Stats for a full-frame 35mm camera, taken from lens manufacturers' spec sheets.

• 50mm = 46 degrees
• 70mm = 34 degrees
• 135mm = 18 degrees
• 200mm = 12 degrees

Now, those are presumably across a circular diameter (ie. the diagonal of a frame).

Working in landscape orientation

For a 3m wide backdrop, your hypotenuse in 3:2 aspect ratio is sqrt(13), or 3.6m.

Now use some trig to convert those angles into 3.6m.

For a 50mm lens

• theta = 23 degrees
• Opposite = 180cm

tan(23 degrees) = 180 / working distance

0.42 = 180 / working distance

1/0.42 = working distance / 180

180/0.42 = working distance

working distance = 428cm?

4.3 metres

My mathematical gut feeling says this is wrong... but it seems about right when I hold the 50mm up to my eye.

70mm lens

theta = 17 degrees

working distance = 180 / tan(17)
                 = 180 / 0.306
                 = 588cm

5.9 metres

135mm lens

theta = 9 degrees

working distance = 180 / tan(9)
                 = 180 / 0.158
                 = 1136cm

11.3 metres

200mm lens

theta = 6 degrees

working distance = 180 / tan(6)
                 = 180 / 0.105
                 = 1712cm

17.1 metres

Working in portrait orientation

For a 3m wide backdrop, your hypotenuse in 2:3 aspect ratio is sqrt(29.25), or 5.4m.

Now use some trig to convert those angles into 5.4m.

For a 50mm lens

theta = 23 degrees

working distance = 270 / tan(23)
                 = 270 / 0.424
                 = 636cm

6.3 metres

70mm lens

theta = 17 degrees

working distance = 270 / tan(17)
                 = 270 / 0.306
                 = 883cm

8.8 metres

135mm lens

theta = 9 degrees

working distance = 270 / tan(9)
                 = 270 / 0.158
                 = 1704cm

17 metres

200mm lens

theta = 6 degrees

working distance = 270 / tan(6)
                 = 270 / 0.105
                 = 2568cm

25.6 metres

Portrait mode with 2m fixed height subject

• 2m high
• 1.33m wide

• 2.4m diagonal

• 1.2m for right-angle triangle (120cm)

50mm lens

• theta = 23 degrees
• working distance = 120 / tan(23)

• 2.82 metres

70mm lens

Working distance = 120 / 0.306 = 3.92 metres

135mm lens

Working distance = 120 / 0.158 = 7.59 metres

200mm lens

Working distance = 120 / 0.105 = 11.4 metres