Calculator Inputs
Plotly Geometry Trend
This graph shows how exact lateral area and exact total area change as the obliquity angle increases for the current geometry basis.
Example Data Table
| Radius | Perpendicular Height | Angle | Axis Length | Center Offset | Volume | Total Surface Area |
|---|---|---|---|---|---|---|
| 2.500 m | 7.800 m | 12.000 deg | 7.974 m | 1.658 m | 153.153 m³ | 163.164 m² |
| 3.200 m | 8.500 m | 18.000 deg | 8.937 m | 2.762 m | 273.444 m³ | 239.668 m² |
| 4.000 m | 10.000 m | 25.000 deg | 11.034 m | 4.663 m | 502.655 m³ | 365.009 m² |
Formula Used
The calculator uses the engineering convention where the obliquity angle is measured from the base normal. Exact lateral area is evaluated with the complete elliptic integral of the second kind.
Base area: A = πr²
Volume: V = πr²h
Axis-length mode: h = a cos(θ)
Height mode: a = h / cos(θ)
Center offset: d = a sin(θ) = h tan(θ)
Exact lateral area: Sₗ = 4raE(sin(θ))
Complete elliptic integral: E(k) = ∫₀^(π/2) √(1 - k²sin²φ) dφ
Total surface area: Sₜ = Sₗ + 2πr²
When θ = 0°, the shape becomes a right circular cylinder. Then the exact lateral area reduces to 2πrh.
How to Use This Calculator
- Select whether you know perpendicular height or axis length.
- Enter the cylinder radius.
- Enter the chosen length basis.
- Provide the obliquity angle in degrees.
- Add density only when you want estimated mass.
- Choose your preferred length unit label.
- Click calculate to show results above the form.
- Review the chart, result table, and derived geometry values.
- Use CSV or PDF export for reporting and design checks.
FAQs
1. What is an oblique circular cylinder?
It is a cylinder whose top base shifts sideways while staying parallel to the bottom base. The side generators lean at a constant angle instead of staying perpendicular.
2. Which angle should I enter?
Enter the angle between the cylinder axis and the base normal. A zero-degree value gives a right cylinder. Larger angles create more skew and more lateral area.
3. Why does volume use perpendicular height?
Volume equals base area multiplied by the perpendicular distance between the circular ends. Leaning the cylinder does not change enclosed volume when radius and perpendicular height stay fixed.
4. Why is lateral area more complex here?
The side surface stretches unevenly around the circumference when the cylinder leans. That creates an elliptic-integral expression instead of the simple circumference-times-height rule used for a right cylinder.
5. Can I use axis length instead of perpendicular height?
Yes. Choose the axis-length mode. The calculator converts axis length and angle into perpendicular height, offset, volume, and exact surface areas automatically.
6. What does center offset mean?
Center offset is the horizontal shift between the centers of the two circular faces. It helps with layout, clearance checks, jig design, and fixture positioning.
7. Can I use very large angles?
Only with care. Very high angles create very large axis lengths and surface areas for a given perpendicular height. Practical engineering designs usually stay well below that limit.
8. What units should I use?
Use one consistent length unit for radius, height, and axis length. Areas return in squared units, volumes return in cubed units, and optional mass follows your density basis.