# Aperture Area Calculator

Created by Luis Hoyos
Last updated: Nov 21, 2022

With this aperture area calculator, you'll be able to:

• Calculate the aperture area and diameter of lenses or other optical systems with circular apertures;
• Calculating the f-number or focal length (although better obtain the latter with our focal length calculator😉); and
• Calculate the focal length required for a given f-number and aperture diameter.

To know how we calculate the aperture diameter and areas in this calculator, keep reading this article and discover it.

## The f-number and the focal length

In an optical system, the aperture is the opening through which light passes. Aperture shapes are typically circular, and their size determines how much light enters the system.

Another characteristic of optical systems is the f-number, which is the ratio of the focal length to the aperture diameter:

n = f/D

, where:

• n — f-number;
• f — Focal length; and
• D — Aperture diameter;

We can also solve for f and obtain an aperture focal length formula: f = nD.

The f-number is a dimensionless number that quantifies the light-gathering ability of the system. When calculating the f-number with the previous equation, no matter the length units used for f and D, as long as they're both the same (our length converter can be helpful here).

The focal length indicates how strongly the system converges or diverges light. For example, the focal length in a lens is the distance from the lens to the point where light rays converge (the focus).

Lenses are the most common type of optical system. You can calculate their aperture focal length using our thin lens equation calculator and Lensmaker equation calculator.

## How to calculate lens diameter and aperture area?

From the previous f-number definition, we can solve for D and obtain the equation for the aperture diameter of an optical system:

D = f/n

And from the circle area formula (A = π × (D/2)²), we obtain the equation for the aperture area (A):

A = π × [f/(2n)]²

For example, let's look at how to calculate the aperture area of a lens aperture with an f-number n = 2 and a focal length of f = 70 mm:

1. First, let's calculate the lens diameter:
D = f/n = (70 mm)/2 = 35 mm;
2. From the calculated lens diameter, let's obtain the aperture area:
A = π × (D/2)² = π × (35 mm/2)²
A = 962 mm²

You can, of course, make the exact computations much faster with our aperture area calculator!

Luis Hoyos
Focal length (f)
mm
f-number (n)
Aperture diameter (D)
mm
Area (A)
mm²
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