Estimate ellipsoid surface area from three semi-axes or diameters using Thomsen's formula, and reverse solve a missing axis from area.
This surface area of an ellipsoid calculator helps you estimate the surface area of an ellipsoid from three semi-axes or three diameters. It is useful for geometry homework, modeling, technical work, and quick measurement checks.
The calculator is also handy when you want to compare elongated or flattened ellipsoids and better understand how the three main axes affect the total outer surface.
$$A\approx 4\pi \left(\frac{a^p b^p+a^p c^p+b^p c^p}{3}\right)^{1/p}$$$$p=1.6075$$
Uses Thomsen's approximation with p = 1.6075.
How do you calculate the surface area of an ellipsoid?To estimate the surface area of an ellipsoid, this calculator uses three semi-axes or three diameters and applies Thomsen's approximation.
What is the difference between semi-axes and diameters?Semi-axes are half-lengths measured along the three main directions of the ellipsoid. Diameters are the full lengths along those same directions. The calculator accepts either input method.
Is the ellipsoid surface area formula exact?For a general ellipsoid, an exact surface area formula is complicated. That is why this calculator uses Thomsen's approximation, which gives very good practical results.
What is an ellipsoid surface area calculator useful for?It is useful for geometry, modeling, engineering estimates, and any calculation where you need the outer surface of an ellipsoid-shaped object.
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