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Formula to find Distance from Exit Velocity and Launch Angle

k heitz
k heitz asked
Hi Experts;
I've tried researching via google and have come up short.
I need assistance with a formula to predict the distance of a projectile.
I have the exit velocity and the launch angle.
I am writing in C#, but am new to it. Mostly, what I need is just a formula.
For extra credit :), I eventually will need to predict the max height of the projectile (using EV, LA and predicted Distance).

Thank you!
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Distinguished Expert 2019

you have to consider atmospheric drag and gravity, wind direction and speed, humidity, initial elevation and terminal elevation. There is a lot of science on external ballistics
(Google search:
distance of a projectile formula

you can find all your answers here: :
Projectile Motion
Basic Equations and Parabolic Path
  • Projectile motion is a form of motion where an object moves in parabolic path; the path that the object follows is called its trajectory.
k heitzsoftware developer


Hi David;
As I research farther I found I definitely need to include gravitational force (or any >0 angles will never come back to earth). I'm working on how to find/apply that value.
Regarding wind, humidity we've determined we can accept results without those variables. My function is limited to 500 ft (baseball stadium). This may also eliminate the need for initial and terminal elevation as the field is flat. But I admit I'm not sure what those terms are referring to (from mountain to sea or bat contact to ground (approx 24 inches)).

I appreciate the link. I'll study.
Thank you.
k heitzsoftware developer


Hi Paul -
Thank you for the resource. I'll study.
bat contact to ground (approx 24 inches)
this is your initial elevation, the projectile falls at 32 ft/sec/sec

the projectile has no acceleration after exit, only exit velocity

in all cases, the maximum range of the projectile is 45°
k heitzsoftware developer


Hi Paul ~
Excellent info. Thank you!
Once the projectile is launched, it experiences a constant downward acceleration of 32 ft per second squared. This downward acceleration due to gravity is what makes the projectile fall towards earth.
k heitzsoftware developer


Hi All;
Thank you very much for the information and references. I spent days studying projectile motion and the ways to calculate range, height and hang time.
Unfortunately, the approach shifted from actual calculations to pre-set data from a table generated from our known data.
Instead we are querying out  'if exit speed >= x and launch angle >= y; result = n'.
None the less, the resources and study are worth it knowing the approach we're starting with will most likely need to be perfected in the future.
Thank you again!