The Dome Surface Area Calculator helps users determine the surface area of various dome structures, such as hemispheres, spherical caps, geodesic domes, and more. Architects, engineers, and designers use these calculations for construction, material estimation, and design planning. Understanding dome surface area is essential for cost estimation, insulation planning, and de construction intégrité.
Formula of Dome Surface Area Calculator
Hemisphere (Half Sphere)
Surface Area = 2πr²Où :
- r est le rayon de le dôme
- This formula includes the base of the hemisphere
Surface Area (without base) = πr²Où :
- This formula calculates only the curved surface area
calotte sphérique
Surface Area = 2πrhOù :
- r est le rayon de la sphère
- h is the height of the cap
Formule alternative :
Surface Area = 2πR²(1-cos(θ))Où :
- R est le rayon de la sphère
- θ is the central angle in radians
Dôme elliptique
Surface Area ≈ 2π × √[(a²b² + a²c² + b²c²)/3]Où :
- a, b, and c are the semi-principal axes of the ellipsoïde
- For a half ellipsoid, divide this result by 2
Dôme géodésique
Surface Area = 4πr² × fOù :
- r is the radius of the underlying sphere
- f is the fraction of the sphere covered by the dome (e.g., 0.5 for a hemisphere)
Paraboloid Dome
Surface Area = (π/6) × [2D² + 4H² + D√(D² + 4H²) + D²sinh⁻¹(2H/D)]Où :
- D is the diameter of the base
- H is the height of the dome
Simplified approximation:
Surface Area ≈ π × [D/2 × √((D/2)² + H²)]Conical Dome
Surface Area = πrsOù :
- r is the radius of the base
- s is the slant height (distance from apex to edge of base)
Alternativement:
Surface Area = πr√(r² + h²)Où :
- h est la hauteur du cône
Conditions générales et tableau de conversion
Below is a reference table to help users quickly determine surface area values for common dome sizes without manual calculations.
| Type de dôme | Rayon (m) | Hauteur (m) | Superficie (m²) |
|---|---|---|---|
| Hémisphère | 5 | - | 157.08 |
| calotte sphérique | 5 | 3 | 94.25 |
| Dôme géodésique | 5 | 4 | 125.66 |
| Paraboloid Dome | 6 | 3 | 150.80 |
| Conical Dome | 5 | 5 | 78.54 |
Example of Dome Surface Area Calculator
Suppose you have a hemispherical dome with a radius of 4 meters. Using the formula:
Surface Area = 2π(4)²
= 2 × 3.1416 × 16
= 100.53 m²Thus, the surface area of the hemisphere is approximately 100.53 square meters.
FAQ les plus courantes
The surface area helps determine material requirements, couverture de peinture, insulation needs, and construction costs.
Yes, but you may need specialized formulas for complex or irregular dome structures.
These formulas provide precise estimates but may need slight adjustments based on real-world construction variations.