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 calculator uses the tangent relationship between height, base length, and tipping angle.
TA = \arctan{\left(\frac{BL}{H}\right)}BL = H \times \tan(TA)
H = \frac{BL}{\tan(TA)}- TA = tipping angle
- BL = base length
- H = height
Height and base length must use the same length basis before calculation. The calculator converts length units internally. The tipping angle must be greater than 0 and less than 90 degrees.
For a symmetric object tipping about an edge, the base length is usually the horizontal distance from the tipping edge to the center of mass. That is often half the total base width, not the full width.
Tipping Angle Reference Tables
| Tipping angle | General meaning |
|---|---|
| 0° to 10° | Very easy to tip. The object is tall compared with its base support. |
| 10° to 25° | Low stability. Small tilts or side loads may matter. |
| 25° to 45° | Moderate stability. |
| 45° or more | High geometric stability, assuming the base and center of mass are measured correctly. |
| If you know this | Use this formula |
|---|---|
| Height and base length | TA = arctan(BL / H) |
| Height and tipping angle | BL = H × tan(TA) |
| Base length and tipping angle | H = BL / tan(TA) |
Example
If the height is 2 m and the base length is 0.5 m, then:
TA = \arctan{\left(\frac{0.5}{2}\right)} = 14.04^\circThis means the object reaches its tipping point at about 14 degrees of tilt, using the entered geometry.
