Enter projectile details
This solver finds real launch angles for a chosen speed, target distance, target height, and gravity. Results appear above this form after calculation.
Sample launch angle cases
Use these example values to test the calculator and compare shallow and steep trajectories under the same launch speed.
| Speed | Distance | Launch Height | Target Height | Gravity | Possible Angles |
|---|---|---|---|---|---|
| 30 m/s | 60 m | 0 m | 0 m | 9.80665 m/s² | 20.41° and 69.59° |
| 35 m/s | 80 m | 1.5 m | 5 m | 9.80665 m/s² | 22.81° and 69.69° |
| 25 m/s | 40 m | 0 m | 8 m | 9.80665 m/s² | 32.78° and 68.53° |
Projectile equations behind the solver
The calculator treats motion as ideal projectile travel with constant gravity and no air resistance. It solves for angle by turning the motion equation into a quadratic in tan(θ).
Δy = ytarget − ylaunch
Δy = x tan(θ) − [g x² / (2 v² cos²(θ))]
Let A = g x² / (2 v²) and T = tan(θ)
A T² − xT + (A + Δy) = 0
T = [x ± √(x² − 4A(A + Δy))] / (2A)
θ = arctan(T)
Time to target: t = x / [v cos(θ)]
Maximum height: ymax = ylaunch + (v sin(θ))² / (2g), when vertical launch speed is positive
Minimum required speed: vmin = √{g [Δy + √(x² + Δy²)]}
How to use this calculator
- Select meters or feet, then keep all entries in the same unit system.
- Choose Earth, Moon, Mars, or enter a custom gravity value.
- Enter initial speed, horizontal distance, launch height, and target height.
- Pick your preferred decimal precision and graph sample count.
- Press Calculate launch angle to show results above the form.
- Review the low and high angle paths, chart, and key flight metrics.
- Download the output as CSV or PDF for reports or homework records.
Launch angle solver FAQs
What does this launch angle solver calculate?
It finds valid launch angles needed to hit a target at a chosen horizontal distance and height. It also reports flight time, apex position, peak height, impact speed, minimum required speed, and trajectory graphs.
Why can two different launch angles reach the same target?
Projectile motion can produce a shallow path and a steep path when the same speed reaches the same point. The lower angle arrives faster, while the higher angle stays airborne longer and peaks much higher.
Why am I seeing no real solution?
That means the selected speed is not enough for the target distance and height under the chosen gravity. Increase speed, reduce distance, lower the target, or check that all units are consistent.
Which launch angle should I choose?
Use the lower angle for faster travel and usually lower exposure to wind. Use the higher angle when you need more clearance over obstacles or want a steeper approach to the target.
Does this calculator include air resistance?
No. It assumes ideal projectile motion with constant gravity and no drag. Real objects may need slightly different angles because air resistance, spin, lift, and launch conditions can change the path.
Can I use feet instead of meters?
Yes. Choose feet as the length unit, then keep speed, distance, heights, and gravity in matching foot-based units. Consistent units matter more than the specific system you use.
What formula is the solver using?
It starts from the projectile equation for vertical position, substitutes tan(θ), and solves a quadratic. From each valid angle, it computes time, apex location, maximum height, and impact speed.
What is the minimum required speed shown in results?
It is the smallest launch speed that can still reach the chosen target under the selected gravity. If your entered speed is below that value, the target cannot be hit with any real angle.