What Is an Ellipse Calculator?
An Ellipse Calculator is a geometry tool that helps
you calculate important measurements of an ellipse
from its semi-major and semi-minor axes.
An ellipse is a closed curved shape that resembles
a stretched circle. Unlike a circle, an ellipse can
have two different radii.
The longer radius is called the semi-major axis,
represented by a, while the shorter
radius is called the semi-minor axis, represented
by b.
This calculator can determine the area, approximate
circumference, full axes, eccentricity, and focal
distance of an ellipse.
How to Use the Ellipse Calculator
Enter the semi-major and semi-minor axis lengths
into the calculator. The tool will automatically
calculate the remaining measurements.
1
Enter Semi-Major Axis
Enter the longer radius of the ellipse
in the first field.
2
Enter Semi-Minor Axis
Enter the shorter radius of the ellipse
in the second field.
3
View Results
Click calculate to instantly see the area,
circumference, axes, and other measurements.
Ellipse Formulas
Area of an Ellipse
The area of an ellipse is calculated by multiplying
pi by the semi-major axis and semi-minor axis.
A = πab
Circumference of an Ellipse
Unlike a circle, there is no simple exact formula
for the circumference of a general ellipse. This
calculator uses the highly accurate Ramanujan
approximation.
C ≈ π[3(a+b) − √((3a+b)(a+3b))]
Eccentricity
Eccentricity describes how stretched an ellipse
is compared with a circle.
e = √(1 − b²/a²)
Focal Distance
The focal distance from the center to either focus
is calculated using the following formula.
c = √(a² − b²)
Ellipse Calculation Example
Suppose an ellipse has a semi-major axis of
10 units and a semi-minor axis
of 6 units.
Its area is:
A = π × 10 × 6
A ≈ 188.496 square units
Its full major axis is:
Major Axis = 2 × 10
Major Axis = 20 units
Its full minor axis is:
Minor Axis = 2 × 6
Minor Axis = 12 units
The calculator can also determine the approximate
circumference, eccentricity, and focal distance
using the same two measurements.
Where Are Ellipses Used?
Ellipses appear in many areas of mathematics,
engineering, science, architecture, and design.
In astronomy, planetary orbits are commonly
described using elliptical paths. Elliptical
shapes are also used in architecture and product
design.
Ellipse calculations can be useful when determining
areas, dimensions, proportions, and geometric
relationships in technical or academic work.
Frequently Asked Questions
What is an ellipse?
An ellipse is a closed curved geometric shape
similar to a stretched circle. It has a major
axis and a minor axis.
What is the formula for the area of an ellipse?
The area of an ellipse is A = πab, where
a is the semi-major axis and b is the
semi-minor axis.
What is the semi-major axis?
The semi-major axis is the distance from the
center of an ellipse to the end of its longer
axis.
What is the semi-minor axis?
The semi-minor axis is the distance from the
center of an ellipse to the end of its shorter
axis.
How do you calculate the circumference of an ellipse?
There is no simple exact elementary formula for
a general ellipse. This calculator uses a highly
accurate Ramanujan approximation.
What is ellipse eccentricity?
Eccentricity measures how much an ellipse differs
from a perfect circle. A circle has an eccentricity
of zero.
What is the major axis of an ellipse?
The major axis is the longest diameter of the
ellipse. It is equal to 2a.
What is the minor axis of an ellipse?
The minor axis is the shortest diameter of the
ellipse. It is equal to 2b.
Can the semi-major axis be smaller than the
semi-minor axis?
By definition, the semi-major axis is the longer
one. If the values are entered in reverse order,
the calculator automatically treats the larger
value as the semi-major axis.
What is the difference between an ellipse and a circle?
A circle has the same radius in every direction,
while an ellipse generally has different
semi-major and semi-minor axes.