Formula Used
When launch angle is known
The calculator uses vertical motion:
Δy = v₀ sin(θ)T - 0.5gT²
Solving for exit velocity gives:
v₀ = (Δy + 0.5gT²) / (T sin(θ))
When horizontal range is known
The calculator first finds components:
vₓ = R / T and
vᵧ = (Δy + 0.5gT²) / T
Then it combines them:
v₀ = √(vₓ² + vᵧ²)
Extra physics outputs
Momentum is p = mv. Kinetic energy is KE = 0.5mv².
Maximum height above launch is h = vᵧ² / 2g.
How to Use This Calculator
- Enter the projectile flight time in seconds.
- Select angle mode if you know the launch angle.
- Select range mode if you measured horizontal travel distance.
- Enter height change as landing height minus launch height.
- Choose the correct gravity preset or enter a custom value.
- Add mass if you want momentum and kinetic energy.
- Enter uncertainty values for a practical speed band.
- Press the calculate button and review the result above the form.
- Use the CSV or PDF button to save your report.
Example Data Table
| Example |
Flight Time |
Angle |
Height Change |
Gravity |
Exit Velocity |
| Equal-height lab shot |
4.00 s |
45° |
0 m |
9.80665 m/s² |
27.74 m/s |
| Steep training launch |
2.00 s |
60° |
0 m |
9.80665 m/s² |
11.32 m/s |
| Low angle launcher |
1.50 s |
30° |
0 m |
9.80665 m/s² |
14.71 m/s |
| Medium arc projectile |
3.00 s |
35° |
0 m |
9.80665 m/s² |
25.65 m/s |
Understanding Projectile Exit Velocity
Why flight time matters
Flight time is one of the clearest clues in projectile motion. It shows how long gravity had to change the vertical speed. When the launch and landing heights are known, the starting vertical component can be recovered. The full exit velocity can then be found from the launch angle or horizontal range.
Angle mode
Angle mode is useful for launchers, sports shots, classroom experiments, and test rigs. You enter the measured time and angle. The tool solves the vertical equation first. Then it separates the result into horizontal and vertical components. This gives a useful picture of the projectile as it leaves the barrel, hand, bat, ramp, or launcher.
Range mode
Range mode is often better when the landing point is measured accurately. In this mode, horizontal speed is distance divided by time. Vertical speed comes from the height equation. The calculator combines both components with the Pythagorean rule. This mode can also estimate the actual launch angle from the measured path.
Height difference
Height change is important. A projectile landing above the launch point needs more vertical speed. A projectile landing below the launch point can stay in the air longer with a lower starting vertical component. Enter height change as final height minus starting height. A lower landing point should be negative.
Real-world limits
The main formula assumes ideal projectile motion. It ignores wind, spin, lift, changing drag, and bounce. The drag screening option gives only a simple warning estimate. For high-speed, light, or large projectiles, real exit speed can be higher than the ideal result. Use careful measurements for serious physics work.
Using the graph
The trajectory graph plots the predicted path from launch to landing time. It helps you check whether the curve looks reasonable. If the graph is too flat, check the angle or height change. If it is too high, check gravity and time values. Small input errors can create large velocity changes.
FAQs
1. What is exit velocity in projectile motion?
Exit velocity is the speed of the projectile at the instant it leaves the launching point. It includes both horizontal and vertical velocity components.
2. Can flight time alone find exit velocity?
Not always. Flight time also needs launch angle or horizontal range. Height change and gravity are also important for a correct result.
3. What does height change mean?
Height change means landing height minus launch height. Use a positive value for a higher landing point. Use a negative value for a lower landing point.
4. Which mode should I use?
Use angle mode when the launch angle is measured. Use range mode when horizontal distance is measured more accurately than the launch angle.
5. Does this calculator include air resistance?
The main calculation ignores air resistance. The drag field gives a simple screening estimate only. It is not a full aerodynamic simulation.
6. Why is gravity selectable?
Gravity changes on different planets and moons. Selecting the correct gravity gives better results for simulations, lessons, and non-Earth examples.
7. Why do I enter projectile mass?
Mass is not needed for ideal exit speed. It is used for momentum, kinetic energy, and the simple drag screening estimate.
8. Why is my result invalid?
An invalid result usually means time, angle, gravity, or height values conflict. Check units and make sure the angle is between 0 and 90 degrees.