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Free fall calculator: time and impact speed

Estimate vertical free-fall time and impact speed with constant-acceleration kinematics and no air resistance.

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Calculate fall time and final speed from height, initial downward velocity and gravity.

Results

Fall time
-
Impact speed
-

Calculation details

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    How does this tool work?

    This free-fall model describes vertical motion under constant gravitational acceleration only. Given the height and an optional initial downward speed, the calculator finds the time to the ground and the speed immediately before impact.

    Distance follows h = v₀t + ½gt². The engine solves the quadratic equation and keeps the positive time root.

    Final speed is then v = v₀ + gt.

    Standard gravity is provided by default but can be changed for another celestial body or a textbook problem.

    How to use this tool

    1. Set height and initial speed

      Enter the vertical distance to the ground and, if the object is already moving downward, its initial speed. A simply dropped object uses v₀ = 0.

    2. Choose gravitational acceleration

      Standard Earth gravity is provided by default. Change it for a specified textbook value or to explore another celestial body.

    3. Solve for fall time

      The engine applies h = v₀t + ½gt² and keeps the positive time solution corresponding to reaching the ground.

    4. Calculate impact speed

      Once time is known, v = v₀ + gt gives the speed immediately before impact in the no-drag model.

    Good to know

    Mass does not appear in ideal free fall

    When gravity is the only force and air resistance is neglected, all objects at the same location share the same acceleration g. Greater mass does not mean greater gravitational acceleration in this model.

    Signs depend on the chosen coordinate direction

    This calculator takes downward as positive so h, v₀ and g remain positive in the displayed equations. With upward chosen positive, acceleration would instead be written −g.

    Air resistance can dominate for some objects

    Feathers, sheets of paper and high-area objects are poorly described by no-drag free fall in air. Drag depends on shape, speed and fluid properties and can lead to terminal velocity.

    Formula

    Free fall is a one-dimensional constant-acceleration problem. Taking downward as positive gives h = v₀t + ½gt² and v = v₀ + gt.

    Free-fall equations

    h = v₀t + ½gt² ; v = v₀ + gt

    The model assumes constant acceleration and no drag.

    h
    height
    v₀
    initial downward speed
    g
    gravitational acceleration

    Assumes constant g and no air resistance, and applies only during the flight phase before contact with the ground or another support.

    Use cases

    Kinematics homework

    Check a vertical-motion calculation by keeping height, initial velocity, acceleration and time distinct. The result provides a quick verification of the standard constant-acceleration equations.

    Object dropped from rest

    With v₀ = 0, estimate fall time and final speed from a known height. This baseline case makes the effect of g easy to see before adding an initial downward velocity.

    Downward launch

    Study an object that is already moving downward when released. At the same height it reaches the ground sooner and with a higher impact speed than an object simply dropped.

    Comparing celestial bodies

    Change gravity to see how the same fall height would behave on the Moon, Mars or a theoretical world while keeping the underlying constant-acceleration model unchanged.

    Examples

    Object dropped from 20 m

    Ignoring air resistance.

    Input

    h = 20 m; v₀ = 0

    Result

    t ≈ 2.02 s; v ≈ 19.81 m/s

    Initial downward speed

    Initial speed contributes to the motion.

    Input

    h = 20 m; v₀ = 5 m/s

    Result

    Shorter time and greater impact speed

    Tips and best practices

    • Air resistance is ignored.
    • Initial velocity is positive downward.
    • At very large altitude, constant g becomes a weaker approximation.
    • For very large fall distances, constant g and zero drag become progressively weaker assumptions.
    • Do not confuse theoretical impact speed with injury or damage prediction; real impact effects also depend on stopping distance, materials and contact area.

    Sources and references

    Frequently asked questions

    Does mass matter?

    Not in ideal free fall: without drag, gravitational acceleration is independent of object mass.

    Can the object start with a downward speed?

    Yes.

    What gravity is used by default?

    9.80665 m/s².

    Why does a feather fall differently in reality?

    Air resistance is large relative to its weight.

    Why do objects of different mass fall together in a vacuum?

    Because they experience the same gravitational acceleration when other forces are negligible.

    Does this calculator include terminal velocity?

    No. Terminal velocity requires an air-resistance model, which is outside this calculator.

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