Calculator inputs
The page stays single-column, while the form itself shifts to three, two, or one columns by screen size.
Plotly graph
The graph plots remaining height and speed against time. Submit the form to render your motion path.
Example data table
| Scenario | Height | Start speed | Gravity | Time to impact | Impact speed |
|---|---|---|---|---|---|
| Rest drop on Earth | 20 m | 0 m/s downward | 9.80665 m/s² | 2.0193 s | 19.799 m/s |
| Rest drop on Moon | 50 m | 0 m/s downward | 1.62 m/s² | 7.8567 s | 12.728 m/s |
| Upward launch then fall | 30 m | 5 m/s upward | 9.80665 m/s² | 3.0346 s | 24.757 m/s |
Formula used
Position equation: y(t) = h + v₀t − ½gt²
Impact time: t = (v₀ + √(v₀² + 2gh)) / g
Impact velocity: v = v₀ − gt
Maximum height for upward launch: hmax = h + v₀² / (2g)
Kinetic energy: KE = ½mv²
Variable meanings: h is starting height above ground, v₀ is signed initial vertical velocity, g is gravity magnitude, t is time, and v is the impact velocity.
This model assumes constant gravity, straight vertical motion, and no air drag. It is ideal for classroom physics, quick engineering checks, simulation setup, and sanity testing of motion estimates.
How to use this calculator
- Enter the object’s initial height above the ground.
- Choose the height unit that matches your value.
- Enter the starting speed and choose whether it points upward or downward.
- Set gravity manually, or click Earth, Moon, or Mars for quick presets.
- Add mass if you also want impact momentum and kinetic energy.
- Choose the number of decimals to display in the output table.
- Press Calculate Free Fall to show the result above the form.
- Use the CSV or PDF buttons to export the current result set.
FAQs
1) Does this calculator include air resistance?
No. It uses the standard constant-gravity free-fall model without drag. For feathers, parachutes, or fast objects in air, actual times and speeds can differ noticeably from these ideal results.
2) Why can the total path travelled exceed the starting height?
If the object starts upward, it first rises before descending to the ground. The calculator adds that upward rise and the later drop, so the travelled distance becomes greater than the original height.
3) What does a downward starting speed mean here?
A downward starting speed means the object is already moving toward the ground when timing begins. That reduces the time to impact and increases the final speed compared with a simple rest drop.
4) Why is the impact velocity shown with a direction?
Velocity includes direction, while speed is only magnitude. The direction label helps you distinguish between upward and downward motion, especially when the object is launched upward before falling back.
5) When should I enter mass?
Enter mass when you want momentum and kinetic energy at impact. Mass does not change free-fall time in this ideal model, but it directly affects energy and momentum outputs.
6) Can I use feet and miles per hour together?
Yes. The calculator converts all inputs internally to SI units, solves the motion, then converts the displayed outputs back into your selected units for convenient reading.
7) Why might my time seem too short?
A short time often comes from entering a downward launch speed, a small height, or a strong gravity value. Check units carefully, especially feet versus meters and mph versus m/s.
8) Is this suitable for physics homework and lab planning?
Yes. It is useful for idealized motion problems, example checking, and quick planning. Still, cite your own class conventions if your instructor uses different sign rules or rounded gravity values.