🍎 Free Fall Calculator
Calculate the velocity and distance traveled by a free falling object.
⚙️ Free Fall Calculator
📊 Calculation Result
Please enter values to calculate.
Calculator Description
Free fall is the motion of an object under the influence of gravity alone. When air resistance is neglected, every object — regardless of its mass — accelerates at the same gravitational acceleration g. This is one of the foundational principles of classical mechanics established by Galileo and Newton.
What this calculator finds
This calculator determines the final velocity (v) and the distance traveled (s) of a falling object from its initial velocity, the fall time, and gravitational acceleration. It applies the standard kinematic equations for uniformly accelerated straight-line motion.
Why it matters
- Predicting impact velocity from drop height or fall time — for safety design and accident analysis
- Understanding and verifying kinematic equations in physics teaching and experiments
- Estimating the reach and timing of dropped or projected objects
Formula
Equations of uniformly accelerated motion
Because gravity produces a constant acceleration g, free fall is described by uniformly accelerated straight-line motion. The velocity grows linearly with time, while the distance grows with the square of time.
- v — Final velocity [m/s]
- v₀ — Initial velocity [m/s]
- s — Distance traveled [m]
- t — Time of fall [s]
- g — Acceleration of gravity (9.80665 m/s²)
How the formula works
- The longer the fall time t, the higher the velocity (linearly) and the greater the distance (quadratically).
- If the initial velocity v₀ is zero (released from rest), the equations simplify to v = g·t and s = ½·g·t².
- The object's mass does not appear in the equations — without air resistance, heavy and light objects fall identically.
Worked example
Dropping an object from rest (v₀ = 0) for 3 seconds (g ≈ 9.80665 m/s²) gives a final velocity of v = 9.80665 × 3 ≈ 29.4 m/s and a distance of s = ½ × 9.80665 × 3² ≈ 44.1 m.
Useful Tips
Practical tips
- For a drop from height h at rest, the time is t = √(2h/g) and the impact speed is v = √(2·g·h).
- g varies slightly with latitude and altitude; the standard value 9.80665 m/s² is Earth's average.
Limitations & cautions
- The calculation assumes vacuum conditions with no air resistance. In reality drag acts on the object, and its effect grows with higher velocity and larger surface area.
- Over a long enough fall, drag balances gravity and the object reaches terminal velocity, at which point the constant-acceleration equations no longer apply.