PTZ Optics Calculator: Field of View & Zoom

The PTZ Optics Calculator on this page works out the horizontal field of view (in degrees) you get from a PTZ (pan-tilt-zoom) camera, given its sensor width, focal length, and optional digital zoom factor. You enter those three values, and it returns the effective field of view and the equivalent focal length after digital zoom. This is the same math used by PTZ camera installers to pick a lens or decide how much optical vs. digital zoom a scene needs.

Formula

The horizontal field of view (FOV) of a lens is calculated using the arctangent of the sensor width divided by twice the focal length:

FOV = 2 × atan( sensor_width / (2 × focal_length) )

• FOV – horizontal angle of view in degrees.
• sensor_width – the active width of the camera sensor in millimeters (e.g., 6.17 mm for a 1/2.5″ sensor).
• focal_length – the lens focal length in millimeters (e.g., 4.5 mm for a wide-angle setting).

When a digital zoom factor is applied, the effective focal length becomes focal_length × digital_zoom, and the effective FOV is recalculated with that value. The formula assumes a rectilinear lens (no fisheye distortion) and that the sensor width is the full active width.

Worked Example

Using the default values from the calculator: sensor width = 6.17 mm, focal length = 4.5 mm, digital zoom = 1×.

1. Calculate the half-angle: atan(6.17 / (2 × 4.5)) = atan(6.17 / 9) = atan(0.6856) ≈ 34.41°.
2. Double it for the full horizontal FOV: 2 × 34.41° ≈ 68.82°.
3. Effective focal length = 4.5 × 1 = 4.5 mm.
4. Effective FOV = same as the optical FOV because digital zoom is 1×.

The calculator displays: horizontal field of view ≈ 68.82°, effective focal length = 4.5 mm, effective FOV ≈ 68.82°.

How PTZ Cameras Use This Math

PTZ cameras have a motorized lens that can zoom in and out. The optical zoom range is determined by the minimum and maximum focal lengths of the lens. For example, a camera with a 4.5 mm to 135 mm lens has a 30× optical zoom. The horizontal FOV at 4.5 mm is wide (about 69° on a 1/2.5″ sensor), and at 135 mm it is very narrow (about 2.6°).

When the camera reaches its maximum optical zoom, it can apply digital zoom, which crops the image and enlarges it electronically. This reduces the effective FOV further, but at the cost of resolution. The calculator helps you determine the exact angle you can cover at any zoom position, which is critical for planning camera placement and coverage areas.

How to Choose the Right FOV for Your Scene

Selecting the right field of view depends on what you need to monitor:

• Wide area coverage – for a parking lot or lobby, you want a wide FOV (60° to 90°) to see as much as possible with one camera.
• Facial recognition or license plates – you need a narrow FOV (5° to 15°) so that the subject fills a large portion of the frame. This usually requires a long focal length or high zoom.
• Mixed scenes – a PTZ camera can start wide to detect motion, then zoom in to identify a subject. The calculator helps you set preset positions with known FOVs.

As a rule of thumb, doubling the focal length halves the field of view. To cover a specific width at a known distance, you can use the formula: width = 2 × distance × tan(FOV/2). For example, at 20 m distance with a 68.82° FOV, the horizontal coverage is about 27 m.

Common Mistakes and Misconceptions

One common mistake is confusing horizontal FOV with vertical or diagonal FOV. The calculator uses sensor width, but if you use sensor height, you get the vertical FOV. Many camera specs list only diagonal FOV, which is always larger than horizontal. Always check which one you need.

Another mistake is ignoring the effect of digital zoom on resolution. Digital zoom does not increase detail; it crops the image and upscales it, so a 4× digital zoom on a 2 MP sensor gives an effective resolution of about 0.5 MP. For identification, you generally need at least 100 px/m (pixels per meter) at the object distance.

Also, the formula assumes a flat sensor and a rectilinear lens. Fisheye or 360° cameras have a different projection and will not match this calculation. PTZ cameras typically use rectilinear lenses, so the formula is accurate for them.

Limitations of the Formula

The main limitation is that it does not account for lens distortion, which can be significant at the wide end of a zoom lens. Most PTZ lenses have some barrel distortion at wide angles, so the actual FOV may be slightly larger than the calculated value. For most planning purposes, the error is small (a few degrees) and acceptable.

Another limitation is that the sensor width is not always the full chip width. Some cameras use a portion of the sensor for electronic image stabilization or to enable a wider zoom range. If you know the active sensor width (from the spec sheet), use that. If not, the physical sensor width is a good approximation.

Finally, the calculator gives the FOV at a single zoom position. For a PTZ camera, you need to recalculate for each preset. The effective focal length output helps you see how digital zoom multiplies the optical focal length.

Comparing Optical vs. Digital Zoom

Optical zoom uses the lens to magnify the image, preserving full resolution. Digital zoom crops the sensor image and enlarges it, reducing resolution. For example, a 30× optical zoom lens on a 1/2.5″ sensor has a focal length range of 4.5 mm to 135 mm. At 135 mm, the horizontal FOV is about 2.6°. If you apply 2× digital zoom, the effective focal length becomes 270 mm and the FOV drops to about 1.3°, but the image is now only 1/4 the original resolution.

For identification, optical zoom is always preferred. Digital zoom is useful for getting a closer look at a small area when you cannot move the camera physically. The calculator lets you see the trade-off: as you increase digital zoom, the FOV shrinks, but the effective resolution per square meter of scene drops.

Frequently Asked Questions

What is a typical sensor width for a PTZ camera?

Common PTZ cameras use 1/2.8″, 1/2.5″, or 1/3″ sensors. Their approximate widths are 5.57 mm, 6.17 mm, and 4.8 mm respectively. Check the spec sheet for the exact active sensor width, as it can vary slightly between models.

Does the calculator work for vertical FOV?

Yes, if you replace the sensor width with the sensor height. For a 16:9 sensor, the height is roughly 56% of the width. For example, a 6.17 mm wide sensor has a height of about 3.47 mm. Using that in the formula gives the vertical FOV.

Why does my camera spec list a different FOV than the calculator?

Specs often list diagonal FOV, which is always larger than horizontal. Also, the sensor width may be the full chip size, not the active area used for video. If the difference is large, the lens may have distortion. For most PTZ cameras, the calculated horizontal FOV should be within a few degrees of the spec.

How do I calculate the FOV at a specific zoom position?

Find the focal length at that zoom position from the camera’s spec sheet (often given as a range, e.g., 4.5–135 mm). If you know the zoom ratio, you can interpolate. Then plug the focal length into the calculator. Many PTZ cameras report the current focal length in their web interface or API.

What is the minimum FOV needed to read a license plate?

For license plate recognition, you typically need at least 100 px/m at the plate. If your camera has 2 MP resolution (1920×1080), a 1.9° horizontal FOV at 20 m distance gives about 0.66 m width, which is roughly 2900 px/m – plenty. In practice, you also need good lighting and a fast shutter speed.

Can I use this calculator for a fixed lens camera?

Yes, the same formula applies to any rectilinear lens. Just set the digital zoom to 1× and enter the sensor width and focal length of your fixed camera. This is handy for selecting a lens for a new installation.

Related

• Calculator Topics Foundation: Core Math Explained
• Calculator Optimization Techniques
• Calculator Option Pricing: How It Works

in sensor_w | Sensor width | mm | 6.17 | 0
in focal | Focal length | mm | 4.5 | 0
in digital_zoom | Digital zoom factor | x | 1 | 1
out fov | Horizontal field of view | deg | 2 * atand(sensor_w / (2 * focal)) | 2
out eff_focal | Equivalent focal length | mm | focal * digital_zoom | 1
out eff_fov | Effective field of view | deg | 2 * atand(sensor_w / (2 * focal * digital_zoom)) | 2