Camera Lens Focal Length and Field of View Reference

The short answer

Focal length and field of view move in opposite directions. A shorter focal length produces a wider angle of view; a longer focal length produces a narrower, more magnified view that reaches farther. On the 1/2.8-inch sensor common in modern IP cameras (5.12 mm wide), a 2.8 mm lens sees roughly 85 degrees horizontally, a 4 mm lens about 65 degrees, a 6 mm lens about 46 degrees, and a 12 mm lens about 24 degrees. The exact relationship is fixed optics, not marketing.

The governing equation is horizontal angle of view = 2 x arctan(sensor width / (2 x focal length)). Because sensor width is fixed for a given camera, focal length is the only variable you control, and the same focal length yields a different angle on a different sensor size. Every degree of extra width you gain at the wide end costs reach and pixel density at distance. A wide 2.8 mm lens is right for covering a room or a driveway apron; a narrow 12 mm lens is right for reading a gate, a register, or a license plate at range. Choose focal length by the job the camera must do, not by which number sounds larger.

Choosing Focal Length by Coverage Goal

Pick focal length by asking two questions: how wide an area must the camera see, and at what distance must a subject be identifiable? Wide coverage and long-range identification are opposing goals on a single fixed lens, because the sensor collects a fixed number of pixels and spreads them across whatever angle the lens admits. A 2.8 mm lens spreading roughly 85 degrees across a 1920-pixel-wide sensor puts far fewer pixels on a face 40 feet away than an 8 mm lens covering about 35 degrees at the same distance.

A useful design anchor is pixels-per-foot (PPF), sometimes stated as pixels-per-meter. Common industry rules of thumb: about 25 PPF for detection (something is there), about 40-50 PPF for recognition (a known person), and roughly 80-100+ PPF for identification (a stranger, or a readable plate). You compute PPF as horizontal resolution divided by the scene width the lens covers at the target distance. Widen the lens and PPF drops; the same camera can detect across a whole parking lot yet fail to identify anyone in it.

When one lens cannot serve both goals, the standard answer is more cameras, each with a purpose-matched focal length, rather than one wide camera asked to do everything. Overview plus a tighter choke-point camera is a common pairing.

• Wider area, shorter distance -> shorter focal length (2.8-4 mm); ~85-65 deg horizontal on a 1/2.8-inch sensor.
• Longer distance, narrower target -> longer focal length (8-12 mm); ~35-24 deg horizontal on the same sensor.
• Detection ~25 PPF, recognition ~40-50 PPF, identification ~80-100+ PPF are widely used design targets, not a legal standard.
• PPF = horizontal pixel count / scene width covered at the target distance; wider lens = lower PPF at any given range.
• One fixed lens rarely serves overview and identification at once; pair a wide overview camera with a tighter choke-point camera.
• Match focal length to the task (door, aisle, gate, driveway, plate), not to the largest coverage number.

The Angle-of-View Formula

Angle of view is set by two things only: the size of the image sensor and the focal length of the lens. The relationship is trigonometric. For the horizontal angle: AoV_horizontal = 2 x arctan(sensor_width / (2 x focal_length)). The vertical and diagonal angles use the same formula with the sensor's height or diagonal substituted for its width. Because the three dimensions differ, a single lens has three different angle-of-view numbers, and vendors sometimes quote the largest (diagonal) to make coverage sound wider.

The formula assumes a rectilinear lens focused near infinity; at very close focus the effective angle narrows slightly. Real security lenses also add barrel distortion at the wide end, which stretches the extreme edges and makes the marketed angle a rough figure rather than a lab-exact one. Manufacturer spec sheets typically round, and two 2.8 mm lenses from different makers can differ several degrees because their glass and true sensor coverage differ.

The critical consequence: quoted angle of view is meaningless without the sensor size. A 4 mm lens is about 65 degrees horizontal on a 1/2.8-inch sensor but about 62 degrees on a smaller 1/3-inch sensor and about 77 degrees on a larger 1/2-inch sensor. Always read focal length and sensor format together.

• Horizontal AoV = 2 x arctan(sensor_width / (2 x focal_length)); swap in height or diagonal for the other two angles.
• Only two inputs matter: physical sensor width and focal length; resolution (2 MP vs 8 MP) does NOT change the angle.
• 1/2.8-inch 16:9 sensor is about 5.12 mm wide x 2.88 mm tall, ~5.87 mm diagonal (a common modern IP format).
• Diagonal angle is always the largest of the three; treat a single quoted 'FOV' as diagonal unless labeled otherwise.
• Barrel distortion and near-focus reduce real-world accuracy, so treat spec-sheet angles as approximate (+/- a few degrees).
• The same focal length gives a wider angle on a larger sensor; never compare focal lengths across different sensor sizes.

Real FOV Values for Common Lenses

The tables below are computed directly from AoV = 2 x arctan(w / (2f)) for the two most common CCTV sensor widths. On a 1/2.8-inch sensor (5.12 mm wide, the typical 16:9 IP format) the horizontal angles are: 2.8 mm ~ 85 deg, 3.6 mm ~ 71 deg, 4 mm ~ 65 deg, 6 mm ~ 46 deg, 8 mm ~ 36 deg, and 12 mm ~ 24 deg. For a 1/2.8-inch sensor the full horizontal/vertical/diagonal set for a 2.8 mm lens is roughly 85/54/93 degrees, and for a 12 mm lens roughly 24/14/28 degrees.

On a smaller 1/3-inch sensor (4.8 mm wide) the same lenses run a little narrower: 2.8 mm ~ 81 deg, 3.6 mm ~ 67 deg, 4 mm ~ 62 deg, 6 mm ~ 44 deg, 8 mm ~ 33 deg, 12 mm ~ 23 deg. On a larger 1/2-inch sensor (6.4 mm wide) they run wider: 2.8 mm ~ 98 deg, 4 mm ~ 77 deg, 6 mm ~ 56 deg, 12 mm ~ 30 deg. These are the horizontal values, which are the ones that matter most for aisle, hallway, and perimeter coverage.

Use these as engineering starting points. Verify against the specific model's published spec sheet, because true sensor coverage and lens design shift the real figure by a few degrees. Ultra-wide fisheye and panomorph lenses (often 1.1-1.6 mm) exceed 180 degrees and do not follow the simple rectilinear formula.

• 1/2.8-inch (5.12 mm) horizontal: 2.8mm~85, 3.6mm~71, 4mm~65, 6mm~46, 8mm~36, 12mm~24 degrees.
• 1/3-inch (4.8 mm) horizontal: 2.8mm~81, 3.6mm~67, 4mm~62, 6mm~44, 8mm~33, 12mm~23 degrees.
• 1/2-inch (6.4 mm) horizontal: 2.8mm~98, 3.6mm~83, 4mm~77, 6mm~56, 8mm~44, 12mm~30 degrees.
• 1/2.8-inch full H/V/D: 2.8mm ~85/54/93, 4mm ~65/40/73, 6mm ~46/27/52, 12mm ~24/14/28 degrees.
• Doubling focal length does NOT halve the angle; the arctangent makes the change nonlinear, largest near the wide end.
• Fisheye/panomorph lenses (~1.1-1.6 mm) reach 180+ degrees and require dewarping; the rectilinear formula does not apply.

Fixed, Varifocal, and Motorized Lenses

A fixed (prime) lens has a single focal length set at the factory, such as a 2.8 mm or 4 mm bullet or dome. It is the lowest-cost, most compact option and holds focus permanently, but you commit to one angle of view before installation. If the coverage is wrong, the fix is a hardware swap or physically remounting the camera. Fixed lenses suit well-defined spots: a single doorway, a stairwell, a small room.

A varifocal lens covers a focal-length range, commonly 2.8-12 mm or 2.7-13.5 mm, adjusted by hand with a zoom-and-focus ring on the lens. It lets the installer dial the exact angle on site and refocus, which is valuable when the final view is uncertain or the target distance is long. The trade-off is a bulkier housing, higher cost, and manual adjustment that requires physical access to the camera.

A motorized-zoom lens is a varifocal whose zoom and focus are driven by small motors, adjustable remotely from the recorder or app, often with autofocus. It gives the same optical range without a ladder, useful on high or hard-to-reach mounts. Note that optical motorized zoom is genuine focal-length change and preserves resolution; digital zoom merely crops pixels and degrades the image and should not be confused with it.

• Fixed/prime: one focal length (e.g., 2.8 or 4 mm), lowest cost, smallest housing, no post-install angle change.
• Varifocal: a manual range such as 2.8-12 mm, set by hand on site, ideal when the required angle is uncertain.
• Motorized zoom: varifocal driven by motors, adjusted remotely from the NVR/app, often with autofocus; best for high mounts.
• Optical zoom changes true focal length and keeps full resolution; digital zoom only crops and loses detail.
• Varifocal and motorized lenses cost more, run larger, and slightly reduce low-light throughput versus a matched prime.
• Reserve varifocal/motorized for long-range or uncertain scenes; use fixed lenses for defined, unchanging views.

Trading Width for Distance and Detail

The core trade is fixed by geometry: a wider angle spreads the sensor's pixels over a larger scene, so each object occupies fewer pixels; a narrower angle concentrates the same pixels on a smaller scene, so each object occupies more. This is why a 2.8 mm camera gives a sweeping overview but cannot read a face across a lot, while a 12 mm camera reads the face but sees only a narrow slice of the scene.

Scene width at a distance follows from the angle: scene_width = 2 x distance x tan(AoV_horizontal / 2). A 2.8 mm lens (~85 deg) covers about 73 feet of width at 40 feet of range, while an 8 mm lens (~36 deg) covers about 26 feet at the same range. Divide horizontal resolution by that width for PPF: a 1920-wide (2 MP) image at 40 feet yields about 26 PPF on the 2.8 mm and about 74 PPF on the 8 mm, which is the difference between merely detecting motion and recognizing a person.

Higher-resolution sensors raise PPF at any angle, so an 8 MP (3840-wide) camera can hold identification-grade detail over a wider view than a 2 MP camera at the same focal length, though larger sensors and lenses and more storage are the cost.

• Scene width = 2 x distance x tan(horizontal_AoV / 2); it grows linearly with distance for a fixed lens.
• 2.8 mm (~85 deg) covers ~73 ft wide at 40 ft; 8 mm (~36 deg) covers ~26 ft wide at 40 ft.
• PPF = horizontal resolution / scene width; a 2 MP feed at 40 ft is ~26 PPF on 2.8 mm vs ~74 PPF on 8 mm.
• Detail is finite: a wide lens trades identification range for coverage; a narrow lens trades coverage for reach.
• Raising resolution (2 MP -> 8 MP roughly doubles horizontal pixels) lifts PPF at any focal length, at a storage cost.
• For license plates, narrow angles (8-12 mm or long motorized zoom) plus adequate PPF and shutter control are typically required.

Frequently asked questions