Free fall calculator (time, height and impact speed)
Enter your values. The answer and the full worked solution update as you type.
Result
| Time (s) | Height above the ground (m) | Velocity, up positive (m/s) |
|---|---|---|
| 0 | 20 | 0 |
| 0.4039 | 19.2 | −3.962 |
| 0.8077 | 16.8 | −7.924 |
| 1.212 | 12.8 | −11.89 |
| 1.615 | 7.2 | −15.85 |
| 2.019 | 0 | −19.81 |
Air resistance is neglected.
Calculate the motion of an object falling under gravity without air resistance. Enter the drop height, the fall time or the impact speed, and optionally an initial vertical velocity, upward or downward, and the calculator finds the other two values. For an object thrown upward it also gives the highest point. A table shows the height and velocity during the fall, and you can change g for the Moon or Mars.
Step-by-step solution
Equations of motion with constant acceleration g
Solve for the unknowns
Key formulas
- Velocity
- v = v0 + a·t
- Displacement
- s = v0·t + ½·a·t²
- Without time
- v² = v0² + 2·a·s
- Units
- 1 m/s = 3.6 km/h
How to solve free fall problems
- Choose a direction as positive. Here up is positive, so the acceleration is −g with g = 9.81 m/s² on Earth.
- Write the position as y(t) = h + v₀·t − ½·g·t² and the velocity as v(t) = v₀ − g·t, where h is the starting height above the ground.
- Dropped from rest (v₀ = 0), the fall time is t = √(2h/g) and the impact speed is v = √(2gh) = g·t.
- With an initial velocity, set y(t) = 0 and solve the quadratic equation for the positive root: t = (v₀ + √(v₀² + 2gh))/g.
- For an object thrown upward, the highest point is reached when v = 0: after v₀/g seconds, at v₀²/(2g) above the start.
Questions and answers
Do heavy objects fall faster than light ones?
Not without air resistance: all objects fall with the same acceleration g, whatever their mass. In air, light and broad objects such as feathers fall more slowly because drag is large compared with their weight.
How long does it take to fall 20 m?
Dropped from rest, t = √(2·20/9.81) = 2.02 s, and the object hits the ground at about 19.8 m/s, or 71 km/h.
When can I ignore air resistance?
For compact, dense objects over short drops, at speeds well below their terminal velocity. A falling person reaches a terminal velocity of about 55 m/s, so for long drops the formulas here overestimate the speed.
What value of g should I use?
Usually 9.81 m/s²; the standard value is 9.80665 m/s², and the real value varies from about 9.78 at the equator to 9.83 at the poles. On the Moon g is 1.62 m/s² and on Mars 3.71 m/s².
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