APS-C crop factor 1.5x or 1.53x

Question

I'm having issues wrapping my head around how to get crop factor based on 35mm. I understand what crop factor is but my math is confusing me.

For example, everyone knows that aps-c is a 1.5x crop but from my calculations an aps-c sensor with the dimensions "23.6x15.6" will give you a 1.53x crop.

Is this correct, or is it standard practice to round to only the first place with crop factor? I'm working on a super accurate focal length calculator so it seems this should be right.

My math is as follows:

(√((23.6^2)+(15.6^2))) / 43.2666153056

Answer 1

You are correct.

Like most manufacturers, Nikon APS-C sensor sizes vary depending on the camera model. Nikon crop factor can be 1.52, 1.53, 1.55, or 1.56

A list of the most common crop factors for APS-C, from the Wikipedia article on APS-C:

A crop factor (sometimes referred to as a "focal length multiplier", even though the actual focal length is the same) can be used to calculate the field of view in 35 mm terms from the actual focal length. The most common multiplier ratios:

• 1.7× — Sigma DP1, Sigma DP2, Sigma SD15, Sigma SD14, Sigma SD10, Sigma SD9, Canon EOS DCS 3†
• 1.6× — Canon EOS 7D†, 7D Mark II, 50D†, 60D†, 70D†, 77D (9000D), 80D, 550D (T2i)†, 600D (T3i/X5)†, 650D (T4i/X6i)†, 700D (T5i/X7i)†, 750D (T6i/X8i), 760D (T6s/8000D), 800D (T7i/X9i) 1100D (T3/X50)†, 1200D (T5/X70)†, 1300D (T6/X80); Canon EOS M†, M2† (sold in Asia only), M3 (not sold in North America until Oct 2015), M5, M6, M10
• 1.56× — Nikon D3100†
• 1.55× — Sony Alpha 58, Nikon D3200†
• 1.54× — Pentax K20D,†[5] Samsung NX5†, Samsung NX10†, Samsung NX11†, Samsung NX100†, Sony NEX-5†
• 1.53× — Pentax K-3, K-S1, K-S2, K-5 II†, K-5†, K10D†, K200D†, Ricoh GR, Nikon D3300†, Nikon D5300†, Nikon D5500, Nikon Coolpix A, Sony NEX-7,† Sony NEX-6, Sony α6000†, Sony α6300, Sony Alpha 77, Sony Alpha 77 II, Sony Alpha 65, Sony Alpha 57, Sony Alpha 37, Sony Alpha 580, Sony Alpha 500, all Samsung NX except NX5, NX10, NX11, NX100
• 1.52× — All Nikon DX format DSLR cameras except D3100, D3200, D3300, D5300, and D5500; Pentax K-30†, K-01, K-50, K-500;† all Fujifilm interchangeable lens X-system cameras and Fujifilm X100 series; Sony Alpha 100; Sigma SD1, Sigma SD1 Merrill, Sigma DP1 Merrill, Sigma DP2 Merrill
• 1.35× — Sigma SD Quattro H
• 1.3ׇ — Canon EOS-1D Mark IV†, 1D Mark III†, 1D Mark II† (and Mark II N), EOS-1D†, Kodak DCS 460†, Kodak DCS 560†, Kodak DCS 660†, Kodak DCS 760†, Leica M8, M8.2

Notes:

^{† Discontinued
‡ A 1.3× Focal Length Multiplier is also known as APS-H. Actual multiplier factor is 1.255× for the 1D Digital, 1.28× for the Canon EOS-1D Mark III and 1.29× for the Canon EOS-1D Mark IV. Leica M8 is 1.33×}

Answer 2

Nikon 1.5X APS-C sensors in their current lineup are actually 1.52-1.53X depending on the exact measurements of the various different sensors in different models. Some older, discontinued models in the D3x00 series are slightly smaller at 1.55-1.56X.

The difference between 1.52X and 1.53X is 0.65789 percent.

The difference between 1.5X and 1.53X is a mere 2 percent.

The difference between Nikon 1.5X APS-C sensors (actually 1.52-1.53X depending on the exact measurements of various different sensors in different models) and Canon 1.6X APS-C sensors (actually 1.6-1.61X depending on the specific sensor) is only around 5 percent.

The difference between stated/marketed focal lengths of lenses and the actual focal length of the same lens can be as high as 10% or more when the lens is focused at infinity.

There are some fairly expensive lenses that breathe so heavily that the field of view can vary by 30% or more when focused at the minimum focus distance. Take for instance, the Nikon AF-S 70-200mm f/2.8G VR II. At maximum zoom (marked 200mm) and minimum focus distance the field of view projected onto a full frame sensor is equivalent to a focal length of only about 134mm! That's only 67% of the stated focal length!

Can you see where this is going?

Answer 3

It doesn't really matter, but two decimal digits is more precision than is practically useful.

... or is it standard practice to round to only the first place with crop factor?

This is good practice, if not always standard practice.

That's because in practice, it doesn't matter. Few other things are going to be so precise that going to two decimal places makes a noticeable difference. A lens that is nominally "50mm" only has that focal length when focused at infinity — and may be actually not 50mm exactly even then.