# How to calculate the change of angle of view when to crop factor of the DSLR is known when using ful

Discussion in 'Digital Photography' started by Mulperi, Sep 17, 2006.

1. ### MulperiGuest

For example the angle of view is 100 degrees in lens x with full frame
camera and the crop factor is 1.5 in smaller frame camera . So what would be
the final angle of view with that smaller frame camera with that lens x.

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Juha Heinonen
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Mulperi, Sep 17, 2006

2. ### Ben BrugmanGuest

One can calculate the angle, but it is far more
easier to calculate the field of view. (And from there calculate the angle).

All measurements are metric.

Focal length = f (in mm).
Distance = D (in meters)
Sensor Width = w (in mm).

Field of view = D*w/f

Example
D = 100 meters
f = 45 mm
w = 24 mm (Aps size sensor).

Field of view (at 100) meters = 100 meters * 24 mm / 45 mm
Field of view (at 100) meters = 100 * 24 / 45 * meters * mm / mm
Field of view (at 100) meters = 2400 / 45 * meters
Field of view (at 100) meters = 53.33 meters

35 mm film is about 24mm * 36 mm and is diagonal about 43 mm.
aps size sensor (1.5 factor) is about 16mm * 24mm and it's diagonal is about
29 mm

The angle is Atan(FieldOfView/(2*D))*2
Or the angle is Atan(w/(2*f))*2

You can use mm for the focal length and the sensor size and any
other length for the Distance and Field of View. (For example yards or feet,
as
long as Distance and Field of View use the same).
Field of view (at 100) feet = 100 feet * 24 mm / 45 mm

The angle does not behave lineair, Field of view, distance, sensor size etc.
do behave lineair.
*) At very short distances be the field of view should not be used. (think
macro).

Good luck,
Ben Brugman

Ben Brugman, Sep 17, 2006

3. ### Don Stauffer in MinnesotaGuest

For telephoto focal lengths, merely divide the original field angle by
the crop factor. This will work reasonably well except for wide angle,
where you do need to use the trig functions (tangent). So for the wide
angle you must actually take focal length and half of format size (36
mm/2 =18mm) divided by crop factor. Then take ratio of that format
size and lens fl, take arctangent of ratio.

Don Stauffer in Minnesota, Sep 17, 2006
4. ### Dave MartindaleGuest

The tangent trig function converts angles into relative distances
perpendicular to the optical axis (i.e. in either the subject or image
plane). But you have to work with the angle from the axis to the edge,
which is half the angle from edge to edge.

1. the half-angle of 100 degrees is 50 degrees

2. relative size on the full-frame sensor (really the ratio of half
sensor width to lens focal length is tan(50 deg) = 1.192.

3. portion of the image that falls on the smaller sensor:
1.192 / 1.5 = 0.795

4. half-angle at the edge of the smaller sensor: arctan(0.795) = 38.5 deg

5. full angle: 2 * 38.5 = 77 degrees

For the general case:

small_sensor_FOV = 2 * arctan(tan(FF_FOV / 2) / crop_factor)

Dave

Dave Martindale, Sep 18, 2006