Enter the horizontal shot distance and the elevation difference (rise or drop) into the Calculator. The calculator will evaluate the Archery Angle (the angle of the shot relative to horizontal).
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Archery Angle Formula
AA = ATAN (H/D)
Variables:
- AA is the Archery Angle (degrees or radians)
- D is the horizontal shot distance (same units as H)
- H is the elevation difference (rise or drop, same units as D)
To calculate Archery Angle, take the inverse tangent of the elevation difference divided by the horizontal shot distance.
How to Calculate Archery Angle?
The following steps outline how to calculate the Archery Angle.
- First, determine the horizontal shot distance (ft).
- Next, determine the elevation difference (rise or drop) (ft).
- Next, gather the formula from above = AA = ATAN (H/D).
- Finally, calculate the Archery Angle.
- After inserting the variables 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.
horizontal shot distance (ft) = 600
elevation difference (ft) = 213
Archery Angle (degrees) ≈ ATAN(213/600) ≈ 19.5581°
FAQ
What is the significance of calculating the Archery Angle?
Calculating the Archery Angle helps you understand how steep the shot is (uphill or downhill). Combined with a range estimate, it can help you determine the effective horizontal “shoot-for” distance used for most sight/pin setups.
Can the Archery Angle formula be used for other projectiles?
The same right-triangle geometry can be used in any situation where you know a horizontal distance and a vertical difference. However, it is not a full ballistic/trajectory model by itself.
How does elevation affect the accuracy of an arrow?
Gravity acts the same regardless of elevation, but steep uphill or downhill shots reduce the effective horizontal distance compared to the line-of-sight distance. That difference is why archers often “shoot for” the horizontal distance rather than the line-of-sight distance.
Are there any tools or devices that can help measure the Archery Angle in real-time?
Yes, there are several modern devices, such as laser rangefinders with inclinometers, that can measure distances and elevation changes, providing real-time data to calculate the Archery Angle for improved accuracy in archery.
