Kenneth Morris Lee

Formulas for Bellows Extension and Compensation

How Close Can We Get ?

Given a 200mm lens and 315mm of bellows draw, how close can we get ?

**1/F = 1/D + 1/B**

where F = focal length, D = distance, B = Bellows Draw

F = 200mm, B = 315mm

1/200 = 1/D + 1/315

1/D = 1/200 - 1/315

1/D = 0.005 - 0.003174603174603

1/D = 0.001825396825397

Distance = 547mm

How Much Bellows Extension Do We Need ?

Given a 360mm lens and 1500mm distance how much bellows draw is required ?

**1/F = 1/D + 1/B**

where F = focal length, D = distance, B = Bellows Draw

F = 360mm, D = 1500mm

1/360 = 1/1500 + 1/B

1/B = 1/360 - 1/1500

1/B = 0.0027 - 0.0007

1/B = 0.002

Bellows Draw = 500mm

How Much Bellows Extension Do We Need ?

Given a 210mm lens where the desired magnification is 1:3, how much bellows extension is required ?

**M = (B-F) / F**

where M = magnification ratio, B = bellows extension, F = focal length

M = 1/3, F = 210mm

1/3 = (B-210) / 210

1/3 * 210 = B - 210

70 = B - 210

Bellows Extension = 280mm

How Much Magnification Can We Get ?

Given a 200mm lens and 320mm bellows draw, how much magnification can we get ?

**M = (B-F) / F**

where M = magnification ratio, B = bellows extension, F = focal length

M = (320-200) / 200

M = 120/200

Magnification = 60%

Given a 150mm lens and 320mm of bellows draw, how much magnification can we get ?

M = (320-150)/150

M = 170/150

Magnification = 1.133 : 1 or 113%

How Much Magnification Do We Get ?

Given a 300mm lens and a distance of 10 feet, how much magnification do we get ?

**M = F / (D-F)**

where M = magnification ratio, D = distance, F = focal length

F = 300mm, D = 10ft = 3048mm

M = 300 / (3048-300)

M= 300 / 2748

= 10.9 %

Given a 450mm lens and a distance of 15 feet, how much magnification do we get ?

F = 450mm, D = 15ft = 4572mm

M = 450 / (4572-450)

M= 450 / 4122

= 10.9 %

How Much More Exposure Time Is Required ?

Given a 300mm lens, 450mm of bellows draw and a 2-second exposure, how long should the exposure be ?

**Compensation = (B / F) squared**

where B = Bellows extension and F = Focal length

Compensation = (450/300) ^2

Compensation = 1.5 ^2 = 2.25

Adjusted exposure time is 2 x 2.25 seconds, or 4.5 seconds

How Many More f/stops are Required ?

Given a 150mm lens, 300mm of bellows draw and a 2-second exposure, by how many f/stops should we adjust the exposure ?

**Compensation = (((B / F)^2) log2) stops**

where B = Bellows extension and F = Focal length

Compensation = ((300 / 150)^2) log2 stops

Compensation = (2^2) log2 stops

Compensation = 4 log2 stops

Compensation = 2 stops

We adjust exposure by an additional 2 f/stops

Rules of Thumb

For the purposes of this article, distance D is measured from the lens board.

At **1:1** magnification, bellows draw = 2 x focal length and exposure compensation is 4x or **2 f/stops**.

At **0.75X** magnification, bellows draw = 1.75 x focal length and exposure compensation is 3x or **1.6 f/stop**.

At **0.4X** magnification, bellows draw = 1.4 x focal length and exposure compensation is 2x or **1 f/stop**.

Vintage telephone at 1:1 magnification, 150mm lens on 4x5 film.

Exposure increased from 1 second to 4 seconds due to bellows extension of 300mm.

Exposure increased from 1 second to 4 seconds due to bellows extension of 300mm.