Enter the final height, velocity, and time into the calculator to determine the initial height from which an object was dropped or thrown vertically. This calculator assumes the only force acting on the object is gravity.

Initial Height Formula

The following formula is used to calculate the initial height:

H_i = H_f + V * t + 0.5 * g * t^2


  • H_i is the initial height (meters)
  • H_f is the final height (meters)
  • V is the velocity (meters per second)
  • t is the time (seconds)
  • g is the acceleration due to gravity (9.80665 m/s^2)

To calculate the initial height, add the final height to the product of the velocity and time, then add half of the product of the acceleration due to gravity and the square of the time.

What is Initial Height?

Initial height is the height from which an object starts its motion when dropped or thrown vertically upwards or downwards. It is an important parameter in kinematics for determining the motion of objects under the influence of gravity.

How to Calculate Initial Height?

The following steps outline how to calculate the Initial Height.

  1. First, determine the final height (H_f) in meters.
  2. Next, determine the velocity (V) in meters per second.
  3. Next, determine the time (t) in seconds.
  4. Use the formula H_i = H_f + V * t + 0.5 * g * t^2 to calculate the initial height (H_i).
  5. After inserting the variables 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.

final height (H_f) = 20 meters

velocity (V) = 5 meters per second

time (t) = 3 seconds