Apertia · Library
How can you estimate the width of a flat subject at a finite distance?
A 100 mm lens on full frame focused at 1 m covers about 283.4 × 189 mm, not the 360 mm a simple angle suggests, and at 400 mm it shows exactly 36 × 24 mm.
Magnification, not angle
For a flat subject at a finite distance, the field-of-view tool computes the thin-lens magnification m = v ÷ u from the sensor-plane distance and the focal length, then divides the sensor's width and height by m. The quick estimate distance × sensor width ÷ focal length ignores that the lens moves away from the sensor as it focuses closer, so it overstates the scene, and the error grows as the subject approaches.
At four focal lengths from the sensor the object and image distances are both 2f, magnification reaches 1 and the frame covers an area exactly the size of the sensor. Apertia's model stops there.
Worked example
At 2000 mm sensor-plane focus distance, the 50 mm model and 36 × 24 mm sensor cover approximately 1367.052 × 911.368 mm at the focus plane.
- Estimated scene width (mm)
- 1367.051975
- Estimated scene height (mm)
- 911.367983
Estimate a flat subject's coverage
- Measure from the camera's sensor-plane mark to the subject, not from the lens front.
- Enter the sensor preset, the real focal length and that distance as the focus distance.
- Read scene width, scene height and magnification.
- Compare the subject's dimensions with both values and leave a margin for framing.
Worked example: 100 mm close to the subject
With 100 mm on the 36 × 24 mm preset at 1000 mm, the magnification is about 0.127, so the frame covers roughly 283.4 mm by 189 mm. The simple ratio 1000 × 36 ÷ 100 predicts 360 mm, about 27 percent too wide. At 400 mm, four times the focal length, the magnification is 1 and the scene is 36 mm by 24 mm. Even far away the difference does not vanish entirely: 50 mm at 2000 mm gives about 1367 mm against a simple 1440 mm.
- 100 mm at 1000 mm
- 283.4 × 189 mm · m 0.127
- Simple estimate at 1000 mm
- 360 mm wide
- 100 mm at 400 mm
- 36 × 24 mm · m 1
- 50 mm at 2000 mm
- 1367 mm (simple: 1440 mm)
Common mistakes
- Using the infinity angle of view to size a label or artwork at arm's length.
- Entering a distance closer than four focal lengths, which this model does not accept.
- Measuring a tilted subject as if it were square to the camera.
- Relying on a tight fit without a test frame; real lenses can breathe as they focus.
Model boundary
The estimate treats the lens as a single thin lens. Internal-focus designs can change their effective focal length up close, and distortion bends the frame edges; the DOFMaster equations and Nikon angle-of-view guide below describe the ideal relation only.