Physics
Projectile Motion Calculator
Model ideal projectile motion from launch speed, angle, initial height, and gravitational acceleration. Review flight time, range, peak height, trajectory samples, angle sensitivity, and a professional PDF report.
Horizontal range0 m
Flight time0 s
Maximum height0 m
Horizontal velocity0 m/s
Initial vertical velocity0 m/s
Ideal flight path
Trajectory from launch to landing
Height over horizontal distanceAir resistance excluded
| Flight progress | Time | Horizontal distance | Height | Vertical velocity | Speed |
|---|
Flight arc
Projectile path from launch to landing
Range, flight time, peak height, and launch components remain visible on the arc.
Projectile path from launch to landing
Range0 m
Flight time0 s
Launch velocity0 / 0
How to use Projectile Motion Calculator
- Enter launch speed, launch angle, initial height, and gravity.
- Review range, flight time, peak height, horizontal velocity, and initial vertical velocity together.
- Use the trajectory samples to see how height and vertical velocity change through the flight.
Calculator guide
Understanding Projectile Motion Calculator
Ideal projectile motion separates horizontal constant-speed motion from vertical motion under gravity. The resulting trajectory is useful for education and initial estimation when aerodynamic effects are intentionally ignored.
Calculation method
How the calculation works
For level-ground launch without drag: range = v^2 sin(2 theta) / g and flight time = 2v sin(theta) / g. Resolve launch speed using sine and cosine, solve the vertical position equation for positive landing time, multiply horizontal speed by flight time, and sample the path for the trajectory table and chart.
Projectile model
Physics assumptions
Worked situations
Practical examples
- Estimate the ideal range of a level-ground launch.
- Compare trajectory range at several launch angles.
- Include an elevated starting point and inspect the sampled flight path.
Better inputs
Useful tips
- Use consistent meters, seconds, and meters per second.
- Enter initial height relative to the landing level.
- Treat the angle comparison as an idealized sensitivity study.
Before relying on the result
Limitations and common mistakes
- Air drag, wind, spin, lift, and Earth curvature are excluded.
- The ground is assumed level at the landing elevation.
- Results are unsuitable for safety-critical targeting or real ballistic use.
Reference
Key terms
- Launch angle
- Angle of initial velocity above horizontal.
- Gravity
- Downward acceleration used by the model.
- Range
- Horizontal distance from launch to modeled landing.
- Apex
- Highest point of the trajectory.
Important note
Calculated from the entered values using the displayed physical model. Confirm that its assumptions, units, boundary conditions, and safety limits match the application.
Frequently asked questions
Why is 45 degrees often associated with maximum range?
For equal launch and landing height without drag, 45 degrees maximizes range at fixed speed.
What changes when initial height is positive?
The projectile remains airborne longer, so the best range angle can be below 45 degrees.
Does this include air resistance?
No. It is an ideal vacuum-style model.
Can I change gravity?
Yes. The input supports alternative gravitational acceleration for educational comparisons.