Calculate Field of View From Focal Length

Calculate a lens’s field of view (FOV) from its focal length and the camera sensor’s width, height, or diagonal. Enter a focal length in millimeters and a sensor dimension in millimeters; the calculator returns the angle of view in degrees for that dimension.

Formula

The rectilinear-lens formula is FOV = 2 × arctan(sensor dimension ÷ (2 × focal length)). The calculator uses 2 * atand(s / (2 * f)), which returns the result in degrees.

• FOV is the angular field of view, in degrees.
• s is the sensor dimension being measured, in millimeters.
• f is the lens’s focal length, in millimeters.

Use the sensor’s width to calculate horizontal FOV, its height for vertical FOV, or its diagonal for diagonal FOV. The values must use the same units. Because both are entered in millimeters here, the ratio is unitless and the angle is unaffected by whether the dimensions were originally measured in millimeters or converted from inches.

Worked Example

Using the calculator’s defaults, the focal length is 50 mm and the sensor dimension is 36 mm. This is a common full-frame sensor width, so the result is horizontal FOV:

1. Divide the sensor dimension by twice the focal length: 36 ÷ (2 × 50) = 36 ÷ 100 = 0.36.
2. Take the inverse tangent in degrees: arctan(0.36) ≈ 19.8°.
3. Double it: 2 × 19.8° ≈ 39.6°.

So a 50 mm lens on a sensor 36 mm wide covers approximately 39.6° horizontally. The calculator rounds to one decimal place.

How Focal Length Determines FOV

Focal length describes the lens’s optical geometry; it does not by itself determine the scene angle recorded by a camera. The sensor size matters too. At a fixed sensor size, a longer focal length gives a narrower FOV, while a shorter focal length gives a wider one. At a fixed focal length, a larger sensor captures a wider angle than a smaller sensor.

The formula comes from the geometry of the image projected onto the sensor. In a simplified rectilinear model, the sensor dimension and focal length form the sides of a right triangle. The half-angle is the inverse tangent of half the sensor dimension divided by the focal length. Doubling that half-angle gives the full FOV.

This is an angular measure, not the width of a scene at a particular distance. To estimate the width covered at a flat subject plane, use the distance to that plane as well. For a centered camera aimed perpendicular to the plane, the approximate width is 2 × distance × tan(FOV ÷ 2). Keep the distance and width in the same units. Perspective and depth mean that objects at other distances will occupy different amounts of the image.

Choose the Sensor Dimension

“Field of view” can refer to three different angles, so match the measurement to the question you are asking:

• Horizontal FOV: use the sensor’s active width. This is often the most useful measure for framing landscapes, architecture, or a wide room.
• Vertical FOV: use the active sensor height. This helps determine how much vertical space appears in a shot.
• Diagonal FOV: use the sensor’s diagonal, calculated as √(width² + height²). Camera and lens specifications sometimes report this angle.

For example, a sensor measuring 36 × 24 mm has a diagonal of √(36² + 24²) ≈ 43.3 mm. With a 50 mm lens, the diagonal FOV is about 46.8°, while the horizontal FOV is about 39.6°. Those are different answers for the same lens because they describe different directions across the sensor.

Crop Factor and Equivalent Focal Length

Crop factor is a comparison between a camera’s sensor size and a reference format, commonly 35 mm full frame. It is not an extra multiplier needed in the FOV formula: use the actual sensor dimension and the lens’s actual focal length to calculate the angle directly.

Equivalent focal length is a shorthand for comparing framing across formats. A 50 mm lens on a smaller sensor has a narrower FOV than a 50 mm lens on a full-frame sensor. Multiplying the lens’s actual focal length by the camera’s crop factor gives an approximate full-frame-equivalent focal length for comparing angle of view. It does not change the lens’s physical focal length or its aperture.

Check the crop factor convention before using it: manufacturers or references may define it using sensor diagonal, and formats with different aspect ratios can have different horizontal and vertical comparisons. For a precise FOV, the sensor’s actual active width or height is more direct than an equivalent-focal-length estimate.

Limits and Common Calculation Mistakes

This formula is a good approximation for ordinary rectilinear lenses, which aim to keep straight scene lines straight. Fisheye lenses use a different projection, and their FOV is not generally described accurately by the rectilinear formula. Lens distortion, focus breathing, stabilization, and in-camera cropping can also make the recorded angle differ from a calculation based on nominal focal length and sensor dimensions.

• Using focal length alone: you also need the relevant sensor dimension.
• Mixing dimensions: convert both measurements to the same unit before calculating. For reference, 1 inch = 25.4 mm.
• Using the wrong sensor measurement: width, height, and diagonal produce different FOVs.
• Confusing angle with coverage: degrees describe an angle; the scene width at a chosen distance requires a separate calculation.
• Rounding too early: keep full precision through the calculation, then round the final angle to a sensible number of decimal places.

Frequently Asked Questions

Can I calculate FOV from focal length alone?
No. You also need the sensor width, height, or diagonal, depending on which direction’s FOV you want. The same lens gives different angles on different sensor sizes.

What is the FOV of a 50 mm lens?
There is no single answer without a sensor size and a direction. On a sensor 36 mm wide, a 50 mm lens has a horizontal FOV of about 39.6°. A smaller sensor gives a narrower horizontal angle.

Does crop factor change focal length?
No. Crop factor describes how a smaller sensor frames a scene relative to a reference format. The lens’s actual focal length remains the same; the resulting FOV changes because the sensor dimensions differ.

How do I calculate FOV in degrees?
Use FOV = 2 × arctan(sensor dimension ÷ (2 × focal length)), with inverse tangent evaluated in degrees. Make sure the sensor dimension and focal length use matching units.

Is FOV the same as angle of view?
In photography, the terms are often used for the same angular coverage. Specifications may mean horizontal, vertical, or diagonal angle of view, so check which sensor dimension the stated figure uses.

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in f | Focal length | mm | 50 | 0
in s | Sensor dimension | mm | 36 | 0
out fov | Field of view | degrees | 2 * atand(s / (2 * f)) | 1