Free Fall Calculator

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.

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.

1. Enter the Drop height above the impact level and choose metres, feet, or yards.
2. 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.
3. Choose the Gravity field or enter a positive Custom gravity in m/s². The selected value stays constant for the entire path.
4. Open Advanced to add Mass for impact energy or change displayed precision. A zero mass leaves energy unrequested without changing time, speed, or path. For optional model checks, enter Terminal speed and Gravity centre distance, then choose an Acceleration screen limit. The limit defaults to 5% and accepts values greater than 0 through 100%.
5. 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.

The Model checks tab reports the drag and gravity-variation checks separately. During a modeled flight, zero terminal speed or centre distance leaves the corresponding check Unassessed. Missing or invalid screening inputs affect the checks while valid primary ideal-motion results remain available. Correct any Unavailable input in Advanced before judging applicability.

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.

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

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.

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.

Quadratic-drag acceleration screen

With quadratic drag, drag force grows with speed squared. At terminal speed, drag balances weight, so their ratio at another speed is:

D is drag force, W is weight, and v and terminal speed v_t use the same speed unit. The screen uses the maximum ideal-path speed: the greater of the absolute initial vertical velocity and the ideal impact speed. Multiplying the ratio by 100 gives the displayed percentage of weight. This is an acceleration screen derived from the drag and terminal-speed relations, not a solution of the drag trajectory.

The terminal speed must apply to the same object, fluid and density, orientation, and gravity, with a valid constant quadratic-drag approximation. It is not a universal property of the object across different conditions.

Inverse-square gravity screen

In an inverse-square field, gravity decreases with distance from the centre. The percentage decrease from the impact level to the highest point is:

δ_g is the gravity decrease in percent, r is the centre distance at impact, and H_peak is maximum height above the impact level, including any initial upward rise. Both distances use the same unit. This screens the suitability of constant gravity without changing the ideal trajectory.

The centre-distance check applies to a point-mass field or the field outside a spherically symmetric body, with the selected g specified at the impact level. It does not model an interior field or general spatial variations in gravity.

Each check compares its percentage separately with the chosen acceleration limit. A percentage at or below the limit is within it; a larger percentage exceeds it.

Limitations and Safety Notes:

This is an ideal one-dimensional motion model. The selected impact level is a single reference level, not a terrain or ground-profile 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.

The chosen acceleration percentage does not bound time or speed error and does not certify safety, even when both model checks are within the limit. These checks do not assess wind, buoyancy, rotation, or nonvertical motion; those require appropriate models or measurements.

Worked Examples:

References:

• NIST Guide to the SI, Appendix B.9, National Institute of Standards and Technology, updated 2025.
• Flight Equations with Drag, NASA Glenn Research Center.
• University Physics Volume 1, 13.1 Newton's Law of Universal Gravitation, OpenStax.