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Ellipsoid Volume Calculator

Work out ellipsoid volume instantly with clear inputs, formula shown and shareable results.

About Ellipsoid Volume Calculator

An ellipsoid is a sphere scaled independently along three axes, so V = ⁴⁄₃πabc. Its surface area has no closed form; the Knud Thomsen approximation with p = 1.6075 is accurate to about 1%.

Formulas

Volume

V = ⁴⁄₃π·a·b·c

Knud Thomsen surface

S ≈ 4π[((ab)^p + (ac)^p + (bc)^p)/3]^(1/p), p = 1.6075

Worked example

With the default values below, Ellipsoid Volume Calculator returns Volume of 301.5929. Change any input above and every figure here is recalculated in your browser.

Inputs used

Semi-axis aminimum 0
6
Semi-axis bminimum 0
4
Semi-axis cminimum 0
3

Results

Volume
301.5929
Surface area (Knud Thomsen)
231.2760
Equal-volume sphere radius
4.1602
a × b × c
72.0000

Step by step

  1. 1Values used
  2. 2Volume
  3. 3Knud Thomsen surface
  4. 4Volume= 301.5929
  5. 5Surface area (Knud Thomsen)= 231.2760
  6. 6Equal-volume sphere radius= 4.1602
  7. 7a × b × c= 72.0000

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What if all three axes are equal?

The volume reduces to ⁴⁄₃πr³ and the surface approximation returns exactly 4πr².

Why is the surface area only approximate?

The exact area requires elliptic integrals; no elementary closed form exists for a general triaxial ellipsoid.

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