Free Fall Distance Calculator
Calculate how far an object falls from rest under gravity using d = 1/2 * g * t^2. Enter fall time in seconds and local gravitational acceleration. Also returns final velocity and impact kinetic energy per unit mass.
How to use this tool
- Enter fall time (t) and gravity (g) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your distance fallen and the full breakdown beneath it.
Formula
d = 0.5 * g * t^2; v = g * t
How it works
An object dropped from rest in a uniform gravitational field falls a distance d = ½gt² in time t and reaches velocity v = gt (ignoring air resistance).
Worked examples
3-second drop on Earth
Drop on the Moon
Common mistakes to avoid
- Using g = 10 m/s^2 as an approximation when precision is needed — the standard value is 9.80665 m/s^2; the 2% error accumulates with longer fall times.
- Neglecting air resistance — this formula models free fall in a vacuum; real objects reach terminal velocity and fall shorter distances than predicted for long falls.
- Squaring t before multiplying by g/2 in mental arithmetic, leading to order-of-operations errors; always apply the formula as d = 0.5 * g * t^2.
Key terms
Frequently asked questions
- What is the final velocity when an object hits the ground after free falling for time t?
- v = g * t (in m/s). Alternatively, v = sqrt(2*g*d). This ignores air resistance.
- How far does an object fall in the first second under standard gravity?
- d = 0.5 * 9.81 * 1^2 = 4.905 metres. In two seconds, d = 0.5 * 9.81 * 4 = 19.62 m. Distance grows with the square of time.
- Does the mass of the object affect how far it falls?
- No, in a vacuum all objects fall identically regardless of mass. This was demonstrated by Galileo and later confirmed by the Apollo 15 hammer-and-feather drop on the Moon.