Mathematics is a complex **science** but applicable in almost all segments of everyday life.

If you are a fan of math and want to learn more about the **ellipsoid **and how to determine the volume, you are at the right place. On the other hand, if you are not a fan of **math **and need help with determining the **volume of an ellipsoid**, you can use our calculator.

## What is ellipsoid

For an **ellipsoid**, we can say that it is a body whose all plane sections through one of the **axes are ellipses**, and all other sections are ellipses or circles. The best example is the example of **planet Earth**.

The Earth has the shape of a geoid, a body similar to a **rotating ellipsoid**.

Imagine a sea surface that passes beneath all land, and you will get a **geoid**. As the Earth’s surface is shown on maps, the geoid needs to be approximated by an ellipsoid. An ellipsoid is formed by rotating an ellipse about a shorter (polar) axis.

Another key point is that an ellipsoid is a second-order surface or a centrally **symmetric surface**. In the center of the ellipsoid, three mutually **perpendicular axes** (main axes) of symmetry intersect. Two of these axes define three mutually vertical planes of symmetry. If the significant axes are taken as coordinate axes, the ellipsoid equation reads:

where a, b and c are the semi-axes of the ellipsoid.

## How to calculate the volume of an ellipsoid?

Notably, all are plane cross-sections of an **ellipsoid**. Two strands of parallel planes have circular cross-sections with the ellipsoid. A **rotating ellipsoid** is created by rotating an ellipse about one of its axes, with two equal semiaxes (for example, c = b). **The volume of the ellipsoid is:**

## How to use the ellipsoid calculator?

All you need to determine the volume of the ellipsoid are **semi-axises**.

To point out, here is an example of calculating the volume with the help of **our calculator**.

We have an ellipsoid whose semi-axis A is 5cm, semi-axis B is 8cm and semi-axis C is 6cm.

We want to **calculate its volume** expressly.

The calculation formula is:

V = \frac{4}{3}\cdot \pi \cdot a\cdot b\cdot cIt follows from this formula that the volume of this ellipsoid is equal to:

V = \frac{4}{3}\cdot 3.14 \cdot 5\cdot 8\cdot 6 = \frac{3014.4}{3} = 1004.8 cm^{3}As a result, you have that a volume of the ellipsoid is equal to 1004.8 cm^{3}.

## Real-life applications

In the first place, a **reference ellipsoid** is a surface that approximates a geoid in **geodesy**. Moreover, in the context of standardization and geographical applications, the **geodetic reference ellipsoid** is a math model that you can use as the basis of spatial reference systems or definitions of geodetic data.

In 1687, Isaac Newton published * Principio*. He included evidence that a rotating self-gravitational fluid body in equilibrium has the shape of a

**flattened ellipsoid**generated by an ellipse rotated around its small

**diameter**. That shape he called a flattened spheroid.

Generally speaking, it is important to realize that many ellipsoids have been used to **model the Earth in the past**. In the first place, planet Earth was showing with different assumed values of a and b and different assumed center positions and different axis orientations relative to solid Earth. To demonstrate, the primary use of reference ellipsoids is the basis for the **latitude** (north/south), **longitude** (east/west), and ellipsoidal height coordinate systems.