Calculations with an egg shape. An egg in most cases is an ovoid, a three-dimensional oval, whose calculation is extremely complicated. Here, a solid made of two half spheroids with equal base radiuses is used as an approximation. For many eggs, especially chicken eggs, this is a good approximation. Enter base radius and both half heights and choose the number of decimal places. Then click Calculate.

Formulas:
h = h_{1} + h_{2}
b = 2 * a

if a > h_{i}: A_{i} = πa * [ a + h_{i}² / √ a² - h_{i}² * arsinh( √ a² - h_{i}² / h_{i} ) ]
if a < h_{i}: A_{i} = πa * [ a + h_{i}² / √ h_{i}² - a² * arcsin( √ h_{i}² - a² / h_{i} ) ]
if a = h_{i}: A_{i} = 2πa² (hemisphere)
A = A_{1} + A_{2}

V = 2/3 * π * a² * h

pi:
π = 3.141592653589793...

Radius, heights and width have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^{-1}.

Another egg shape can be obtained by creating a solid of revolution based on an oval in Dürer's construction. Its pointed side is more pointed than in the egg shape above made of two half spheroids. The Dürer egg always has a hemisphere at the flat end, which can of course also be represented with a half spheroid. However, calculating a solid of revolution and thus the Dürer egg is much more complicated than that of the one above.
In general, round, three-dimensional shapes are easier to calculate the more spherical they are, and the volume is usually easier to calculate than the area of the surface. With the sphere, everything depends on the number π, with the spheroid, you have to dig deeper into the mathematical bag of tricks to calculate the surface area, and with the ellipsoid, you have to struggle with integrals to get exact values. This also applies if the round shape is defined by a mathematical curve. If this is not the case, the only thing that helps is measuring or estimating. Since the term egg shape is not precisely defined, the simplest option is used unless there is a good reason to choose a more complicated one.