Field of View vs Angle of View

“Is there a difference between angle of view (AoV) and field of view (FoV)?“

This seems to be a topic that has many beginner and professional photographers confused.

Field of View (FoV) and Angle of View (AoV) are often used interchangeably, when they actually refer to different concepts in photography. 

FoV refers to the length of a scene that is captured by the lens, while AOV refers to the angle at which the lens is able to capture that scene.

• Angle of View is affected by the Focal Length of the lens and the Sensor Size.
  • A wide-angle lens has a wider AoV than a telephoto lens.
  • AoV is measured in degrees.
• Field of View is affected by the Focal Length and AoV of the lens.
  • A lens with a longer Focal Length will have a narrower FOV than a lens with a shorter Focal Length.
  • FoV is measured as a length in meters or feet) on the horizontal plane of the frame.

In short, AOV is the angle of the lens that is captured, FOV is the length of the scene that is captured by the lens.

Let’s take a deeper look on how to calculate each of these.

What is Angle of View (AoV)

Angle of View (AoV) is the angle that the lens allows in light, which dictates the Field of View that it can capture, and is determined by both the Sensor Size and the Focal Length of the lens. 

It is measured in degrees and it refers to the Angle between the horizontal edges, vertical edges, or diagonal corners of an image that are captured by the Camera’s Sensor, with respect to the lens. 

• A wide-angle lens will have a Wider AoV
• A telephoto (zoom) lens will have a narrower AoV.

Calculating the AoV Width

To calculate the Angle of View (AoV) of the Width of the image, we can use the following equation:

• Width AoV = 2 * arctan (Sensor Width / (2 * Focal Length))

If you are using a 50mm lens at f/8 on a full-frame camera with a sensor size of 36mm x 24mm, shooting at a Focal Distance of 6m, the AoV would be calculated using a scientific calculator as follows::

• Width AoV = 2 * arctan (36 / (2 * 50)) 
• Width AoV= 39.59775271 degrees

Calculating the AoV Height

To calculate the Angle of View (AoV) of the Height of the image, we can use the following equation:

• Height AoV = 2 * arctan (Sensor Height / (2 * Focal Length))

If you are using a 50mm lens at f/8 on a full-frame camera with a sensor size of 36mm x 24mm, shooting at a Focal Distance of 6m, the AoV would be calculated using a scientific calculator as follows:

• Height AoV = 2 * arctan (24 / (2 * 50))
• Height AoV = 26.99146656 degrees

Calculating the AoV Diagonal

To calculate the Angle of View (AoV) of the Diagonal of the image, we can use the following equation:

• Diagonal AoV = 2 * arctan (Sensor Diagonal / (2 * Focal Length))

Example using a 50mm lens at f/8 on a full-frame camera with a sensor size of 36mm x 24mm, shooting at a Focal Distance of 6m.

Calculate Diagonal of Full Frame Sensor

First we would calculate the Diagonal of the Sensor using Pythagorean Theorem:

• Sensor Diagonal = √ (Sensor Width² + Sensor Height²)
• Sensor Diagonal = √ (36² + 24²) 
• Sensor Diagonal = 43.266mm

Now we can enter it and the other variables into the AoV equation:

• Diagonal AoV = 2 * arctan (43.266 / (2 * 50)) 
• Diagonal AoV = 46.79627031 degrees

AoV Summary

Here is a calculator that uses the above formula to calculate it for you. Simply enter the Sensor Width (mm) & Height (mm), as well as the Focal Length (mm):

We can therefore summarize that a Full frame sensor with a Focal Distance of 6m has the following Angle of Views:

• Width AoV= 39.597 degrees
• Height AoV = 26.991 degrees
• Diagonal AoV = 46.793 degrees

We can now use these to calculate the Field of View (FoV).

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What is Field of View (FoV)

Field of View (FoV) refers to the area or distance covered of a scene that can be captured by a camera, and is determined by the sensor size and the focal length of the lens. 

It is a distance measured in feet or meters that covers what the camera can see between the horizontal edges, vertical edges, or diagonal corners of an image. 

A wide-angle lens will have a wider FOV than a telephoto lens.

Calculating the FoV Width

To calculate the Field of View (FoV) of the Width of the image, we can use the following equation:

• Width FoV = 2 (Tan (Width AoV / 2) * Distance to Subject)

If you are using a 50mm lens at f/8 on a full-frame camera with a sensor size of 36mm x 24mm, shooting at a Focal Distance of 6m, the FoV would be calculated using a scientific calculator as follows:

• Width FoV = 2 * Tan (39.59775271 / 2) * 6
• Width FoV = 4.32m

Calculating the FoV Height

To calculate the Field of View (FoV) of the Height of the image, we can use the following equation:

• Height FoV = 2 (Tan (Height AoV / 2) * Distance to Subject)

If you are using a 50mm lens at f/8 on a full-frame camera with a sensor size of 36mm x 24mm, shooting at a Focal Distance of 6m, the FoV would be calculated using a scientific calculator as follows:

• Height FoV = 2 (Tan (26.99146656 / 2) * 6)  
• Height FoV = 2.88m

Calculating the FoV Diagonal

To calculate the Field of View (FoV) of the Diagonal of the image, we can use the following equation:

• Diagonal FoV = 2 (Tan (Diagonal AoV / 2) * Distance to Subject)

If you are using a 50mm lens at f/8 on a full-frame camera with a sensor size of 36mm x 24mm, shooting at a Focal Distance of 6m, the FoV would be calculated using a scientific calculator as follows:

• Diagonal FoV = 2 (Tan (46.7962703 / 2) * 6)
• Diagonal FoV = 5.19m 

FoV Summary

Here is a calculator that uses the above Angle of View and Field of View formulas to calculate it for you. Simply enter the Sensor Width (mm) & Height (mm), as well as the Focal Length (mm) and Focal Distance (m):

We can therefore summarize that a Full frame sensor with a Focal Distance of 6m has the following Field of Views:

• Width FoV= 4.32m
• Height FoV = 2.88m
• Diagonal FoV = 5.19m

Check Dimension Ratio using Pythagorean Theorem

We can double check this using Pythagorean Theorem:

• Diagonal FoV = √ (Width FoV² + Height FoV²)
• Diagonal FoV = √ (4.32² + 2.88²) 
• Diagonal FoV = 5.19m

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Enlargement Ratio from Sensor

We can also calculate how much of an Image Enlargement the Field of View is, compared to our camera sensor size of 36x24mm.

First we need to multiply the FoV dimensions by 1000 to get it into mm as well:

• Width FoV= 4.32m x1000 = 4320mm
• Height FoV = 2.88m = 2880mm
• Diagonal FoV = 5.19m = 5190mm

Now we simply divide the Field of View dimension by the Sensor dimension. We only need to do this to any of the dimensions (as we already checked that the ratios are correct using the Pythagorean Theorem, but I’ll illustrate it with all dimensions 3 anyway:

Width Image Enlargement

• Width Enlargement = 4320mm / 36mm
• Width Enlargement = 120x

Height Image Enlargement

• Height Enlargement = 2880mm / 24mm
• Height Enlargement = 120x

Diagonal Image Enlargement

• Diagonal Enlargement = 5190mm / 43.27mm
• Diagonal Enlargement = 120x

Therefore, the image (photo taken) is 120 times larger than the camera sensor using a 50mm Focal Length lens.

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Conclusion

In summary, FoV refers to the distance (length) of a scene that is captured by a camera, while AoV refers to the angle of the lens that the sensor can capture. 

Both are related and are determined by the sensor size and focal length of the lens.

Angle of View Tables

Using the same Focal Length lens, the Angle of View will change depending on the size of the camera sensor.

Full Frame (36x24mm) sensor AoV

Here is a table with the Horizontal (Width), Vertical (Height) and Diagonal, Angle of Views of a wide array of Focal Lengths using a Full Frame (36x24mm) sensor:

APS-C Cropped (23.5×15.6mm) sensor AoV

Here is a table with the Horizontal (Width), Vertical (Height) and Diagonal, Angle of Views of a wide array of Focal Lengths using a APS-C Cropped (23.5×15.6mm) sensor:

Micro-Four Thirds (17.3x13mm) sensor AoV

Here is a table with the Horizontal (Width), Vertical (Height) and Diagonal, Angle of Views of a wide array of Focal Lengths using a Micro-Four Thirds (17.3x13mm) sensor:

Field of View Tables

Here are the associated Field of View tables, based on the above Angle of Views. Note that the below tables are using a 6m Focal Distance as per the examples in this tutorial. Naturally if your Focal Distance is different, your Focal Length will be as well. Make sure to use the explained equations to recalculate the correct FoV.

Full Frame (36x24mm) sensor FoV

Here is a table with the Horizontal (Width), Vertical (Height) and Diagonal, Field of Views of a wide array of Focal Lengths using a Full Frame (36x24mm) sensor at a 6m Focal Distance:

APS-C Cropped (23.5×15.6mm) sensor FoV

Here is a table with the Horizontal (Width), Vertical (Height) and Diagonal, Field of Views of a wide array of Focal Lengths using a APS-C Cropped (23.5×15.6mm) sensor at a 6m Focal Distance:

Micro-Four Thirds (17.3x13mm) sensor FoV

Here is a table with the Horizontal (Width), Vertical (Height) and Diagonal, Field of Views of a wide array of Focal Lengths using a Micro-Four Thirds (17.3x13mm) sensor at a 6m Focal Distance: