Machine Vision Field of View: Calculation, Angle of View, and Common Pitfalls
The FOV formula takes three inputs, and it fails for three reasons: nominal sensor names, distortion, and fisheye projection. This guide covers the formula, the angle-of-view relationship, and the checks that keep the numbers honest.
Field of view (FOV) in machine vision is the physical size of the scene the camera captures at a given working distance. For a rectilinear lens it is FOV = (sensor width × working distance) / focal length, where sensor width is the active imaging dimension in millimeters, not the nominal format name.
The formula fails when engineers use nominal sensor dimensions, ignore lens distortion, or apply it to fisheye lenses. Verify final numbers with the field of view calculator before ordering hardware.
What is field of view in machine vision?
Field of view (FOV) in machine vision is the physical area of the scene the camera captures at a given working distance, expressed in linear units at the object plane. A 120mm horizontal field of view means the camera sees a 120mm-wide strip at the inspection distance.
FOV is not a property of the lens alone. It depends on three inputs:
- A longer focal length narrows the field of view.
- A larger active sensor widens the field of view.
- Moving farther from the object widens the field of view.
Change any one of these and the field of view changes, which makes FOV a system-level calculation, not a lens spec lookup. Working distance is a design variable early in a project and fixed once the mechanics are committed. The Commonlands working distance guide covers that tradeoff. Linear FOV at the object plane is what inspection tasks specify.
How do you calculate the field of view of a camera?
For a rectilinear lens, horizontal field of view equals active sensor width times working distance, divided by focal length. Use the active sensor dimensions from the camera datasheet, not the nominal format name. Measure working distance from the front of the lens to the object. That point stands in for the lens's front focal point, and the offset matters only at short working distances.
Horizontal and vertical coverage use the same relation with the corresponding sensor dimension, and the diagonal follows from Pythagoras. The relation is exact for rectilinear projection, not a thin-lens approximation (Hecht, Optics, 5th ed., §5.2).
Use the active imaging width from the camera datasheet, not the nominal format name. A sensor labeled 1/2" has an active width near 6.4mm. Entering 12.7mm (half of 25.4) produces a result nearly double the real field of view.
Worked example
A 1/2.3" sensor has an active width of approximately 6.17mm. At 300mm working distance with a 6mm lens:
Choosing focal length from a target field of view
Rearrange the formula to solve for focal length when you know the scene size to cover:
Round to an available focal length and re-check the coverage: a 12mm lens gives 213mm and a 16mm lens gives 160mm at that distance. The Commonlands focal length selection guide walks through the tradeoff.
Ground sample distance (scene width per pixel) is FOV_H divided by the pixel column count, and it decides whether the system resolves the required feature sizes. The Commonlands spatial resolution guide covers how it interacts with lens MTF and pixel size.
What is the difference between angle of view and field of view?
Angle of view is an angular property of the lens and sensor, measured in degrees, and stays effectively constant at any working distance. Field of view is the physical scene coverage, in millimeters, that the angle produces at a specific working distance on a specific sensor. The two are related by FOV_H = 2 × WD × tan(AoV_H / 2).
| Property | Angle of view (AoV) | Field of view (FOV) |
|---|---|---|
| Unit | Degrees | Millimeters, meters, or inches |
| Depends on working distance? | Effectively no; fixed for a lens and sensor pair except at very close focus | Yes; it doubles when working distance doubles |
| Useful for | Lens specification, comparing sensor formats | Scene coverage at a known inspection distance |
Because sensors are rectangular, the angle differs by axis: HFOV uses the active width, VFOV the active height, and DFOV the diagonal. On a 6.3mm × 4.7mm active area, a 4mm lens gives roughly 76° HFOV, 61° VFOV, and 89° DFOV. Datasheets do not always state which axis a quoted angle uses, so check before comparing lenses.
To convert a target scene width to the required angle, use the Commonlands angle of view calculator to confirm a lens and sensor combination hits it.
How do focal length and sensor size affect field of view?
Field of view scales directly with active sensor width and inversely with focal length: doubling the sensor width doubles the FOV, and halving the focal length doubles it. Angle of view responds nonlinearly, so short focal lengths need tighter specification. The same scaling lets pairings match: an 8mm lens on a 2/3" sensor and a 6mm lens on a 1/1.8" sensor give similar horizontal coverage at the same distance.
Active area vs nominal format name
Nominal sensor format names are historical designations from tube camera outer diameters. They do not describe the physical size of the imaging area, and using them as dimensions corrupts the FOV calculation:
| Nominal format | Common active width (mm) | Common active height (mm) | Error if the format fraction is used as the width |
|---|---|---|---|
| 1/4" | ~3.6 | ~2.7 | Using 6.35mm gives ~76% error |
| 1/3" | ~4.8 | ~3.6 | Using 8.47mm gives ~76% error |
| 1/2.3" | ~6.17 | ~4.55 | Using 11.04mm gives ~79% error |
| 1/2" | ~6.4 | ~4.8 | Using 12.7mm gives ~98% error |
| 1/1.8" | ~7.18 | ~5.32 | Using 14.11mm gives ~97% error |
| 2/3" | ~8.8 | ~6.6 | Using 16.93mm gives ~92% error |
Active dimensions vary by manufacturer and pixel count within a nominal format, so check the specific camera model. The CMOS sensor size guide explains the naming convention, and the Commonlands image sensor reference lists active dimensions for common sensors.
Why do distortion, fisheye projection, and image circle change the real answer?
The rectilinear FOV formula assumes straight lines map to straight lines on the sensor. Barrel distortion, fisheye projection, and an image circle mismatched to the sensor each break that assumption, so the formula can misstate usable coverage.
Barrel Distortion Splits Coverage Into Raw and Usable
Barrel distortion makes the formula answer two questions with one number, so read its result against the quantity you care about:
| Quantity | What barrel distortion does | Formula error |
|---|---|---|
| Total angular field | Local magnification falls with field height, so the lens sees more scene than a rectilinear lens of the same focal length | Understates the true angular coverage |
| Usable low-distortion region | Geometry stays accurate only over a smaller central radius | Overstates the coverage you can measure on |
| Edge pixel scale | Each edge pixel covers more scene, so a rectified image must stretch the edges back out | Understates the scene width each edge pixel spans |
Many standard machine vision lenses approximate rectilinear projection closely enough that the gap is small. Below about 4mm focal length on smaller sensors, barrel distortion becomes visible: treat the formula result as the raw angular field, then derate for the low-distortion region the task needs. For measurement or alignment, specify low-distortion lenses. The Commonlands low distortion lens guide covers how they are specified.
Fisheye lenses require a different calculation entirely
Fisheye lenses do not follow the rectilinear model. They use alternative projections such as equidistant, equisolid, stereographic, or orthographic mapping. Neither the arctan formula nor the tan conversion applies:
A 180° fisheye images a 90° half-angle cone, and converting that to a scene width needs the projection function, not the tan formula. Use the manufacturer's mapping data, which the Commonlands fisheye and wide-angle distortion guide treats in depth.
Image circle and sensor crop
Lenses project a circular image. If the sensor diagonal exceeds the lens image circle, the corners vignette and the usable field is smaller than the formula result. If the image circle is larger than the sensor, the sensor crops the projection: a lens rated for 2/3" sensors on a 1/2" sensor sees a narrower angle than its datasheet states.
Verify the image circle covers the sensor diagonal, and calculate with your sensor's active dimensions. The Commonlands sensor size and lens compatibility guide covers both failure modes.
Which lenses cover wide, standard, and narrow fields of view?
Focal lengths from 2.6mm to 25mm produce horizontal fields of view from roughly 712mm down to 74mm at 300mm working distance.
Top lenses ranked by field of view band
These five Commonlands lenses span the range at a fixed working distance, ranked widest to narrowest, from the CIL227 190° fisheye to the CIL250 25mm telephoto.
| FOV band | Lens | Mount / EFL | Published coverage | Best-fit application |
|---|---|---|---|---|
| Ultra-wide fisheye | CIL227 2.7mm fisheye | M12, 2.7mm | 190° FOV at an 8.0mm image circle (equidistant projection) | Hemispheric coverage for security, drones, and presence detection |
| Wide | CIL059 6mm low-distortion | M12, 6mm | 76° FOV at an 8.8mm image circle | Low-distortion wide coverage for measurement on 1/1.7" sensors |
| Wide | CIL062 6mm no-distortion | M12, 6mm | ~359mm at 300mm WD on a 1/1.8" sensor | Clean geometry for gauging and alignment at a lower price |
| Medium | CIL531 8mm C-mount | C-mount, 8mm | ~330mm at 300mm WD on a 2/3" sensor (~58° HFOV) | Adjustable-iris depth control on 12MP 2/3" sensors |
| Narrow telephoto | CIL250 25mm telephoto | M12, 25mm | ~74mm at 300mm WD on a 1/2.3" sensor (~14° HFOV) | Small-feature inspection at longer working distances |
Coverage figures come from the 300mm scene-coverage table later in this section or the lens product-page datasheet. The fisheye value is equidistant-projection coverage, not a rectilinear formula result.
How focal length changes scene coverage at 300mm working distance
This Commonlands reference table shows approximate horizontal field of view for rectilinear lenses at 300mm working distance on common sensor formats. All values use active sensor widths.
| Focal length | Sensor format | Active width (mm) | FOV_H at 300mm WD (mm) | Coverage category |
|---|---|---|---|---|
| 2.6mm | 1/2.3" | 6.17 | ~712 | Very wide |
| 6mm | 1/2.3" | 6.17 | ~309 | Standard |
| 6mm | 1/1.8" | 7.18 | ~359 | Standard (larger sensor) |
| 8mm | 2/3" | 8.8 | ~330 | Standard (C-mount) |
| 25mm | 1/2.3" | 6.17 | ~74 | Telephoto / narrow |
The C-mount row adds an adjustable iris, so stopping down extends depth of field when a target field of view also carries a depth requirement.
Frequently asked questions
What is field of view in machine vision?
Field of view (FOV) in machine vision is the physical area of the scene the camera captures at a given working distance, measured in millimeters at the object plane. A horizontal field of view of 120mm means the camera sees a strip 120mm wide at that distance. FOV is set by focal length, active sensor dimensions, and working distance together.
How do I calculate machine vision field of view?
For a rectilinear lens: FOV_H = (sensor width × working distance) / focal length, all in millimeters. Use the actual active sensor dimensions, not the nominal format name. A 1/2" sensor has an active width of approximately 6.4mm, not 12.7mm. To find the focal length for a target FOV, rearrange: f = (sensor width × working distance) / target FOV. Fisheye and high-distortion lenses need a projection-corrected calculation.
Why do wide-angle and fisheye lenses break simple FOV math?
The standard formula assumes rectilinear projection, where straight lines in the scene map to straight lines on the sensor. Wide-angle lenses with barrel distortion compress the image edges, so the usable undistorted coverage differs from the formula prediction. Fisheye lenses use a different projection model entirely (equidistant or equisolid), so the arctan and tan formulas do not apply at all.
What is the difference between horizontal, vertical, and diagonal angle of view?
Horizontal AoV (HFOV) uses the active sensor width, vertical AoV (VFOV) uses the active sensor height, and diagonal AoV (DFOV) uses the sensor diagonal. For a rectangular sensor, DFOV is the largest of the three. Lens datasheets may quote any axis without saying which, so check before comparing lenses. DFOV can exceed VFOV by more than 30 degrees on a 16:9 sensor.
How do I choose focal length from a target field of view?
Rearrange the FOV formula: f = (sensor width × working distance) / target FOV, all in millimeters. Start from the active sensor width in the camera datasheet, the working distance your system geometry dictates, and the required scene coverage. Round to the nearest available focal length, then verify the resulting FOV with the Commonlands field of view calculator before ordering hardware.
Need help hitting a target field of view?
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