Two Moving Points Closest Approach Calculator
Find the earliest minimum separation of two points moving at constant 2D velocities within a chosen future interval.
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
Subtract positions and velocities to form relative motion. Minimize squared separation and clamp the candidate time to the entered interval.
t*=−(relative position·relative velocity)/|relative velocity|²; t=clamp(t*,0,horizon)
Worked example
Points (0,0) at velocity (1,0) and (10,3) at velocity (-1,0) have minimum separation 3 at time 5. A horizon of 2 instead gives distance √45 at time 2.
Assumptions and input details
Positions share one length unit; velocity components use that length per one common time unit, matching the horizon. Point objects, constant velocities and no acceleration. Equal velocities keep separation constant and return earliest time zero. No object dimensions, uncertainty, curved routes or avoidance advice. Negative velocity components indicate direction; the horizon is nonnegative.
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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