Image Circle & Camera Movement Calculator
Tell us the circle your lens throws and the size of your film or sensor, and we work out how far you can raise, drop or slide the frame before a corner falls off the edge and goes dark. It also shows how much extra you get when you focus close. Everything runs in your browser, nothing uploaded.
Looking at the film from behind the lens
What shift costs you in rise
Every pair on the curve puts a frame corner exactly on the edge of the circle. Anything under the curve is safe, anything over it goes dark in the corner.
Learn more: image circle against camera movements
One inequality decides everything
Wikipedia defines the image circle as the cross section of the cone of light a lens throws onto the image plane, and notes that a lens for a camera with movements has to project a circle larger than the image format. The question this page answers is how much larger, in millimetres of actual rise and shift.
Start with the frame centred on the lens axis. It is w wide and h tall, so its corners each sit a distance of half the diagonal from the axis. Rise of v and shift of s slide the frame so its worst corner lands at (w/2 + s, h/2 + v), and that corner has to stay inside the circle of radius R.
Rearranged for rise, that is the whole calculation: v = sqrt(R squared minus (w/2 + s) squared) minus h/2. It lives in lib/coverage.js, and swapping w for h gives the shift version.
Why spare coverage goes less far than it looks
The 4x5 image area is 120 by 96 mm, a diagonal of 153.7 mm, which is exactly the figure Michael K. Davis's 4x5 coverage table on the Large Format Page uses. A Schneider APO-Symmar 150mm publishes a 220 mm circle there, so there is 66.3 mm of coverage beyond the diagonal.
That 66.3 mm does not become 66.3 mm of rise. Feed R = 110, w = 120, h = 96 into the formula with no shift and you get 44.2 mm. The reason is that rise pushes the top corners up and away at a slant, so they close on the edge of the circle faster than a figure measured along the diagonal suggests.
The same table publishes a max rise column for every lens, which makes this app checkable rather than trusted. Its values match the formula above to the published hundredth of a millimetre: 44.20 mm for that APO-Symmar, 9.35 mm for the Super-Angulon XL 47mm on its 166 mm circle, 142.79 mm for the Nikkor-SW 150mm on its 400 mm circle.
Diagonal movements are worse again, because both terms grow at once. Hold rise and shift equal on that APO-Symmar and the limit is 23.5 mm each, against 44.2 mm of rise or 39.0 mm of shift on its own. Half the budget disappears into the corner.
Focusing close buys coverage back
A published image circle is quoted at infinity focus and usually at f/22. The circle is not a fixed object, though. B&H's large format primer puts it plainly: when a nearby object is focused on, the lens moves further from the film plane and the image circle grows.
The angle of coverage is what stays fixed, which is why makers publish that instead. This page derives it as 2 x arctan(R / f), giving 72.5 degrees for the 150mm on its 220 mm circle and 121.0 degrees for the Super-Angulon XL 47mm. Those sit on the 72 and 120 degrees the same table publishes.
Because the angle is fixed, the circle scales with how far the lens sits from the film, and that distance is f x (1 + M) for magnification M. So the circle scales by (1 + M) too. The calculation is in lib/focus.js.
At 1:4 reproduction the APO-Symmar's 220 mm circle lands as 275 mm and rise on 4x5 landscape goes from 44.2 mm to 75.7 mm. At 1:1 the circle doubles to 440 mm. This is why a lens that looks tight for architecture can be generous for tabletop work, and worth knowing before you buy a wider one.
What the number does not cover
This page is pure geometry on the published circle, so it tells you where the corners go dark and nothing else. A published circle is a circle of acceptable definition, not of even illumination, and corners near the edge still dim from natural falloff, which is what centre filters exist to even out.
Tilt and swing are a different question again, since they turn the circle's relationship to the film rather than sliding it. If you need the angle to put a receding plane in focus, our tilt angle calculator handles that side, and this page tells you whether the movements you then pile on still fit.
Camera hardware is the other limit. A lens with 60 mm of rise on paper is no use on a field camera whose front standard stops at 30 mm, so treat the figures here as the optical ceiling and check your own camera's travel against it.
FAQ
How big an image circle do I need for 4x5?
153.7 mm just to fill the frame with the lens axis centred, which is the diagonal of the 120 by 96 mm image area. Every millimetre past that is movement budget, and it does not go as far as it looks: a 220 mm circle is 66.3 mm wider than the diagonal but buys only 44.2 mm of rise, because rise pushes the top corners out along a slant rather than straight at the edge of the circle.
Why does shift eat my rise so fast?
Because the corner distance adds in quadrature, not linearly. A Schneider APO-Symmar 150mm with its 220 mm circle gives 44.2 mm of rise on 4x5 landscape with no shift, but apply 20 mm of shift and the rise left drops to 27.5 mm, so 20 mm of shift costs 16.7 mm of rise. Used together and kept equal, the limit is 23.5 mm each, barely half of what either movement reaches on its own.
Does focusing closer give me more movement?
Yes, and more than most people expect. Published circles are quoted at infinity focus, and the circle grows in proportion to the bellows extension, so it scales by 1 plus the magnification. A 220 mm circle at 1:4 reproduction becomes 275 mm, and the rise available on 4x5 landscape goes from 44.2 mm to 75.7 mm. At 1:1 the circle doubles to 440 mm.