You don't need to know the size of the aperture or the number of pixels. To calculate the field of view you need to know the focal length and the size of the sensor in length, not pixels. If you have the focal length and the size of the sensor in the same units (e.g. millimeters) then the FOV is
FOV = sensor size / focal length.
The answer is in radians. Multiply by 57.3 degrees per radian to convert to degrees.
FOV in degrees = 57.3 * sensor size / focal length.
For example, if your sensor is 10mm and your focal length is 600 then your FOV is 57.3 * 10 / 600 = 0.955°.