Crop Factor Calculator

Background.

Crop factor is the number that tells you what a lens becomes when it is mounted on a sensor smaller — or larger — than the 36 × 24 mm 35 mm frame. This calculator computes it from the sensor's actual imaging-area dimensions, then converts both the focal length and the aperture in whichever direction you need: your real lens to its 35 mm equivalent, or a 35 mm look you are chasing back to the real lens you would have to buy.

The definition is simple and there is only one right version of it. Crop factor is the ratio of the 35 mm frame diagonal, 43.2666 mm, to the diagonal of your sensor. The diagonal is the correct measure because the quantity being preserved is the angle of view, and the angle of view depends on frame size divided by focal length. Everything else — the "1.5×", "1.6×", "2×" and "0.79×" numbers manufacturers print — falls out of that single ratio. This page shows the diagonal it used, so you can see the arithmetic rather than trust a lookup table.

It is worth being precise about what crop factor is not, because the popular shorthand is actively misleading. Zeiss put it plainly in their technical article on depth of field: there is a crop factor, but "we do not talk about an extension of the focal length, it doesn't exist in this case. After all, the lens does not know how much of its image circle we are capturing with our sensor." A 300 mm lens on an APS-C body is still a 300 mm lens. It has not gained reach, magnification or compression. You are simply recording a smaller rectangle out of the middle of the same image circle, and then enlarging that rectangle more to reach the same print size. Everything called "crop factor" is a consequence of that extra enlargement.

The aperture conversion is the half that most calculators leave out, and it is where the real confusion lives. Depth of field at a fixed framing and distance depends on the entrance pupil diameter, which is focal length divided by f-number. If the focal length scales by the crop factor, the f-number has to scale by the same factor for the entrance pupil — and therefore the depth of field and the background blur — to match. Zeiss state it directly: "There are therefore equivalent f-numbers for all formats, corresponding to the linear format size." So a 25 mm f/1.8 on Micro Four Thirds frames like a 50 mm and blurs like an f/3.6 on full frame.

And then the trap, which the same source flags in the very next sentence: "a converted f-number would be incorrect as an exposure parameter." This is why the page reports the actual and the equivalent f-number as two separate results. Your light meter, your shutter speed and your ISO care only about the actual one; f/1.8 is f/1.8 on any sensor ever made. The equivalent one is a statement about depth of field and background blur, and nothing else. Confusing the two is how photographers end up two stops underexposed while arguing about equivalence on the internet.

One quantity deliberately does not appear on this page: an "equivalent ISO". Noise performance depends on read noise, quantum efficiency and pixel design, not on geometry, and no manufacturer publishes a standard conversion. Instead the page reports the honest geometric fact behind that argument — the ratio of imaging areas — and lets you draw your own conclusion.

Below the widget you will find the derivation, a worked Micro Four Thirds example computed by hand, the four independent manufacturer conversion factors this method reproduces to within a fraction of a percent, why APS-C is not one format but four, and why a sub-1.0 crop factor on medium format works exactly the same way in reverse.

What is crop factor calculator?

Crop factor — manufacturers call it the focal length conversion factor or the angle-of-view conversion factor — is the ratio of the 35 mm still-frame diagonal to the diagonal of the sensor in question: crop = √(36² + 24²) / √(w² + h²) = 43.2666 / d. Multiplying a lens's real focal length by it gives the 35 mm-format focal length that would produce the same diagonal angle of view, which is the only thing the number describes. It says nothing about the lens: focal length is a property of the glass, fixed by its optical construction, and mounting it on a smaller sensor changes neither the focal length nor the perspective nor the compression of the scene. What changes is the fraction of the image circle recorded and, consequently, the enlargement needed to reach a given print size. Because depth of field at matched framing depends on the entrance pupil diameter f/N, matching depth of field across formats requires the f-number to scale by the same crop factor — the equivalent aperture. That conversion is valid for depth of field, entrance pupil, background blur and total light collected at matched framing, and invalid for exposure: the actual f-number remains the exposure parameter regardless of sensor size. Note also that APS-C is not a standard. Nikon DX is 23.5 × 15.7 mm (crop 1.531), Canon APS-C is 22.3 × 14.8 mm (crop 1.617), and Sony and Fujifilm sit between them, which is why this page offers two APS-C presets and a Custom option rather than a single number. Finally, because crop factor is defined on the diagonal while light collection scales with area, the area ratio equals the crop factor squared only when the two formats share an aspect ratio — Micro Four Thirds is 4:3 against 35 mm's 3:2, so its 3.84× area ratio differs slightly from its 2.00× crop squared.

How to use this calculator.

1. 01Choose the direction. "My lens → its 35 mm equivalent" is the shopping-list check on gear you already own. "A 35 mm equivalent → the real lens I need" is the one to use when a tutorial or a rental list is quoted in full-frame terms and you shoot a smaller format.
2. 02Pick the sensor format. If your camera is not listed, choose Custom and enter the imaging-area width and height in millimetres from your own specification sheet — not the sensor package size and not the marketing "type" designation.
3. 03In the first direction, enter the focal length engraved on the lens barrel and its f-number. Enter 25 and 1.8 for a 25 mm f/1.8. Never enter an equivalent value here or the crop factor gets applied twice.
4. 04In the second direction, enter the 35 mm-equivalent focal length and aperture you are trying to match — for example 24 mm and f/2.8 for a classic wide-angle landscape look.
5. 05Read the crop factor first and sanity-check it against what your manufacturer publishes. Nikon DX should land near 1.5, Canon APS-C near 1.6, Micro Four Thirds at essentially exactly 2, and Fujifilm GFX below 1.
6. 06Use the equivalent focal length for framing decisions and the equivalent aperture for depth-of-field and background-blur decisions only.
7. 07Use the actual f-number, never the equivalent one, for exposure. Set that number on the lens, meter with it, and expose with it. The equivalent aperture is a comparison figure and dialling it into a meter will cost you the exact number of stops the crop factor represents.
8. 08Check the area ratio if you are comparing formats for low light. It is the honest geometric part of the noise argument — how much more light the larger sensor collects at matched framing and equivalent aperture — with no assumptions about sensor generation or read noise baked in.

The formula.

Start from the frame diagonals.

d(35 mm) = √(36² + 24²) = √1872 = 43.266615 mm d(sensor) = √(w² + h²) crop = 43.266615 / d(sensor)

Why the diagonal and not the width or the height? Because the thing being held constant is the angle of view, and the angle subtended by a frame dimension X at focal length f is 2·arctan(X / 2f). Scaling f by the ratio of diagonals preserves the diagonal angle of view exactly. It preserves the horizontal and vertical angles too, but only when the two formats share an aspect ratio — Micro Four Thirds at 4:3 against 35 mm at 3:2 is very slightly taller and narrower than the diagonal conversion implies, and no single number can fix that.

For the focal length:

f_eq = f × crop f = f_eq / crop

For the aperture, the reasoning runs through the entrance pupil. Zeiss: "the depth is only dependent on the size of the entrance pupil if we have the same distance and the same angular field. The pupil diameter is the quotient of the focal length and the f-number. If the focal length then changes by a factor determined by the image format, we only have to multiply the f-number by the same factor. Then the quotient, that is to say the entrance pupil, has the same value again and we have the same depth of field relationships." So:

N_eq = N × crop N = N_eq / crop

A 25 mm f/1.8 on Micro Four Thirds has an entrance pupil of 25 / 1.8 = 13.9 mm. A 50 mm f/3.6 on full frame has an entrance pupil of 50 / 3.6 = 13.9 mm. Same pupil, same framing, same distance, same depth of field, same background blur. That is the whole of the equivalence argument in two lines of arithmetic.

The caveat is not a footnote, it is part of the source: "The widely spread practice of describing the angular field of lenses by calculating the equivalent 35 mm focal length is therefore inconsistent if it does not convert the aperture as well. But on the other hand there would be a conflict: a converted f-number would be incorrect as an exposure parameter." The f-number is defined as focal length over entrance pupil diameter, and image illuminance depends on it directly. A scene metered at f/1.8 and 1/500 s is correctly exposed at f/1.8 and 1/500 s on Micro Four Thirds, on APS-C, on full frame and on 8 × 10 sheet film. Nothing about sensor size changes that.

The area ratio is computed separately and honestly:

area ratio = (36 × 24) / (w × h)

For Micro Four Thirds that is 864 / 224.9 = 3.84, not 2.00² = 4.00, because the aspect ratios differ. This is the geometric part — and only the geometric part — of the low-light argument between formats: at matched framing and equivalent apertures the larger sensor gathers that many times more light in total. What it does with that light depends on the sensor generation, and no calculator can tell you that, which is why no "equivalent ISO" is offered here.

One last practical point the formula cannot express. The crop factor tells you nothing about whether a lens will cover the sensor. Mounting a lens designed for a small format on a larger one produces vignetting or a dark circle, and the arithmetic here will happily compute a number for a combination that cannot physically be photographed.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Nasse, H. H. (2010). 'Depth of Field and Bokeh.' Carl Zeiss Camera Lens Division. Source for what crop factor is not — 'there is a crop factor. We do not talk about an extension of the focal length, it doesn't exist in this case. After all, the lens does not know how much of its image circle we are capturing with our sensor' — and for the equivalent f-number: 'If the focal length then changes by a factor determined by the image format, we only have to multiply the f-number by the same factor... There are therefore equivalent f-numbers for all formats, corresponding to the linear format size', together with the warning that 'a converted f-number would be incorrect as an exposure parameter.'
2. [2]Nikon Corporation. D7500 Online Manual, Technical Notes — Specifications. Gives the Nikon DX imaging area as '23.5 × 15.7 mm CMOS sensor' and the conversion as 'focal length in 35 mm [135] format equivalent to approx. 1.5× that of lenses with FX format angle of view'. The diagonal method returns 1.5309.
3. [3]Canon Inc. EOS R7 Product Manual, Specifications. Gives the Canon APS-C sensor as 'Approx. 22.3 × 14.8 mm' and states the angle of view is equivalent to 'Approx. 1.6 times the focal length indicated on the lens'. The diagonal method returns 1.6166.
4. [4]Canon Inc. EOS R6 Product Manual, Specifications — Image Sensor. Gives the full-frame sensor size as 'Approx. 35.9×23.9 mm', the measured dimension behind the nominal 36 × 24 mm reference frame this page divides by.
5. [5]OM Digital Solutions. OM SYSTEM OM-1 Mark II Specifications. Lists the imaging area as 'Aspect ratio & area 4:3 / 17.3 x 13.0 mm' and, in the image-stabiliser notes, 'Focal length: 40mm (35mm equivalent: 80mm)' and 'Focal length: 150mm (35mm equivalent: 300mm)' — an exact 2× conversion. The diagonal method returns 1.99938.
6. [6]FUJIFILM Corporation. GFX100 II Specifications. Lists the image sensor as '43.8mm×32.9mm', the dimensions behind the sub-1.0 medium-format crop factor.
7. [7]FUJIFILM Corporation. FUJINON GF63mmF2.8 R WR Specifications. Lists the focal length as 'f=63mm (50mm in 35mm format equivalent)', i.e. a 0.794× conversion for the GFX format. The diagonal method returns 0.7898.