Estimate baseball carry from exit velocity and launch angle with a numerical drag-and-lift model, or reverse the same model for a target distance.
Baseball Launch Angle and Carry Distance
This calculator uses a two-dimensional baseball flight model rather than treating the ball as a vacuum projectile. Gravity, aerodynamic drag, and backspin-driven Magnus lift are recalculated throughout flight and integrated with fourth-order Runge-Kutta steps.
Flight Coefficients
The model uses the 2017 Alan Nathan drag and lift relationships. Drag coefficient changes with spin, while lift coefficient changes with the dimensionless spin factor formed from baseball radius, angular speed, and ball speed.
Numerical Trajectory
The calculation starts from the entered exit velocity, angle, and contact height. Every 0.005 seconds it updates position and velocity using RK4. The final ground crossing is interpolated so the distance is not rounded to a whole time step.
Reverse Distance Mode
Target mode applies a 60-step bisection search from 60 to 160 mph. Each candidate velocity runs the complete trajectory, keeping the inverse answer consistent with the forward model.
Supporting Results
Carry appears first, followed by hang time, apex, landing speed, vacuum range, coefficients, and a plus-or-minus 300 rpm sensitivity check. Advanced controls expose backspin, air density, and contact height without crowding the primary workflow.
Browse the complete Baseball & Softball calculator collection or return to the Sports & Fitness Calculators hub.
Sources
Alan M. Nathan. Analysis of Baseball Trajectories.
Alan M. Nathan. What New Technologies Are Teaching Us About the Game of Baseball.
Major League Baseball. Statcast Glossary: Exit Velocity and Launch Angle.