Projectile Motion Calculator
Compute vacuum projectile flight time, maximum height and range from launch speed, launch angle and gravitational acceleration.
Description
Calculate ideal flight time, maximum height, and horizontal range from launch speed and angle.
The projectile motion calculator models a launch and landing at the same elevation under constant gravity with no air resistance. It is useful for physics exercises and for understanding how speed, angle, and gravity affect the ideal trajectory.
When to use Projectile Motion Calculator
- Check a textbook projectile-motion exercise
- Compare range at different launch angles
- Compare ideal trajectories under different gravitational acceleration
How the calculation works
Initial velocity is split into horizontal and vertical components. Vertical symmetry gives flight time, the zero-vertical-velocity point gives maximum height, and constant horizontal velocity gives range. Standard gravity defaults to 9.80665 m/s².
time = 2v sin(θ)/g; height = v²sin²(θ)/(2g); range = v²sin(2θ)/g Interpreting the result
At fixed speed and equal launch/landing height, complementary angles have the same ideal range and 45° maximizes it. Maximum height is measured above the launch point, not above sea level.
Important limitations
- Air drag, wind, lift, spin, Earth curvature, and changing gravity are ignored.
- Launch and landing elevation must be equal.
- Do not use the ideal model for safety-critical ballistics or real-world impact prediction.