Home Run Distance Calculator (Baseball Exit Speed & Angle)

Calculate home run distance from exit velocity and launch angle, or the exit speed needed to reach a distance, using an ideal no-air flight model.

Related Calculators

Home Run Distance Formula

For launch and landing at the same height, the ideal no-air horizontal range is given by the following special case. It is not a measured or aerodynamic baseball-distance prediction.

D = (v² × sin(2 × θ)) / g

Variables:

D is the home run distance
v is the initial velocity
θ is the launch angle in degrees
g is the acceleration due to gravity (approximately 9.81 m/s²)

For nonzero contact height h above the landing ground, use t = (v sinθ + √((v sinθ)² + 2gh))/g and D = v cosθ × t. Convert speed to m/s and height to meters before using g = 9.80665 m/s². The inverse solve is v = √(gD²/[2cos²θ(h + Dtanθ)]). Fence height is evaluated only before ground impact, and equality with the top is not clearance.

What is a Home Run Distance?

This calculator reports horizontal travel to ground level under constant gravity, rather than the curved path length or distance to a glove, wall or seat. Real baseball flight also depends on aerodynamic forces and conditions omitted here. NASA’s ballistic-flight equations explain the ideal approximation and the limitation from drag.

How to Calculate Home Run Distance?

The following steps outline how to calculate the Home Run Distance.

First, determine the initial velocity (v) of the ball.
Next, determine the launch angle (θ) of the ball.
Enter contact height above landing ground, using 0 for the equal-height special case. The calculator uses fixed g = 9.80665 m/s².
Calculate ideal horizontal range using the contact-height flight-time equation above. Use D = v² sin(2θ)/g only when contact height is zero.
After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Initial Velocity (v) = 45 m/s

Launch Angle (θ) = 30 degrees

Contact height h = 0 m; gravity g = 9.80665 m/s². Ideal range = 45² × sin(60°)/9.80665 = 178.8278 m. Select m/s for exit speed and meters for output to reproduce it. This no-air result is not an expected real baseball carry distance.