Calculate the bellows extension exposure factor, compensation in f-stops, corrected shutter speed, and effective aperture from extension or magnification.
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Bellows Extension Exposure Factor Formula
When you rack the bellows out past the focal length to focus close, the light spreads over a larger area before it reaches the film, and the image gets dimmer by the square of the extra draw. The basic formula is:
BEF = (BE / FL)^2
Converted to f-stops of compensation:
Stops = 2 * log2(BE / FL)
When camera movements make the extension hard to measure, you can get the same factor from magnification instead:
BEF = (1 + M)^2
For asymmetric lenses, the pupil-corrected model uses measured magnification and pupil magnification. It does not correct an inaccurate lensboard-distance measurement:
BEF = (1 + M/p)^2
Variables:
- BEF is the bellows extension exposure factor, the multiple of the metered exposure you actually need
- BE is total optical image distance from the rear principal plane to the film/sensor; it equals FL at infinity in the thin-lens model. Lensboard distance is only an approximation for suitable near-symmetric lenses, and BE is not added tube length.
- FL is the focal length of the lens, in the same unit as BE
- M is the magnification, the size of the image on the ground glass divided by the size of the subject
- p is the pupil magnification, the exit pupil diameter divided by the entrance pupil diameter (about 1 for the near-symmetric lenses normally used on view cameras)
The default mode of the calculator takes FL and BE and returns the factor, the compensation in exact stops and to the nearest third stop, and the approximate subject distance. The magnification mode uses (1 + M)^2, with M entered directly or computed from a subject measurement and its image on the ground glass, which is the reliable method when you are using swings and tilts. The third mode reverses the geometry: give it a target magnification and it returns the bellows draw you need, BE = FL * (1 + M). In every mode, adding your metered shutter speed returns the corrected time (metered time multiplied by BEF) with the nearest listed standard speed only within the reference list, and adding your metered f-number shows both the effective aperture and the open-up alternative. The advanced option applies the pupil magnification correction.
Compensation by Extension Ratio and Asymmetric Lens Corrections
The first table covers the symmetric-lens approximation. Find the total optical image-distance ratio and read across. One third stop occurs at BE/FL = 2^(1/6), about 1.12246, corresponding to an object distance about 9.1658 focal lengths from the front principal plane. Smaller corrections still exist; the acceptable rounding depends on your exposure requirements. The table gives nearest-third-stop compensation, applied through more time or a wider aperture.
| Extension ratio (BE / FL) | Exposure factor | Exact stops | Set on the lens |
|---|---|---|---|
| 1.0 (infinity) | 1.00 | 0 | 0 |
| 1.1 | 1.21 | +0.28 | +1/3 |
| 1.2 | 1.44 | +0.53 | +2/3 |
| 1.3 | 1.69 | +0.76 | +2/3 |
| 1.4 | 1.96 | +0.97 | +1 |
| 1.5 | 2.25 | +1.17 | +1 1/3 |
| 1.6 | 2.56 | +1.36 | +1 1/3 |
| 1.8 | 3.24 | +1.70 | +1 2/3 |
| 2.0 (1:1) | 4.00 | +2.00 | +2 |
| 2.5 | 6.25 | +2.64 | +2 2/3 |
| 3.0 (2:1) | 9.00 | +3.17 | +3 1/3 |
The second table shows why the simple formula fails on asymmetric designs. At 1:1 magnification the symmetric formula always predicts +2 stops, but the true compensation depends on the pupil magnification. A strong telephoto used for close work at the symmetric setting comes out more than a stop underexposed, while a retrofocus wide angle comes out overexposed.
| Pupil magnification p | Typical design | True factor at 1:1 | True stops | Error if you assume +2 |
|---|---|---|---|---|
| 0.5 | Strong telephoto | 9.00 | +3.17 | 1.17 stops under |
| 0.7 | Moderate telephoto | 5.90 | +2.56 | 0.56 stops under |
| 1.0 | Symmetric view camera lens | 4.00 | +2.00 | None |
| 1.5 | Mild retrofocus wide | 2.78 | +1.47 | 0.53 stops over |
| 2.0 | Strong retrofocus wide | 2.25 | +1.17 | 0.83 stops over |
You can estimate p yourself: look into the front of the lens and judge the diameter of the aperture opening, then look into the rear and do the same. The rear view divided by the front view is the pupil magnification. Manufacturer data sheets sometimes list it directly.
Example Problems
Example 1: You are shooting a still life with a 150 mm lens and the bellows measures 300 mm from lens board to film plane. Your handheld meter reads 1/8 s at f/22.
BEF = (300 / 150)^2 = 4, which is +2 stops. Multiply the time by 4 to get 1/2 s at f/22, or keep 1/8 s and open up two stops to f/11. If you left everything alone, the marked f/22 would behave like f/44 and the negative would come out two stops thin.
Example 2: With a 210 mm lens and heavy front tilt you cannot measure the draw, so you place a ruler in the scene. A 60 mm stretch of the ruler spans 30 mm on the ground glass, and the meter reads 1 s.
M = 30 / 60 = 0.5, so BEF = (1 + 0.5)^2 = 2.25, which is +1.17 stops, or +1 1/3 on the lens. The corrected time is 1 x 2.25 = 2.25 s before any reciprocity correction. For reference, that magnification needs 210 x 1.5 = 315 mm of draw.
Frequently Asked Questions
At what point does bellows extension start to matter?
For a symmetric lens, a third stop occurs at about 12.25 percent extra optical draw, or an object distance about 9.1658 focal lengths from the front principal plane (about 1.925 m for 210 mm). Compensation changes continuously; there is no universal distance at which it becomes zero or a film-latitude rule that makes ignoring it appropriate.
Do I need this correction with a DSLR, mirrorless camera, or TTL metering?
TTL metering can account for extension loss already. Do not add the factor again when metering or the camera/lens effective-aperture readout has compensated. External-meter/manual-flash settings may need correction. At 1:1 the symmetric model predicts two stops; actual lenses may differ, so use lens-specific data and test your workflow.
Why is the measured-extension method wrong for telephoto lenses?
Lensboard-to-film distance need not equal distance from the rear principal plane to the film, and real lens pupil asymmetry also affects exposure. Internal focusing can change the effective focal length and pupils. Measure image-to-subject magnification and use a known pupil ratio rather than assuming the lensboard geometry. Required extension and subject distance remain thin-lens approximations and refer to principal planes.
