Trajectory Calculator

This page describes a "trajectory calculator", a tool for calculating your own trajectories of pitched or batted baseballs or softballs. This is the new 3D version. Click here for the old version or here for the new 2D version. Click here for a special version I have created for golf.

Baseball Trajectory Calculator--new 3D version (updated, November 13, 2021) Click on the link to download an Excel spreadsheet that can be used to calculate baseball or softball trajectories for both pitched and batted balls.

The tab PitchedBallTrajectory is, as the name suggests, for pitched baseballs, with independent adjustments possible for backspin, sidespin, and gyrospin. Be sure to read the README to learn how to adjust the initial parameters to coincide with Statcast data.

For batted balls, the present version is a fully 3-dimensional calculation, and includes the direction (or "spray angle"). This version is my best attempt at reproducing average batted ball distances for given initial conditions and atmospheric conditions, but be aware that there will be considerable variance of actual distances about those average values. Some of the variance is due to small differences in the drag coefficient of the baseball and some is due to unknown wind conditions. The parameters associated with the the drag and Magnus forces are fixed, having been adjusted to best fit the 2016 Statcast data for batted balls, as discussed in my August 24, 2017 article in The Hardball Times entitled Fly Ball Carry and the Home Run Surge. A more technical article about the analysis method used to arrive at the drag and lift coefficients is here. As with the previous version, it is still possible to adjust atmospheric conditions, such as the temperature, elevation, relative humidity, and wind. There is an extensive README page that I suggest you read before using the spreadsheet. In particular, note that there are two versions: one in which the spin of the batted ball is fixed at average Statcast values and another in which you are free to adjust the spin.

There are lots of possibilities, especially if you want to investigate some of the effects of overriding the specified values of the drag coefficient, backspin, etc. My suggestion is that you download a clean copy of the spreadsheet and save it; then make your own "working copy" that you can use to play around. If you get in trouble, you can always go back to your clean copy. Please contact me via email if you have questions, run into problems, or have found a bug.