Calculate closing distance and closing speed for two objects moving toward each other or in a chase: remaining separation, time to contact or speed needed.

Constant speeds on one straight line; the model stops at first contact. Not a braking or collision-avoidance tool.

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Closing Distance Formula

The following formula is used to calculate the closing distance between two objects moving towards each other.

Dc = Di - (v1 + v2) × t

Variables:

  • Dc is the remaining separation before first contact
  • Di is the initial distance
  • v1 is the speed of object 1
  • v2 is the speed of object 2
  • t is the time

For head-on motion, subtract (v1 + v2) × t from the initial separation. For a chase with A behind B, use vA − vB instead. If this closing speed is zero or negative, there is no future contact at constant speeds. For positive closing speed, the calculator stops at first contact and reports zero remaining separation thereafter; it does not model motion after contact.

What is Closing Distance?

Closing distance refers to the distance between two objects that are moving towards each other. This concept is often used in scenarios such as collision avoidance, pursuit, and interception. The closing distance decreases over time as the objects approach each other, and it can be calculated using the initial distance, the speeds of both objects, and the time elapsed.

How to Calculate Closing Distance?

The following steps outline how to calculate the closing distance.

  1. First, determine the initial distance (Di) between the two objects.
  2. Next, determine the speed of object 1 (v1).
  3. Next, determine the speed of object 2 (v2).
  4. Next, determine the time (t) during which the objects are moving towards each other.
  5. Finally, calculate the closing distance using the formula Dc = Di - (v1 + v2) * t.
  6. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Initial Distance (Di) = 100 meters

Speed of Object 1 (v1) = 10 meters per second

Speed of Object 2 (v2) = 15 meters per second

Time (t) = 2 seconds