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Equivalent Horizontal Range

There is no difference mathematically. Either your rangefinder is doing the trig or your calculator is. It is pretty simple to always have your rangefinder set to EHR and just leave the angle of inclination in your calculator at zero. Makes for less manual entry into the calculator and reduces the chances of accidentally leaving an angle of inclination in the calculator that is wrong.
You do this and your wind hold be right but your elevation will be wrong. The answer is both ranges are necessary but only one is input into the BC. It all depends on how you set it up and what youre used to, but typically, true horizontal range is in input into the calculator along with the angle. The wind hold (hypotenuse of the right triangle) is calculated in the background using these two factors.

As with anything there are multiple ways to skin this cat. But garbage in always equals garbage out.
 
There is no difference mathematically..
I have to disagree with this statement. When you use EHR then you are asking for an approximation. It's a method called the "Riflemans Rule". There is error in the result.

If you enter Line-of-Sight distance and angle of inclination then the ballistic calculator can more accurately consider what gravity is doing to the bullets trajectory.

As another bit of information related to this topic, there is another approximation that can be used to arrive at an elevation correction. It's called the "Improved Riflemans Rule". With this method you take the elevation correction called for on a level horizontal shot and multiply it by the cosine of the inclination angle. This method also has some error but not as much as the "Riflemans Rule".
 
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I have to disagree with this statement. When you use EHR then you are asking for an approximation. It's a method called the "Riflemans Rule". There is error in the result.

If you enter Line-of-Sight distance and angle of inclination then the ballistic calculator can more accurately consider what gravity is doing to the bullets trajectory.

As another bit of information related to this topic, there is another approximation that can be used to arrive at an elevation correction. It's called the "Improved Riflemans Rule". With this method you take the elevation correction called for on a level horizontal shot and multiply it by the cosine of the inclination angle. This method also has some error but not as much as the "Riflemans Rule".

After reading your post I agree with you. I'm going to delete my above post so it doesn't mislead others on this topic.