Estimate home run distance (baseball carry) from exit velocity and launch angle, or find the exit velocity needed to hit a ball 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. These empirical coefficients were fitted to a subset of 2016 batted balls with exit speeds of at least90mph and launch angles20โ35ยฐ; other settings within this calculatorโs computational range are extrapolations. 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 a40-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 spin sensitivity check of up to300rpm in each direction, bounded to0โ5,000rpm. Advanced controls expose backspin, air density, and contact height without crowding the primary workflow.
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Sources
Alan M. Nathan. Analysis of Baseball Trajectories (August28,2017), equations10โ11. This simplified model assumes constant pure backspin, zero wind, no spin decay and a ground-level landing. It is not the authorโs newer3D/spin-decay calculator or a guarantee of actual carry.
Alan M. Nathan. What New Technologies Are Teaching Us About the Game of Baseball.
Major League Baseball. Statcast Glossary: Exit Velocity and Launch Angle.
