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The engineering toolbox has a screw withdrawal strength calculator but it assumes the screws are perpendicular to the grain.

I could not find a calculator for screws installed parallel to the grain, but I did find a nice meta-analysis of endgrain withdrawal force research for nails.

Based on the most conservative numbers there plus my blind assumption that the endgrain-to-sidegrain strength ratios for screws would be similar to nails, does it make sense to say, as a rule of thumb, that screws in the endgrain would have 0.5 the withdrawal force of screws in the sidegrain? Does this match peoples’ experience?

If not, is there a calculator or formula to determine endgrain withdrawal force given the screw diameter and density of the wood?

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    For here, I think specifying certain parameters would be considered ideal so as not to be too broad (there being so many different screw types now). But in the FPL's big document referenced a few times previously, Wood as an Engineering Material the section on screws is fairly succinct on this point, "The withdrawal loads of screws inserted in the end grain of wood are somewhat erratic, but when splitting is avoided, they should average 75% of the load sustained by screws inserted in the side grain." [contd] – Graphus supports Monica Oct 23 '18 at 13:03
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    Interestingly they give the same estimate for lag screws, but I don't think we can extrapolate too broadly from this. And note that this will be strictly with properly sized pilot holes (varied by wood type/hardness and, interestingly, screw length). – Graphus supports Monica Oct 23 '18 at 13:14
  • Absolutely. After years of lazy assumptions, I have finally learned that there is a right way to install wood screws, and that the right way has a huge impact on overall utility. In those cases where it matters, it really matters. – jdv Nov 7 '18 at 16:20
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The resistance of screws to being pulled free has been studied widely and for a long time (1920s or earlier), both by individual companies testing their own and competitor products and by government bodies doing work for the benefit of their industries. Perhaps most well known of the latter is the USDA's Forest Products Laboratory, the FPL. In their (primary?) publication Wood as an Engineering Material, chapter 8, Fastenings, it states:

The withdrawal loads of screws inserted in the end grain of wood are somewhat erratic, but when splitting is avoided, they should average 75% of the load sustained by screws inserted in the side grain.

My emphasis. The individual character of the wood at the exact site of each screw is going to be important, a mere 1/2" (13mm) to one side or another the one piece of wood can exhibit great variability in grain direction, and therefore in how well it can hold a screw.

In the next entry on lag screws:

The resistance to withdrawal of a lag screw from the end-grain surface of a piece of wood is about three-fourths as great as its resistance to withdrawal from the side-grain surface of the same piece.

Although I suspect the picture is much more complex that this indicates this gives us a rough guide. As I mentioned in a Comment early on I don't think it can be assumed that all types of screw have the same relationship between their withdrawal resistance in long grain and end grain1,2.

Maximising screw holding power
The publication repeatedly mentions the need for properly sized pilot holes and this is important. Apart from being unsightly when wood splits the holding power of fasteners is greatly reduced.

Splitting is largely avoided by the drilling of correctly sized pilot holes for screws3. Although there are some screws that don't need pilot holes they may still benefit from them in some circumstances.

It's vital to know that pilot hole size, as referenced briefly in previous Answers, is not fixed for a given screw diameter and type. While it's broadly true that pilot holes need to be smaller for woods of low density and larger for woods of high density other factors (including screw length perhaps counter-intuitively) determine the ideal pilot hole size. In practice though, due to the limited availability of drill bits of fractional sizes in many workshops, the closest match to the shank diameter is what will be used in all cases!

Summary for end grain
A few clear tips emerge from reading the literature:

  • Drill as close to the ideal pilot hole as you can.
  • Use a larger size of screw than you might otherwise.
  • Use the longest screw that is practical.

Note that these can lead to screws being very difficult to drive fully home as resistance builds up and builds up the deeper a screw goes, especially in harder species. And sometimes this can exceed the turning ability of an under-powered battery drill/driver or a hand screwdriver. Lubricating the screws — with soap, wax or oil — is well worth doing to help with this but it may not be enough, so it might prove necessary to switch to a different driver, e.g. a corded drill/driver or a carpenter's brace.

One additional tip:

  • Drive screws at a slight angle if possible (to involve more long grain), and with a pair of screws oppose the angles (to give a dovetail hold).

1 Worth noting that withdrawal resistance isn't even the same for radial and longitudinal grain, although these are commonly lumped together as 'long grain' as I have here.

2 Self-tapping screws in particular may present a different picture in end grain than in long grain as they sever the fibres rather than pushing them aside and largely leaving them intact.

3 And sometimes for nails too.

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+100

I would not presume to address the strength of end grain for holding screws, but I do concur that it's hit-and-miss, and not as strong as perpendicular. If it won't be obvious or unsightly, you can get a stronger joint by drilling into the face of the wood and inserting and gluing a dowel. You then drill your pilot hole into the end grain, through the dowel, and sink your screw there. It'll hold much better than a screw into end grain alone. It's kind of like inserting a poor man's barrel nut.

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    Although doesn't directly answer the question, it does offer a valid alternative for the concern. – user3158591 Nov 16 '18 at 14:12
  • This is a great suggestion. – Jason C Nov 16 '18 at 23:28

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