Paraboloid Calculation

A paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. Elliptical paraboloids can be found, for example, on the surfaces of satellite dishes and as energy depletion diagrams. For more information see Wikipedia.

To calculate the paraboloid, enter the shape parameter and the value a. Then click on the 'Calculate' button

Paraboloid calculator  Input Delete Entries Shape parameter s Input value a Decimal places 0 1 2 3 4 6 8 10  Results Height h Lateral surface L Surface area S Volume V

Paraboloid from Krishnavedala, CC BY-SA 3.0, via Wikimedia Commons

Paraboloid formulas

Height (\(\small{h}\))

\(\displaystyle h = s\cdot a^2\)

Lateral surface (\(\small{L}\))

\(\displaystyle L = \frac{π \cdot a }{ 6 \cdot h^2} \cdot (a^2 + 4\cdot h^2 )^{3/2} - a^3)\)

Surface area (\(\small{S}\))

\(\displaystyle S= L + π \cdot a^2\)

Volume (\(\small{V}\))

\(\displaystyle V= \frac{1}{2}\cdot π \cdot a^2 \cdot h\)