Aperture Area Calculator
This aperture area calculator helps you to compute the aperture area of a lens. Try the calculator right now, or keep reading to learn about the aperture diameter, fnumber, and the aperture area equation.
Aperture diameter and fnumber
An aperture is a hole, or an opening, in an optical system through which the light enters. The larger the aperture, the more light can enter. At the same time, the light is less collimated. Smaller aperture results in more collimated light entering at the cost of lower intensity. If you want to learn about different ways of measuring light intensity, check the lumen calculator. The aperture diameter is just the diameter of the opening.
The other characteristics of an optical system, such as a lens, are the fnumber and the focal length. The focal length is the distance over which the initially collimated light rays are brought to focus. The larger the focal length, the more distant objects can be seen sharply. You can check the thin lens equation or lensmaker equation calculators to study how to compute the focal length of a lens.
The fnumber n
is simply a ratio of the focal length f
and the aperture diameter D
:
n = f / D
In commercially produced lenses, we can usually set the fnumber to some prescribed values like 1.4, 2, 2.8, 4, 5.6, ...
. They correspond to decreasing the aperture diameter by a factor of √2
. In turn, the aperture area decreases by a factor of 2
.
Aperture area equation
We can write the aperture area equation in two ways:
A = π (D / 2)² = π (f / (2 × n))²
,
where:
D
– Aperture diameter;f
– Focal length;n
– The fnumber; andA
– Aperture area.
For example, if we set the fnumber
to be 1.4
for a standard lens of a focal length f = 70 mm
, then the aperture diameter is D = 50 mm
. Using the aperture area calculator, we find that the aperture area is A = 1963.3 mm².
What's aperture area?
Aperture area is the area associated with the lightcollecting section of an optical system. Larger values correspond to more light entering, brighter images, and greater focal lengths, whereas smaller ones translate into darker images and shorter focal lengths.
What's the aperture area equation?
It’s possible to write the aperture area equation in two ways:

One of them in terms of the aperture diameter
D
as:A = π (D / 2)²
WhereA
is the aperture area of the optical system. 
Another approach is by considering the focal length and the fnumber:
A = π (f / (2 × n))²

You can use the one for which you have the input values.
What's the aperture area of a microscope of diameter D=12mm?
The microscope's aperture area is 113.1 mm^{2}. You can easily find this value by substituting the diameter (D = 12 mm) into the aperture area equation:
A = π (D / 2)²
A = π (12 mm / 2)²
A = 113.1 mm²
What's the fnumber `n` of a telescope of diameter 40 in and focal length 64 ft?
The fnumber is 19.2. To obtain this value:

We can find the fnumber
n
as the ratio of the focal lengthf
and the aperture diameterD
:n = f / D

Substitute the values of our problem and perform the corresponding conversions:
n = 64 ft / 40 in
n = 64 ft × (12 in / 1 ft)/ 40 in
n = 768 in / 40 in
n = 19.2

That's it! These values correspond to the specifications of the Yerkes Observatory's telescope.