How to Choose Focal Length for Machine Vision: Formula, Sensor Size, and Selection Steps
Focal length is a geometry problem with a specific answer for each setup. This guide covers the formula, what effective focal length actually means, the full selection sequence, and when a telephoto is the right call.
To choose a focal length for machine vision, start from three measured numbers: the scene width the camera must cover, the working distance from the front of the lens to the target, and the active width of your sensor. The required focal length is EFL = (WD × sensor_width) / FOV_width. For rectilinear lenses this holds whenever the working distance is much longer than the focal length, which covers nearly all machine vision setups.
Pick the nearest stock focal length, then verify distortion, depth of field, and image circle before ordering. The field of view calculator checks any lens and sensor pairing in seconds.
How do I calculate the focal length I need?
Required focal length equals active sensor width multiplied by working distance, divided by required scene width. A 1/2.7" sensor (5.37mm active width) imaging a 120mm-wide part from 400mm needs (5.37 × 400) / 120 = 17.9mm, which makes 16mm and 21.8mm the practical high-resolution stock candidates.
For rectilinear lenses this geometry needs no distortion correction factor (Hecht, Optics, 5th ed., §5.2), but it does assume the working distance is much longer than the focal length; at short conjugates, near 1:1 magnification, solve the thin-lens equation 1/f = 1/s + 1/s' directly. It is the same geometry behind the Commonlands angle of view calculator, where EFL = sensor_width / (2 × tan(AOV / 2)). Fisheye and F-theta lenses use different projections; for those, use datasheet FOV values instead.
A worked example
The nearest stock M12 focal lengths to 17.9mm are 16mm below and 18mm, 19mm, and 21.8mm above. The 18mm and 19mm options are lower-resolution designs rated for 2MP sensors and below, so on a high-resolution sensor the practical shortlist is 16mm and 21.8mm. A 16mm lens at 400mm covers about 134mm of scene width, 12% more than required, which leaves margin for placement tolerance. A 21.8mm lens covers about 99mm, narrower than the part, so it only works if the working distance can grow. Run both candidates through the field of view calculator before ordering; the EFL calculator solves the same geometry in the other direction.
A second example with a larger sensor shows how the numbers move. A 1/2" sensor (6.4mm active width) inspecting a 200mm-wide tray from 600mm needs (6.4 × 600) / 200 = 19.2mm. A 16mm lens covers about 240mm at that distance (a comfortable margin), while a 25mm lens covers about 154mm and clips the tray. Same scene, same distance, different sensor, different answer: the sensor width term is why a lens recommendation without a sensor part number is a guess.
Rearranging the formula
The same equation answers the other two layout questions. Fix any two of the three quantities and the third is determined; these rearrangements hold in the same long-working-distance regime as the main formula.
One input deserves special care: sensor_width must be the active sensor width from the sensor datasheet, not the nominal format number. A "1/2 inch" CMOS has roughly a 6.4mm active width, not 12.7mm, and that substitution alone produces focal length errors of about 2×. The CMOS sensor size guide explains the format-name legacy; the field of view guide covers linear versus angular FOV in more depth.
What is effective focal length?
Effective focal length (EFL) is the distance from a lens's rear principal plane to its focal point when the lens is focused at infinity. It is the parameter that sets field of view and magnification, and the mm value printed on a machine vision lens listing (6mm, 12mm, 35mm) is the EFL.
EFL is one of three lengths that get conflated. Back focal length (BFL) and its mechanical variant MBFL measure from the rear of the lens to the image plane. They are packaging numbers that decide whether a lens reaches focus in a specific holder or adapter. Flange focal distance (FFD) is a mount standard: 17.526mm for C-mount, 12.526mm for CS-mount, and undefined for M12, which has no standardized flange. Two lenses with identical EFL can have very different BFL values. The back focal length section of the mount guide covers the mechanical side.
| Term | What it is | What it controls |
|---|---|---|
| EFL (effective focal length) | Optical parameter of the lens prescription | Field of view and magnification |
| BFL / MBFL (back focal length) | Per-lens rear spacing dimension | Holder and adapter clearance (whether the lens can reach focus) |
| FFD (flange focal distance) | Mount standard specification | Lens interchangeability (17.526mm C-mount, 12.526mm CS-mount, none for M12) |
On the object side, EFL = (WD × sensor_width) / FOV_width gives linear coverage, as above. On the image side, the same rectilinear geometry written as an angle is:
A 12mm lens at 500mm working distance on a 1/2.3" sensor (6.17mm wide) covers 500 × 6.17 / 12 ≈ 257mm of object width. EFL does not change with working distance. Move the same camera to 100mm and coverage shrinks to about 51mm at higher magnification, but the lens is still a 12mm lens. For quick comparisons, effective magnification at a given working distance is approximately EFL / WD: a longer EFL at the same distance magnifies more, which helps resolve small features but leaves less margin for part placement variation.
Sensor size changes framing just as strongly as focal length does. The lens projects the same image circle regardless of what sits behind it; a larger sensor samples a bigger portion of that circle and frames a wider scene. The table below shows the same two focal lengths across five common formats: moving a lens from a 1/2.3" camera to a 2/3" camera adds roughly 40% angular coverage without touching the optics, provided the lens image circle covers the larger sensor's diagonal.
| Sensor format | Active width (approx.) | HFOV at 12mm EFL | HFOV at 35mm EFL |
|---|---|---|---|
| 1/2.7" | 5.37mm | 25.2° | 8.8° |
| 1/2.3" | 6.17mm | 28.8° | 10.1° |
| 1/1.8" | 7.18mm | 33.3° | 11.7° |
| 1/1.7" | 7.60mm | 35.1° | 12.4° |
| 2/3" | 8.80mm | 40.3° | 14.3° |
Many designs below roughly 4mm EFL diverge from rectilinear, and any lens described as fisheye, ultra-wide, or F-theta uses a non-rectilinear projection by design. Not all short lenses break the rule (a low-distortion 3.3mm design can still match the arctan formula), but a 3.2mm wide-angle lens with a measured 113° HFOV on a 1/2.3" sensor would compute to about 88°. Verify short focal lengths against datasheet FOV values; the F-theta lens guide explains the projection difference.
The EFL calculator runs the rectilinear math interactively for common sensor formats and flags where the wide-angle caution applies.
How do you select a machine vision lens, step by step?
Machine vision lens selection runs in a fixed order: field of view, working distance, sensor dimensions, and feature size first; focal length calculation second; mount family third; image quality verification last. Each step depends on the numbers from the one before it, so skipping a step can produce a lens that fits mechanically but not optically.
- Define the field of view. Write the scene dimensions in millimeters at the target plane, plus a 10–20% margin for placement tolerance. A 200mm-wide board becomes a 240mm design field.
- Measure the working distance. Working distance runs from the front of the lens to the target. It is a mechanical fact of the enclosure, arm, or gantry, measured rather than chosen. Commonlands M12 lenses focus from 50mm to infinity (uncorrected); C-mount working distance varies by product, typically 100mm to infinity. The working distance guide covers how this constraint hardens as a design matures.
- Pull the active sensor dimensions. Pixel count × pixel pitch from the sensor datasheet, never the nominal format label. The image sensor database lists active areas for common parts.
- Set the smallest feature to resolve. Divide scene width by horizontal pixel count for ground sampling distance (mm/pixel); keep at least 2 pixels per feature (Nyquist), 3–4 in practice. The spatial resolution guide covers the math.
- Calculate the focal length. EFL = (WD × sensor_width) / FOV_width, then shortlist the nearest stock values. The EFL calculator does this in one step.
- Choose the mount family. M12 for compact, light, board-level builds; C-mount for larger sensors, an adjustable iris, and cam-compensated refocusing; CS-mount between them. The lens mount guide compares thread, flange, and coverage in detail.
- Verify image quality. Image circle at least as large as the sensor diagonal (see the sensor compatibility guide), and depth of field spanning the object height range (run the depth of field calculator).
Two more checks complete step 7: distortion against the application's position-error budget, covered in the low-distortion lens guide, and lens MTF at the feature's spatial frequency, covered in the MTF curve guide. A lens that threads on is not necessarily a lens that works; mechanical fit says nothing about optical fit.
Spectral filtering and holder mechanics are deliberately out of scope on this page. The bandpass filter guide covers wavelength selection, and the filter collection lists stock options.
Should you choose a short, medium, or long focal length?
Medium focal lengths (5mm to 16mm in M12) fit most factory inspection setups. Short focal lengths under 5mm buy scene coverage from close range at the cost of distortion. Long focal lengths above 16mm buy pixel density on the target at the cost of depth of field. Start medium unless the geometry forces you elsewhere.
Short focal lengths (under 5mm in M12)
Short focal lengths produce wide fields of view from short working distances: a 3.3mm M12 lens can cover 500mm or more at modest distances, useful for area coverage, wide conveyor lanes, and cameras mounted close to the target. The cost is barrel distortion: wide lenses introduce systematic position errors at the field edges that grow with distortion; whether they need software calibration depends on the application's position-accuracy budget. Depth of field is generous, which helps when object height varies. The wide-angle and fisheye guide covers projection behavior at these focal lengths.
Medium focal lengths (5–16mm in M12)
This is the most commonly useful range for factory machine vision. A 6mm M12 lens on a 1/1.8" sensor at 500mm working distance covers roughly 600mm, enough for a PCB or tray while keeping component-level resolution. Distortion is lower than wide-angle designs and depth of field is still workable. For a first pass at a new setup, start here and check the numbers with the EFL calculator.
Long focal lengths (above 16mm in M12)
Long focal lengths compress the field of view and raise pixel density: each pixel covers a smaller physical area, which is what fine-feature detection needs. Distortion is typically low. The practical cost is shallower depth of field: parts that vary even a few millimeters in height can fall outside the focus budget. The depth of field guide covers this trade in detail.
| Focal length range | Field of view (relative) | Distortion | Depth of field | Pixel density on target | Typical use |
|---|---|---|---|---|---|
| Short (<5mm) | Wide | Higher | Deep | Lower | Wide coverage, navigation, AMRs |
| Medium (5–16mm) | Moderate | Moderate | Moderate | Moderate | General inspection, barcode reading |
| Long (>16mm) | Narrow | Lower | Shallow | Higher | Fine feature detection, metrology |
The field of view column is deliberately relative, with no degree ranges, because the angle depends on the sensor as much as the lens. The HFOV table above shows why: the same 12mm lens reads 25.2° on a 1/2.7" sensor and 33.3° on a 1/1.8" sensor, so a fixed degree band would put one pairing in a different row than the other. Treat the bands as guidance within a single sensor format, and compute the actual angle for your sensor and lens with the angle of view calculator before classifying a candidate as wide or narrow.
Which M12 focal lengths cover most applications?
Four stock M12 lenses span the working range for most machine vision setups: 3.3mm and 3.6mm for wide coverage, 6.2mm as the general-purpose default, and 12.5mm where pixel density matters. The full M12 catalog runs 0.8mm fisheye to 100mm telephoto.
Commonlands stocks roughly 70 M12 lens models in the US, most offered in several aperture and filter variants. Orders placed before 12 PM PST ship the same day from San Diego, CA.
| Lens | EFL | Sensor format | FOV | Distortion | Price | Best for |
|---|---|---|---|---|---|---|
| CIL036 | 3.3mm | 1/2.7" | 89° at 6.4mm image circle | -0.7% TV | $19 | Wide field with low distortion in tight installations |
| CIL336 | 3.6mm | 1/2.4" | 128° at 7.6mm image circle | -5.5% F-theta | $39 | Very wide coverage in wash-down and dust environments (IP6K9K) |
| CIL062 | 6.2mm | Up to 1/1.8" | 60° at 7.2mm image circle | -2% optical | $19 | Balanced general inspection and the default starting point |
| CIL125 | 12.5mm | Up to 1/2" | 35° at 7.9mm image circle | -1.4% optical | $39 | Tighter field with higher pixel density for fine features and labels |
TV, optical, and F-theta distortion percentages are measured against different references and are not directly comparable row to row.
The CIL062 at 6.2mm is the lens most engineers should try first: low distortion, practical coverage on sensors up to 1/1.8", $19. If the formula puts your requirement anywhere in the 5–8mm range, start there and verify the actual FOV against your scene. The CIL036 is the wide-field option when measurement accuracy still matters: at -0.7% TV distortion it behaves more like a rectilinear lens than a typical ultra-wide. The CIL336 trades distortion for sealing and maximum coverage, and the CIL125 is where pixel density starts to win over scene width.
Top M12 lenses by focal length
Seven M12 focal lengths cover most machine vision work, from wide-area coverage to long-standoff inspection: 3.3mm (CIL036), 3.6mm (CIL336), 6.2mm (CIL062), 12.5mm (CIL125), 26mm (CIL260), 35mm (CIL350), and 50mm (CIL051). Choose by the field of view your working distance and sensor require, then confirm coverage on the field of view calculator before ordering.
How we picked: every entry is a current US-stock Commonlands model with a stated image circle, ranked by effective focal length rather than by price. The application notes reuse the short, medium, and long focal length guidance from the section above, so the order tracks scene geometry instead of a marketing tier.
| Rank | EFL | Lens | Typical application |
|---|---|---|---|
| 1 | 3.3mm | CIL036 wide-angle | Wide field with low distortion in tight installations |
| 2 | 3.6mm | CIL336 sealed (IP6K9K) | Very wide coverage in wash-down and dust environments |
| 3 | 6.2mm | CIL062 low-distortion | Balanced general inspection and the default starting point |
| 4 | 12.5mm | CIL125 telephoto | Tighter field and higher pixel density for fine features and labels |
| 5 | 26mm | CIL260 telephoto | Narrow field on 1/1.7" sensors for small or distant targets |
| 6 | 35mm | CIL350 telephoto | Long-standoff inspection where pixel density outweighs coverage |
| 7 | 50mm | CIL051 telephoto | Long-range aerial robotics and standoff inspection at 1/1.6" |
Edmund Optics and Arducam also supply M12 optics; what separates these picks is published MTF data, US stock that ships the same day from San Diego, and an M12 range that runs from 0.8mm fisheye to 100mm telephoto. Match any candidate to your sensor with the EFL calculator, then open the full M12 lens catalog for aperture and filter variants.
When should you choose a telephoto machine vision lens?
Choose a telephoto machine vision lens when the target is small or distant and the camera cannot move closer. As a rough guide, that means the target occupies only a small fraction of the frame with the lens you have and cannot be enlarged by moving the camera closer. Common telephoto M12 options run 12.5mm to 50mm, with 75mm and 100mm models at the long end of the catalog, and all of them trade scene coverage for magnification, tighter focus tolerance, and higher vibration sensitivity.
In machine vision, "telephoto" means any long-EFL lens used to reach or magnify a target, not the specific photographic construction where the barrel is shorter than the focal length. The geometry is the same formula as everywhere else on this page: doubling the EFL halves the linear field of view at the same working distance and doubles the apparent target size on the sensor. Typical applications are aerial inspection from drones, traffic monitoring at distance, overhead conveyor lines, and barcode or OCR reading at long standoff.
Two effects make telephoto lenses less forgiving than shorter ones. First, focus tolerance: at a given F-number and working distance, depth of field shrinks rapidly as focal length grows, so a focus setting that was forgiving at 6mm becomes critical at 35mm. Second, vibration: image shift on the sensor scales with focal length times the angular disturbance, so a platform wobble that is invisible at 6mm smears pixels at 50mm. Plan stiffer mounts, lock focus after setting it, and re-verify focus after any mechanical service; the focusing guide covers the procedure.
Telephoto is also frequently the wrong answer. If the system must monitor a wide area, inspect several objects per frame, or run on a vibration-heavy platform without precision mounts, a shorter focal length is more robust: it tolerates pointing error and platform motion that would push a narrow frame off target. And when the underlying problem is dim or uneven lighting rather than framing, fixing the illumination beats changing the lens; the stray light guide covers how optical design interacts with ambient and structured lighting at distance.
Near-focus behavior differs by mount system. C-mount telephotos refocus through an internal cam that moves lens groups relative to each other, rebalancing aberrations across the focus range; inside the minimum object distance the cam hits its mechanical stop and the image goes uniformly soft. M12 telephotos are rigid assemblies focused by threading the whole barrel in the holder. There is no hard stop, but short standoffs demand deep holders, and full-field sharpness at close range is limited by field curvature and astigmatism rather than by center focus. The working distance guide treats both cases.
Select telephoto M12 lenses reach 1/1.7" to 1/1.6" sensor coverage in a fixed-aperture board-lens package, the right fit for drones, embedded systems, and weight-limited payloads. Move to C-mount when the sensor is larger, when you need an iris to stop down for depth of field, or when lighting is too dim to fix at a fixed aperture; the low-light section of the F-number guide covers that trade.
| Part | EFL | Format | Resolution | Aperture | Price |
|---|---|---|---|---|---|
| CIL125 | 12.5mm | Up to 1/2" | 12MP | Fixed | $39 |
| CIL121 | 21.8mm | Up to 1/1.7" | 12MP+ | Fixed | $70 |
| CIL260 | 26mm | 1/1.7" | 5MP | F/2.0 | $59 |
| CIL350 | 35mm | 1/1.7" | 8–10MP | Fixed | $59 |
| CIL051 | 50mm | 1/1.6" | 12MP | Fixed | $79 |
Before committing to any telephoto, confirm the image circle covers the sensor diagonal (a 1/1.8" sensor diagonal is roughly 8.9mm and a 1/1.6" diagonal roughly 10.1mm), and verify the framing with the field of view calculator at your actual working distance.
What if the calculated focal length does not exist?
Round to the nearest stock focal length and recompute the field of view. Rounding shorter gives extra coverage you can crop, which is the safe default. Rounding longer gives less coverage and is only acceptable once you have confirmed the scene still fits the sensor. If neither works, a 10–20% working distance change usually closes the gap.
Stock M12 focal lengths jump in discrete steps (2.6mm, 3.3mm, 3.6mm, 6mm, 8mm, 12.5mm, 14.2mm, 16mm, 18mm, 19mm, 21.8mm, 25mm, and up), so a calculated value will often land between them. The steps cluster tightly in the 12–25mm range, where the nearest stock option usually sits within about 10% of the calculated value, and spread wider at the short end. Note that some intermediate steps, including the 18mm and 19mm options, are lower-resolution designs rated for 2MP sensors and below, so check the resolution rating before shortlisting.
Round shorter when the installation has flexibility
A shorter focal length covers a wider scene than required. If you calculated 9mm and the nearest option is 8mm, the 8mm lens captures about 12% more scene width. Crop in software or move the camera slightly closer. This direction gives margin, which is why it is the default when installation geometry is not yet locked.
Round longer when pixel density matters
Rounding from a calculated 9mm up to 12.5mm captures less scene than designed. Only accept this after recalculating the FOV at the actual working distance and confirming nothing clips. Engineers round longer when the feature to detect is small relative to the part and resolution wins the argument over coverage.
Adjust the working distance when possible
If neither rounding direction is acceptable and the mounting allows movement, shift the camera. Moving 50mm farther back with a 12.5mm lens can reproduce the coverage the calculated 9mm lens would have given at the original position. The field of view calculator finds the exact distance for any lens and coverage target.
Whatever the rounding decision, validate with physical test images before locking the design: mount the lens at the planned distance, image a calibration target or the real part, and confirm the features resolve and the scene fits. Test images catch what the math does not: corner vignetting, focus error at the target plane, and distortion in the actual part geometry.
Common focal length selection mistakes
Five errors recur most often in focal length selection. All five are avoidable with the numbers already gathered in the selection sequence above.
Using the nominal sensor format instead of the active area
A "1/2 inch" sensor does not have a 12.7mm active width. The format number is a legacy designation from vidicon tube cameras; the active width of a typical 1/2" CMOS is roughly 6.4mm. Substituting 12.7mm produces a focal length about 2× too long. Use pixel array dimensions and pixel pitch from the sensor datasheet; the sensor compatibility guide covers format naming and image circle matching together.
Ignoring distortion at wide focal lengths
Distortion is not uniform across the field. A single full-field number hides the field dependence: the center of the image is far better corrected than the corners, which carry nearly all of the published value. Applications that measure position near the field edges need either a low-distortion lens or a calibration step; see the lens distortion section of the low-distortion guide.
Ignoring depth of field at long focal lengths
Longer focal lengths have shallower depth of field at the same F-number. A 12.5mm lens at close range with parts varying 10mm in height can leave the near and far parts outside the acceptable focus range. Run the depth of field calculator before finalizing any long focal length.
Optimizing for magnification without resolution math
An image that "looks bigger" in test shots is not evidence of sufficient resolution. A 12.5mm lens on a 1920-pixel-wide 1/2.7" sensor at 500mm covers about 215mm of scene, which is roughly 8.9 pixels per millimeter. A 2mm component body spans about 18 pixels, which is comfortable. A 0.2mm solder bridge spans under 2 pixels, which sits at the Nyquist floor and is unreliable. Calculate ground sampling distance explicitly; the spatial resolution guide shows the full chain from feature size to pixel count.
Assuming mechanical fit means optical fit
A CS-mount lens threads onto a C-mount camera and then fails to reach infinity focus; a C-mount lens needs a 5mm spacer on a CS body; an M12 lens in an adapter may or may not reach focus depending on its mechanical back focal length. Thread engagement proves nothing about flange distance, image circle, or focus travel. Verify the optical stack, not just the thread; the lens mount guide has the compatibility matrix.
Frequently asked questions
How do I calculate focal length from field of view and working distance?
Multiply the active sensor width by the working distance and divide by the required scene width: EFL = (WD × sensor_width) / FOV_width. A 1/2.7" sensor (5.37mm active width) at a 400mm working distance covering a 120mm scene needs (5.37 × 400) / 120 = 17.9mm, so 16mm and 21.8mm are the high-resolution stock candidates (18mm and 19mm options exist as lower-resolution designs for 2MP sensors and below). The EFL calculator runs this directly.
What is effective focal length?
Effective focal length (EFL) is the distance from a lens's rear principal plane to its focal point when the lens is focused at infinity. It sets field of view and magnification. The mm value on a machine vision lens listing (6mm, 12mm, 35mm) is the EFL, not the back focal length and not the flange focal distance.
What steps go into machine vision lens selection?
Machine vision lens selection runs in a fixed order: define the required field of view, measure the working distance, pull active sensor dimensions from the sensor datasheet, set the smallest feature to resolve, calculate focal length with EFL = (WD × sensor_width) / FOV_width, choose the mount family, then verify image circle, distortion, depth of field, and MTF.
What are telephoto machine vision lenses?
Telephoto machine vision lenses are long focal length designs that produce a narrow field of view and higher magnification at a given working distance. Common telephoto M12 options run 12.5mm to 50mm and image small or distant targets (aerial inspection, traffic monitoring, long-standoff barcode reading) at the cost of tighter focus and vibration tolerances.
What happens if my ideal focal length does not exist?
Choose the nearest stock focal length and recompute the field of view. Rounding shorter adds coverage you can crop in software, which is the safer direction. Rounding longer cuts coverage and requires confirming the scene still fits the sensor. Adjusting the working distance by 10–20% often closes the gap exactly; verify any candidate with the field of view calculator before ordering.
How does sensor size change the required focal length?
A larger sensor needs a longer focal length to hold the same field of view at the same working distance. Moving from a 1/3" sensor (about 4.8mm active width) to a 1/1.8" sensor (about 7.18mm) requires roughly 50% more focal length for identical coverage. Always use active dimensions from the sensor datasheet, not the nominal format number.
When should I move from M12 to C-mount?
Move to C-mount when the sensor exceeds what M12 image circles cover (most models top out around 1/1.8", select models reach 1/1.7" to 1/1.6"), when you need an adjustable iris for depth-of-field control, or when field lens swaps must land in focus on the standardized 17.526mm flange. C-mount cam refocusing is also more forgiving at short working distances.
Does a longer focal length always mean better image quality?
No. Longer focal lengths typically lower distortion and raise pixel density on the target, but they narrow the field of view and shrink depth of field. If parts vary in height beyond the focus budget, a longer lens produces softer images than a shorter one. Match focal length to the application geometry, not to a single specification.
Why can't I use simple FOV formulas for fisheye or wide-angle lenses?
Rectilinear formulas assume the lens maps the tangent of the field angle linearly onto the sensor. Fisheye, ultra-wide, and F-theta designs use different projections, so the arctan formula misstates their coverage: a 3.2mm wide-angle specified at 113° computes to about 88° rectilinear on a 1/2.3" sensor. Below roughly 4mm EFL, use the datasheet FOV values instead.
Get a focal length recommendation
Send your working distance, scene size, and sensor part number to our San Diego engineering team and we will run the numbers with you. Orders placed before 12 PM PST ship the same day.