Effective Field of View (W)
-- mm
-- in
Native Lens FOV: -- mm
*Schematic dynamically scaled relative to sensor
When utilizing machine vision lenses, the Crop Factor is best understood as the ratio between the format the lens was designed for and the actual sensor you are using: CF = Lens Diagonal / Sensor Diagonal.
If you place a 2/3" lens on a 1/1.8" sensor, the sensor is smaller than the image circle the lens projects. It essentially "crops" into the center of the lens's native Field of View. The effective physical FOV is therefore: FOVEffective = FOVNative / Crop Factor (calculated linearly along width/height/diagonal).
Conversely, placing a 1/1.8" lens on a 2/3" sensor will result in vignetting, where the lens's native image circle completely fails to cover the corners of the larger sensor format.
The Angular Field of View is the angle of the scene that the lens captures, radiating outward from the optical center. It is strictly dependent on the physical dimension of the sensor format and the focal length of the lens, completely independent of the working distance: AFOV = 2 × arctan(Dimension / (2 × FL)).
Lens manufacturers frequently list a lens's Native Angular Field of View instead of a hyper-precise Focal Length. If you know the AFOV specified for the lens's native designed format, the exact focal length can be reverse-calculated: FL = (Lens Width / 2) / tan(AFOVhoriz / 2)
Many simple photography calculators use the generic approximation FOV ≈ Sensor × (WD / FL), which assumes the subject is essentially at infinity. However, for machine vision and macro applications, this calculator utilizes the exact thin-lens geometric derivation: FOV = Sensor × ((WD / FL) - 1). Because this precise equation inherently incorporates your specific sensor dimensions, it automatically bakes the "crop factor" into the result perfectly.
Note: Working Distance (WD) in fundamental thin-lens equations is measured precisely from the lens's principal plane. In practical hardware setups, WD is commonly measured from the front edge of the lens barrel. For highly precise high-magnification applications, the physical offsets of the principal planes must be strictly accounted for.