Crop Factor and Equivalent Focal Length
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The crop factor is computed from the sensor diagonal, not from its width or height, and the equivalent focal length follows from it. Using width or height gives a different number for every format: different formats have different aspect ratios, and only the image-circle diameter is common to all of them. ⚠️ Equivalent focal length changes the angle of view only, not the f-number: f/2.8 exposes the same on any format, while depth of field does change (f/2.8 on Micro Four Thirds looks like f/5.6 on full frame). Angles are computed as `2·atan(d / 2f)`; a 50 mm lens on full frame covers about 46.8° diagonally. Everything runs in your browser.
Features
- Crop factor from the diagonal, not the width or height
- Full-frame equivalent focal length plus horizontal, vertical and diagonal angles
- Convert to another format: the focal length that matches the same angle
- Depth-of-field estimate: hyperfocal distance, near and far limits, total depth
- Exposure aperture and depth-of-field equivalent aperture listed separately
- Built-in formats: full frame, APS-C Canon and Sony/Nikon, Micro Four Thirds, 1 inch, medium format 44x33 and 53x40
- The far limit reads as infinity once the focus distance passes the hyperfocal distance
- Everything runs locally and nothing is uploaded
How to use
- Pick a sensor format, which sets the crop factor
- Enter the focal length; pick a target format to convert
- For depth of field, enter an aperture and a focus distance (0 skips it)
- Copy any value with its own button
FAQ
- Why is the crop factor based on the diagonal?
- Because formats do not share an aspect ratio (full frame is 3:2, Micro Four Thirds 4:3), and the image-circle diameter is the only measure they have in common. By width, medium format 44x33 gives 36 / 44 = 0.82; by height it gives 24 / 33 = 0.73. Only the diagonal ratio is unambiguous.
- Does the equivalent focal length change the exposure?
- No. The f-number is an absolute aperture and the light gathered depends only on it and the shutter, so f/2.8 exposes the same on any format. The equivalent focal length changes the angle of view; only depth of field shifts with the format, and that row is listed separately.
- Why is a 50 mm lens 46.8 degrees on full frame?
- The diagonal angle is `2·atan(d / 2f)` with d the sensor diagonal, sqrt(36^2 + 24^2) = 43.27 mm, and f = 50 mm, which is about 46.8 degrees. The horizontal angle (d = 36) is about 39.6 degrees and the vertical angle (d = 24) about 27.0 degrees.
- How accurate is the depth of field?
- It is an estimate: the circle of confusion is the diagonal divided by 1500, and dividing by 1730 is an equally common convention, a difference of about 15 percent. Use it to compare formats and apertures rather than as an exact focus range.
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