Calculate the missing tipping angle, height, or base length from two known values using meters, feet, inches, yards, and degrees or radians.
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Tipping Angle Formula
The following formula is used to calculate the tipping angle for a uniform rectangular object tipping about a bottom edge (static tipping threshold).
TA = atan(BL / H) * (180 / π)
Variables:
- TA is the tipping angle (degrees)
- H is the height of the object (any length unit, as long as it matches BL)
- BL is the base length (width) of the object in the direction of tipping (same length unit as H)
To calculate the tipping angle, take the arctangent of the base length divided by the height and then convert the result from radians to degrees. For more general shapes, the critical tipping angle depends on the center of mass location: TA = arctan(xcm / ycm), where xcm and ycm are the horizontal and vertical distances from the pivot edge to the center of mass.
What is a Tipping Angle?
The tipping angle is the critical tilt angle at which an object will begin to tip about an edge in a static situation (for example, when slowly tilting the object or placing it on an incline). Tipping occurs when the vertical line through the center of mass passes through the pivot edge. For a uniform rectangular object, this can be expressed using only its height and base length, but for non-uniform objects the center of mass position must be used.
How to Calculate Tipping Angle?
The following steps outline how to calculate the Tipping Angle.
- First, measure the height of the object (H).
- Next, measure the base length (BL) in the direction the object would tip.
- Use the formula TA = atan(BL / H) * (180 / π) to calculate the tipping angle (TA) in degrees.
- 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.
Height of the object (H) = 5 meters
Base length of the object (BL) = 2 meters
Tipping Angle (TA) = atan(2 / 5) × (180 / π) ≈ 21.80°
