Calculated result
Submit the form to show the final vertical velocity here above the calculator.
Vertical velocity calculator
Plotly graph
The graph plots vertical velocity against time using the solved vertical component and gravity settings.
Example data table
| Scenario | Given values | Computed vertical velocity | Direction |
|---|---|---|---|
| Initial vertical velocity + time | u = 30 m/s, t = 2 s, g = 9.81 m/s² | 10.38 m/s | Upward |
| Initial vertical velocity + time | u = 30 m/s, t = 4 s, g = 9.81 m/s² | -9.24 m/s | Downward |
| Launch speed + angle + time | v₀ = 25 m/s, θ = 60°, t = 1.5 s | 6.94 m/s | Upward |
| Launch speed + angle + time | v₀ = 20 m/s, θ = 35°, t = 3 s | -17.96 m/s | Downward |
| Initial vertical velocity + displacement | u = 18 m/s, Δy = 12 m, descending branch | -9.41 m/s | Downward |
Formula used
This page uses upward as positive. Gravity is applied downward, so acceleration becomes negative in the velocity equation.
How to use this calculator
- Choose the solve mode that matches your known inputs.
- Enter gravity, then add velocity, time, angle, or displacement values.
- Select input units and your preferred output display units.
- For displacement mode, choose ascending or descending velocity branch.
- Press the calculate button to show the result above the form.
- Review the graph, supporting metrics, and export options.
Frequently asked questions
1. What is vertical velocity?
Vertical velocity is the speed component directed upward or downward. It ignores horizontal motion and focuses only on motion along the vertical axis.
2. Why does the sign of velocity matter?
The sign shows direction. Positive values mean upward motion under this convention, while negative values mean downward motion. Zero means the object is momentarily at a turning point.
3. When should I use launch speed and angle mode?
Use that mode when you know the starting speed and projection angle, such as a projectile launched above the horizontal. The calculator converts the launch speed into its vertical component first.
4. Why does displacement mode have two branches?
The same height can be reached while rising and later while falling. The ascending branch gives a positive vertical velocity, while the descending branch gives a negative one.
5. Can I use Earth gravity and custom gravity values?
Yes. Enter 9.81 m/s² for standard Earth gravity, or replace it with another positive value. That makes the page useful for classroom experiments and other gravity assumptions.
6. What does the graph show?
The graph shows how vertical velocity changes with time. A downward sloping line appears because gravity steadily reduces upward velocity and increases downward velocity magnitude.
7. What units can I choose?
You can enter and display velocity in m/s, km/h, ft/s, or mph. Displacement can be shown in meters or feet, and gravity accepts metric or imperial units.
8. What happens if the displacement inputs are impossible?
The calculator checks the discriminant in the displacement relation. If it becomes negative, the page shows an error because no real vertical velocity satisfies those inputs.