Free Fall Calculator

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Drop height:

Changing the unit converts the displayed value and preserves the same physical height.

Initial vertical velocity:

The sign convention is explicit: positive is downward and negative is upward.

Gravity field:

Choose the constant downward acceleration used for the entire modeled path.

Custom gravity:

Use a measured or documented positive acceleration in metres per second squared.

m/s²

Mass for impact energy:

Default zero is neutral and reports energy as not requested.

Displayed precision:

The default three places changes no underlying result when Advanced is opened.

places

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How to use this estimate

Motion path

Model boundary

The calculation assumes vertical motion, constant gravity, and no air resistance. Drag, buoyancy, changing gravity, terrain, horizontal motion, and stopping distance are excluded.

Impact interpretation

A vertical fall is shaped by three starting facts: the object's height above the impact level, its initial vertical velocity, and the downward acceleration acting throughout the motion. Releasing an object from rest is only one case. A downward throw shortens the trip, while an upward throw first raises the object and lengthens both its path and time before impact.

Ideal vertical motion removes air resistance and treats gravity as constant. Under those assumptions, every object at the same place and with the same starting velocity follows the same height-time path regardless of mass. Mass matters only when kinetic energy is requested, because energy scales directly with mass.

The sign convention prevents a common mistake. Downward velocity is positive and upward velocity is negative. An entry of −10 m/s therefore means the object initially travels upward, reaches zero vertical velocity at its peak, then accelerates downward. The total path is longer than the original drop height because it includes that rise and the matching descent back to the release level.

Falling-motion quantities and their practical meaning
Quantity	What it describes	Important limit
Time to impact	Elapsed time until height reaches the selected impact level	Assumes one vertical dimension and constant gravity
Impact speed	Magnitude of vertical velocity at impact	Does not include drag, wind, or lift
Maximum height	Release height plus any rise from an upward start	Equals release height when initial velocity is zero or downward
Kinetic energy	Ideal translational energy at the modeled impact speed	Does not determine stopping force or damage

Real falls can differ sharply from the ideal path. Air drag grows with speed and depends on shape, orientation, area, and air density. Very light, broad, or irregular objects are especially poor matches. The model also excludes changing gravity over enormous distances, rotation, horizontal motion, buoyancy, ground motion, and any collision before the selected impact level.

Impact speed and impact force are not interchangeable. A speed can be estimated at contact, and mass can turn that speed into kinetic energy, but force also depends on how quickly or over what distance the object stops. A rigid surface and a deformable cushion can produce very different peak forces from the same incoming speed.

How to Use This Tool:

Describe the vertical motion at release, choose the acceleration field, and add mass only when ideal impact energy is useful.

Enter the Drop height above the impact level and choose metres, feet, or yards.
Enter the Initial vertical velocity. Use a positive value for downward motion, zero for release from rest, or a negative value for an upward launch.
Choose the Gravity field or enter a positive Custom gravity in m/s². The selected value stays constant for the entire path.
Open Advanced to add Mass for impact energy or change displayed precision. A zero mass leaves energy unrequested without changing time, speed, or path.
Read the time and impact speed first, then check maximum height and total path length when the starting velocity is upward.

Interpreting Results:

Time, speed, height, and path belong to the same ideal trajectory. For a release from rest or a downward start, total path length equals the entered height. With a negative initial velocity, the path includes the upward gain twice: once on the way up and again while descending to the release level.

Treat kinetic energy as an ideal comparison value, not a prediction of injury, structural damage, or stopping force. Confirm that the no-drag, constant-gravity assumptions are reasonable before using the result in an experiment or design decision.

Technical Details:

Vertical position is measured from the release point toward the impact level, with downward chosen as positive. A drop height h, starting velocity v₀, and constant positive acceleration g produce a quadratic displacement. The physically relevant impact time is the nonnegative root.

Formula Core

The displacement equation reaches the impact level when downward displacement equals the entered height.

h = v_{0} t + \frac{1}{2} g t^{2}

Solving that quadratic gives time to impact and the final vertical velocity.

t = \frac{- v_{0} + \sqrt{{v_{0}}^{2} + 2 g h}}{g} v = v_{0} + g t

When the initial velocity is upward, the peak gain and total path are calculated separately. Ideal impact kinetic energy is available only when mass is greater than zero.

h_{p} = \frac{{v_{0}}^{2}}{2 g}, L = h + 2 h_{p}, E = \frac{1}{2} m {| v |}^{2}

Falling-motion symbols and canonical units
Symbol	Meaning	Canonical unit
`h`	Release height above impact level	m
`v₀`	Initial downward-positive vertical velocity	m/s
`g`	Constant positive downward acceleration	m/s²
`t`	Time to impact	s
`h_p`	Height gained before descent when `v₀` is negative	m
`L`	Total vertical path length	m
`m`	Mass used only for energy	kg

Height, velocity, and mass are converted to metres, metres per second, and kilograms before calculation. The trajectory curve samples seven evenly spaced fractions of the final time. Full precision is kept in the model, while the selected 0 to 6 decimal places affect display only.

Limitations and Safety Notes:

This is an ideal one-dimensional motion model. It excludes air resistance, horizontal velocity, changing acceleration, rotation, buoyancy, collisions before the impact level, and deformation during impact.

Do not use the result by itself to judge injury risk, structural loading, protective equipment, or a safe drop zone.
Kinetic energy does not reveal peak force without a stopping distance or stopping time.
Planetary presets and custom gravity act as constant downward accelerations; they do not model altitude or location changes along the path.

Worked Examples:

Upward launch under Mars gravity

From 30 m above the impact level, an initial velocity of −10 m/s under the 3.71 m/s² Mars preset rises for about 2.695 s and gains about 13.477 m. The object then reaches the impact level after about 7.537 s at 17.961 m/s. Its total path is about 56.954 m rather than 30 m. With a mass of 2 kg, the ideal kinetic energy is 322.6 J; that energy still does not specify stopping force.

References:

NIST Guide to the SI, Appendix B.9, National Institute of Standards and Technology, updated 2025.