Vacuum Trajectories

(Revised June 2024)

Main Reference: HyperPhysics Trajectory Page at Georgia State University (LINK)

Unified Vacuum Trajectory Calculator


Velocity (m/sec)
Firing Angle (degrees)
Gravitational Constant (m/sec2)
  • Earth: 9.80665 m/sec2
  • Moon: 1.63
Range (meters)
Maximum Altitude (meters)
Time of Flight (seconds)

Individual Vacuum Trajectory Formulas

Horizontal Range With Zero Launch Height

Where:

R: Horizontal Range (meters)
V: Velocity (m/sec)
θ: Launch Angle (Radians)
g: Gravitational Constant (m/sec2)

Velocity (m/sec)
Firing Angle (degrees)
Gravitational Constant (m/sec2)

Range (m)

Time of Flight with Zero Launch Height

Where:

T: Time of Flight (seconds)
V: Velocity (m/sec)
θ: Launch Angle (Radians)
g: Gravitational Constant (m/sec2)

Velocity (m/sec)
Firing Angle (degrees)
Gravitational Constant (m/sec2)

Time of Flight (seconds)

Peak Height with Zero Launch Height

Where:

H: Peak Height (meters)
V: Velocity (m/sec)
θ: Launch Angle (Radians)
g: Gravitational Constant (m/sec2)

Velocity (m/sec)
Firing Angle (degrees)
Gravitational Constant (m/sec2)

Maximum Height (m)