Focal Length Calculator

Created by Łucja Zaborowska, MD, PhD candidate
Reviewed by Steven Wooding
Last updated: Jan 25, 2023

The focal length calculator is a simple tool that facilitates the process of computing the magnification, focal length, and the angle of view.

Taking a picture of an object from a distance might be challenging - we'll help you find the right focal length to create an image that perfectly fits your cameras' sensor size. 📷

In the article below, we'll teach you how to find the focal length, discover the lens equation, and talk about a few essential principles of photography and the lens choice.

What's the focal length?

Focal length is one of the primary values of a photographic lens. Manufacturers usually give it in millimeters (mm).

Focal length describes the distance between the rear principal point and the sensor - in other words, it's the space starting from the center of the lens, to the point where the light rays converge in the focal point (to form a sharp picture on a surface of a digital sensor, or 35mm film).

Biconvex lens-behaviour of light rays from focal point
Biconvex lens-behavior of light rays from the focal point.
Credit: Kvr.lohith, CC BY-SA 4.0, via Wikimedia Commons.

💡 Focal length can be determined only when the lens is focused at infinity

🖼️ Thanks to the focal length, we're able to calculate the angle of view - this variable informs us of the amount of the scene that will be captured. The wider the angle, the more of the scene can be transferred to a sensor, and be visible on the photograph. Thanks to the angle of view option, we don't really need an additional field of view calculator - we got everything ready!

Lens' Focal length principles

🔍 Thanks to our lens focal length calculator, you may also find the magnification - it allows us to measure how the size of an object changes when transferred to photography.

Still hungry for knowledge? Try our other lens tools, such as the thin lens equation calculator, Lensmaker's equation calculator or the Snell's law calculator 💎

Or ....learn how the concept of focal length is fundamental when we need to calculate parameters like the camera field of view!

How to use the focal length calculator?

Our lens equation calculator has a straightforward structure; fill in at least three fields in order to acquire results.

  • Typical image sizes:

    • 3.6, 4.8, 5.8, 6.4, 8.8, 12.8 mm,
    • or 1/4, 1/3, 1/2.5, 1/2, 2/3, 1 inch.
  • Object distance is measured from the lens's front principal plane to the object itself.

💡 Remember, our calculators work both ways. Your result can simply become another query!

The lens that makes objects appear small will have a small magnification - on the other hand, the lens that magnifies the picture will have a big magnification.

How to calculate focal length?

Finding focal length is an easy and very much needed ability; follow our simple guide to find all the details of these calculations!

  1. The typical focal length formula looks as follows:

    1/Focal length = 1/Image distance + 1/Object distance,

    where:

    • Image distance and Object distance are given in mm.
  2. And here's the transformed equation that we use:

    Focal length = (Object distance / ((1 / Magnification) + 1)) × 1000,

    where:

    • Object distance is given in mm; and
    • Magnification does not have a unit.
  3. In order to copy the lens magnification calculator, you'll need the following equation (take a closer look - it may also serve as an image distance formula!):

    Magnification = Image size / Object size = -(Image distance / Object Distance),

    where:

    • Object size - is the real size of an object, given in mm; and
    • Image size - is the size of the camera's digital sensor or 35mm film, given in mm.
  4. To calculate the angle of view, you need to use the most complex equation of them all:

    Angle of view = (180/π) × 2 × aTan(Image size / (2 × Focal length × (Magnification + 1))),

    where:

    • aTan(x) means the arc tangent , described as the inverse tangent of a function x (in radians).

FAQ

What is the focal length of a lens?

The focal length of a lens is the distance at which every light ray incident on the lens converges (ideally) in a single point. By placing your sensor (or film) at the focal length, you obtain the sharpest image possible. Every lens has its own focal length that depends on the manufacturing process.

How do I calculate the focal lenght of a lens?

To calculate the focal length of a lens, you need to follow a few simple steps:

  1. Measure the distance o between the lens and an object.
  2. Measure the distance i between the lens and the generated virtual image.
  3. Calculate the multiplicative inverse of the focal length with the following formula:
    1/f = 1/i + 1/o.

How do I calculate the focal length if I know the magnification?

To calculate the focal length if you know the magnification, follow these steps:

  1. If you know the image distance, find the object distance with this formula: object distance = image distance/magnification.
  2. Knowing the object distance, calculate the focal length with the following formula:
    f = (object distance / ((1 / Magnification) + 1)) × 1000.

What is the focal length of a lens with magnification 0.00553x at 10 m?

The focal length of a lens with magnification 0.00553x at 10 m is 55 mm. To find this result, use the following formula:
f = (object distance/((1/magnification) + 1)) × 1000
Substitute the values:
f = (10 m/((1/0.00553) + 1)) × 1000 = 55 mm
Don't worry about the low value of the magnification: we are not talking about the zoom but the ratio between the actual height of your subject and the height of it on your sensor: no surprise; it's so small!

Łucja Zaborowska, MD, PhD candidate
Object size
in
Image size
mm
Object distance
ft
Magnification
×
Focal length
mm
Angle of view
deg
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