Calculations with Optical Instruments


Calculation of Zoom Factor, Minimal and Maximal Focal Length

The normal focal length of an objective lens is 36-60 mm. Lenses with smaller values are called wide-angle lens, such with larger telephoto lens. Those that cover both areas are called zoom lens. The zoom factor is the quotient of maximal and minimal focal length. This is the number, when you read something like 3.6x optical zoom at a camera. Enter two values at zoom factor, minimal and maximal focal length, the third will be calculated.

Zoom factor:
Minimal focal length:mm
Maximal focal length:mm

Zoom factor = maximal focal length / minimal focal length

Convert Angle of View and Focal Length

The angle of view indicates the image size in degrees, when the objective is set to ∞. For a shorter distance (closer object), the angle becomes smaller.
The angle of view of course depends from the focal length. At a small focal length, the angle is large (wide-angle), at a large focal length, the angle is small (tele). But also the size of the sensor or the film format is important. Standard film has a width of 35 mm, the APS-C-sensor of a digital camera has a width of 23 mm. The larger the sensor or film width, the wider is the angle. The sensor dimensions should be available at the manufacturer instructions. Please enter two values at a sensor dimension, focal length and at an angle of view.

Sensor width:mm
Sensor height:mm
Sensor diagonal:mm
Focal length:mm
Horizontal angle of view:°
Vertical angle of view:°
Diagonal angle of view:°

α = 2 * arctan[l/(2f)]
l is the sensor width, height or diagonal, f is the focal length α is the according angle.

Crop Factor, Standard Format, Sensor Size

Depending on sensor size, photos with the same focal length have different angular sizes. To compare the image sizes, the focal length is often converted to 35 mm format equivalent. The ratio is called crop factor.
Please enter two of the first three values and optionally one focal length. Or enter the two focal lengths and one of the first three values.

Crop factor:
Sensor size:mm
Standard format:mm
Focal length:mm
Focal length standard format:mm

Crop-factor = standard format / sensor size

Crop-factor = focal length standard format / focal length


The magnification, in comparison to what the naked eye sees, results from focal length and crop factor. In 35 mm format, which actually is 36 mm * 24 mm, a focal length of about 43.3 mm (exactly square root of 1872) refers to a magnification of 1, which means no magnification. 86.5 mm focal length results in a double magnification. Please enter two values, the third will be calculated.

Focal length:mm
Crop factor:
Magnification: times

Magnification = crop factor * focal length / √1872

For zoomed photos, see zoom gallery

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