of a shape and need the rest.
How accurate are the results?
Formulas are evaluated at 30 significant digits of precision internally, including roots and trigonometric functions. Displayed values are rounded for readability, but the underlying computation does not accumulate floating-point drift.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same figure and results for whoever clicks it.