What Is an Ellipsoid Volume Calculator?
An ellipsoid is a smooth, three-dimensional surface that looks like a stretched or squashed sphere. It is defined by three semi-axes — half-lengths measured from the center along each perpendicular direction — usually labeled a, b and c. This calculator computes the enclosed volume of any ellipsoid given those three values, instantly and to full precision.
How to Use It
Enter the three semi-axes a, b and c in any consistent unit (centimeters, inches, meters, etc.). The calculator multiplies them together with the constant \(\frac{4\pi}{3}\) and returns the volume in the cube of that unit. For a perfect sphere, simply set \(a = b = c\) equal to the radius.
The Formula Explained
The volume of an ellipsoid is given by:
$$V = \frac{4}{3}\,\pi\,\text{a}\,\text{b}\,\text{c}$$This generalizes the familiar sphere formula \(V = \frac{4}{3}\pi r^3\). When all three semi-axes equal the radius \(r\), the product \(a\cdot b\cdot c\) becomes \(r^3\) and the equation reduces exactly to the sphere case. The factor \(\frac{4\pi}{3} \approx 4.18879\) is the same constant that appears for spheres.
Worked Example
Suppose an ellipsoid has semi-axes \(a = 3\), \(b = 4\) and \(c = 5\). Then $$V = \frac{4}{3} \times \pi \times 3 \times 4 \times 5 = \frac{4}{3} \times \pi \times 60 = 80\pi \approx 251.33$$ cubic units.
FAQ
Do I use the full axis lengths or half-lengths? Use the semi-axes (half-lengths from center). If you measured full diameters, divide each by two first.
What units does the result use? Whatever unit you entered, cubed. Enter centimeters and you get cubic centimeters.
Can I use it for a sphere or a spheroid? Yes. A sphere uses \(a = b = c = r\); a spheroid (ellipsoid of revolution) uses two equal semi-axes.
