Point Plane Projection Calculator
Calculate signed distance and perpendicular projection of a three-dimensional point onto a plane.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Normalize the entered plane normal only for distance/projection while retaining the stated plane equation.
Signed distance=(n dot point−d)/|n|; foot=point−distance×n/|n|
Worked example
Point(1,2,3) projects to(1,2,1) on plane z=1 with signed distance2.
Assumptions and input details
Nonzero normal, matching coordinate length units and infinite plane. Reversing both normal and d changes signed distance orientation without changing the plane or projected point.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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