Machine Vision Lens Calculator: Focal Length From Sensor and FOV

A machine vision lens calculator does not pick the lens. It estimates a focal length from sensor width, working distance, and field width. The misconception is that the number it prints is a purchase. It is a thin-lens first pass. Image circle, principal-plane offset, distortion, and mount still have to survive a drawing. Treat the calculator as a filter, then open a family.

This is the how-to behind the five-input method in the machine vision lens selection guide. Do the arithmetic, then pick a family: FA C-mount, M12, telecentric, or line-scan. The calculator never names a SKU.

What the Calculator Is Not

Online calculators assume a thin lens, a centred object, and a sensor width you typed correctly. They do not know principal-plane offset, distortion, relative illumination, or whether you typed 2/3″ when the chip is 1.1″. If the first prototype is soft or cropped, the calculator was not “wrong” — it was unfinished.

The Thin-Lens Formula, With Units

f ≈ (W_sensor × WD) / (W_field + W_sensor)

All lengths in millimetres. W_sensor is the active width from the datasheet. WD is object to front of lens. W_field is the object width you must cover, plus placement margin. Horizontal and vertical can be run separately; the longer demand wins. Do not use diagonal unless the object is circular and you mean it.

Worked Example: 2/3 in at 200 mm

2/3″ active 8.8 mm × 6.6 mm (11.000 mm diagonal). WD 200 mm. Object 40 mm wide, use 44 mm with margin. f ≈ (8.8 × 200) / (44 + 8.8) = 1760 / 52.8 ≈ 33.3 mm. Catalog neighbours: 25 mm (more margin, fewer pixels on the part) and 35 mm (tighter field, more sampling). If the smallest feature is 0.1 mm on a 5 MP 2/3″ chip, 35 mm is the better first sample. If the nest walks a few millimetres, 25 mm is safer.

Check Image Circle After Focal Length

The calculator can output 35 mm for a 1.1″ camera and still be optically illegal if the barrel is a 2/3″ design. Diagonal for 1.1″ class is around 17.5 mm. 2/3″ is 11.000 mm. Run the circle check as a second line in the same spreadsheet: circle ≥ diagonal, or the corners go dark no matter how perfect f is.

The Mount the Calculator Ignores

C-mount is 17.526 mm. CS is 5 mm closer. M12×0.5 has no flange. Line-scan M72 is a different throat. A 35 mm estimate on the wrong mount is a mechanical dead end. Write the mount before you write the PO.

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When to Stop Calculating FA Glass

If ΔWD/WD already exceeds the size tolerance, a better f will not save you. Telecentric magnification is the next tool, not a 50 mm instead of a 35 mm. If the sensor is a 41 mm 8K line, stop using area-scan width in the formula and compute line length × pitch. If the camera is a board module, the answer is an M12 EFL, not a C-mount catalog value through an adapter.

From Estimated f to a Named SKU

Round to the nearest catalog EFL, then read the datasheet working distance and circle. The FA C-mount family is the usual landing for discrete industrial bodies. Distortion below 0.05% with 10K+ batch consistency is the FA production claim — it is not in the calculator. Macro SKUs (FA3505W–FA7520W) apply when the conjugate is close and a standard 25–50 mm cell cannot reach it.

What We Check When You Send the Numbers

Send W_sensor, WD, W_field, format, and mount. Hangzhou runs the same thin-lens pass, then circle, then family. First-pass feasibility is 48 hours. Prototype to mass production is 60 working days. Repeat orders are 30 days. Payment 50/50. ISO 9001 certified 2024.

Illustrative numbers: 8.8 mm sensor, 200 mm WD, 44 mm field → 33.3 mm → sample 25 mm and 35 mm FA, 2/3″ circle, C-mount 17.526 mm. If the email adds “1.1″ IMX,” the circle check fails and the estimate is rebuilt on 14 mm-class width, not 8.8 mm.

Conclusion

The calculator is a first pass: f from sensor width, working distance, and field. Then circle, then mount, then family. 33.3 mm is not a SKU. 25 mm or 35 mm on a 2/3″ C-mount with a distortion report is a sample plan.

Key takeaways

• f ≈ (W_sensor × WD) / (W_field + W_sensor). Active width only.
• 2/3″, 200 mm, 44 mm field → 33.3 mm. Neighbours 25 mm and 35 mm.
• Circle must cover 11.000 mm on 2/3″. A 1.1″ chip fails that glass.
• C-mount 17.526 mm. M12 has no flange. Telecentric when Z changes size.

If you already have the three lengths and the mount, send them. Hangzhou will not pretend the calculator is a purchase order. You will get a named FA SKU or a reason to change family. First-pass feasibility is 48 hours.

Frequently Asked Questions