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Which fastener is resisting the pull, because each has its own published equation.
The three NDS equations are separate empirical fits, not one formula with three constants: a lag screw's capacity rises with roughly the three-quarter power of its diameter while a nail's rises linearly, and specific gravity enters at a different power in each. A deformed-shank or ring-shank nail withdraws far better than the smooth-shank value this page gives, and its capacity comes from the manufacturer's own evaluation report rather than from the equation.
The unthreaded shank diameter of the fastener, not the diameter over the thread.
For a lag screw this is the nominal shank, so a 1/2 in lag screw is 0.5 in (12.7 mm) whatever the thread measures. For a nail it is the wire diameter — a 16d common nail is 0.162 in (4.1 mm) and a 10d is 0.148 in (3.8 mm). Measuring over the thread instead of the shank overstates the diameter, and every one of these equations rewards diameter, so the error only ever runs one way.
Tools needed: Vernier caliper, Fastener schedule or product data sheet
How far the fastener actually enters the member that has to hold it.
For a lag screw or a wood screw this is the length of THREAD in the holding member, excluding the tapered tip — the shank passing through the side member does no withdrawal work at all. For a nail it is the length beyond the side member. Withdrawal is directly proportional to this figure, so a fastener 20 per cent short of the specified penetration is 20 per cent short of capacity, and that shortfall is invisible once the head is driven home.
Tools needed: Fastener schedule, Depth gauge or a marked drill bit
The assigned specific gravity of the species the fastener bites into.
Take it from the species combination on the grade stamp, not from a general timber figure: Douglas Fir-Larch is assigned 0.50, Southern Pine 0.55, Hem-Fir 0.43 and Spruce-Pine-Fir 0.42. Specific gravity enters the nail equation at the power of two and a half, so the difference between 0.42 and 0.50 is not a small correction — it is a third of the capacity. Where a fastener passes through one species into another, this is the species holding it, never the one it passes through.
Whether the fastener enters across the fibres or straight into the cut end.
This is the choice with the largest consequence on the page. Withdrawal from side grain works because the fibres wrap and grip the shank; withdrawal from end grain asks the fibres to part along their own length, which they do readily and unpredictably. The NDS reduces a lag screw's withdrawal to three-quarters in end grain and permits no withdrawal design value at all for nails and spikes, which is why selecting end grain for a nail returns zero rather than a small number. A wood screw in end grain also returns zero here, and for the plainer reason that this page holds no citable design value for that case and will not estimate one.
The moisture adjustment your own code table gives for this fastener and this exposure.
Dry in service and dry at fabrication is 1.0 and needs nothing entered. The NDS tabulates reduced factors by fastener type against the moisture condition at fabrication and the condition in service, and the reduction for a smooth nail that was driven dry and then wetted is severe. This page asks for the figure rather than choosing one, because picking the wrong row of that table is a larger error than any arithmetic on this page.
How many fasteners share the pull at this one connection.
Count only the fasteners actually installed and actually engaged. A proprietary strap or hanger is rated with every hole filled with the fastener its evaluation report names; six holes out of ten, or a round wire nail where the report says square-twist, is a different connection from the tested one. Unlike a laterally loaded group, a withdrawal group takes no group action reduction — the fasteners simply add.
Withdrawal capacity of the group
6.811 kips
Side grain, dry service, and the published reference equation for this fastener applied directly. This is a reference design value: the load duration factor and any temperature factor still have to be applied on top of it.
- Withdrawal capacity of one fastener
- 1,135.21 lbf
- Withdrawal resistance per unit of penetration
- 4,540.84 lbf/ft
- Fasteners in the group
- 6 fasteners
- Combined reduction applied for grain direction and moisture
- 1 factor
They open the calculator with your figures already in it
Timber Fastener Withdrawal Capacity Calculator: 6.81 kips — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- ANSI/AWC NDS, National Design Specification for Wood Construction, Chapter 12 — reference withdrawal design values W in pounds per inch of penetration: W = 1380·G^2.5·D for nails and spikes, W = 2850·G²·D for wood screws, and W = 1800·G^1.5·D^0.75 for lag screws, with D the shank diameter in inches and G the assigned specific gravity
- ANSI/AWC NDS — the end grain factor Ceg of 0.75 applied to lag screws loaded in withdrawal from end grain, and the rule that withdrawal design values are not permitted for nails and spikes driven into end grain
- ANSI/AWC NDS assigned specific gravities for common structural species combinations — Douglas Fir-Larch 0.50, Southern Pine 0.55, Hem-Fir 0.43, Spruce-Pine-Fir 0.42 — entered here as a value rather than picked from a built-in table, because the assignment belongs to the species combination and grading agency on the stamp
- EN 1995-1-1 Section 8 and EN 14592, Timber fasteners — the European route to the same quantity works from characteristic density and the withdrawal parameter declared for the specific screw, so a screw covered by a European Technical Assessment is designed on its declared value and not on the equations above
Inputs used
- Fastener Type
- Lag screw or coach screw
- Fastener Shank Diameter
- 0.5 in
- Penetration Into the Holding Member
- 3 in
- Specific Gravity of the Holding Member (G)
- 0.5
- Grain Direction at the Point of Entry
- Side grain — driven across the fibres, the normal case
- Wet Service Factor (CM)
- 1
- Fasteners in the Group (count)
- 6
Intermediate steps
- Withdrawal capacity of one fastener
- 1,135.21 lbf
- Withdrawal resistance per unit of penetration
- 4,540.84 lbf/ft
- Fasteners in the group
- 6 fasteners
- Combined reduction applied for grain direction and moisture
- 1 factor
Confidence note: Side grain, dry service, and the published reference equation for this fastener applied directly. This is a reference design value: the load duration factor and any temperature factor still have to be applied on top of it.
What this calculation does not cover
- Applies the moisture and end-grain adjustments only. The load duration factor CD, the temperature factor Ct and the toe-nail factor are separate multipliers this page does not apply.
- Reference design values are for smooth-shank fasteners. A ring-shank, screw-shank or proprietary structural screw withdraws considerably better, and its capacity comes from the manufacturer's evaluation report, not from these equations.
- Says nothing about head pull-through, about the side member splitting, or about the fastener's lateral capacity — a hold-down usually fails at one of those before the shank ever pulls out of the timber.
- A rated strap, hanger or hold-down is designed on its own tested capacity with every specified hole filled. Where such a product is used, this calculation is a cross-check on the fasteners, not a substitute for the rating.
Add the equipment this sizes
This result is a specification — 6.811 kips — not a quantity. Put the thing it sizes into your project: how many, what you call it, and your supplier’s price.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-08-30 · in the site-wide review of 2026-09-06 · v1.0.0
Regulatory standards & verification citations4
- ANSI/AWC NDS, National Design Specification for Wood Construction, Chapter 12 — reference withdrawal design values W in pounds per inch of penetration: W = 1380·G^2.5·D for nails and spikes, W = 2850·G²·D for wood screws, and W = 1800·G^1.5·D^0.75 for lag screws, with D the shank diameter in inches and G the assigned specific gravity
- ANSI/AWC NDS — the end grain factor Ceg of 0.75 applied to lag screws loaded in withdrawal from end grain, and the rule that withdrawal design values are not permitted for nails and spikes driven into end grain
- ANSI/AWC NDS assigned specific gravities for common structural species combinations — Douglas Fir-Larch 0.50, Southern Pine 0.55, Hem-Fir 0.43, Spruce-Pine-Fir 0.42 — entered here as a value rather than picked from a built-in table, because the assignment belongs to the species combination and grading agency on the stamp
- EN 1995-1-1 Section 8 and EN 14592, Timber fasteners — the European route to the same quantity works from characteristic density and the withdrawal parameter declared for the specific screw, so a screw covered by a European Technical Assessment is designed on its declared value and not on the equations above
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