Screw Pull-Out Strength Calculator

Introduction: The Force That Yanks a Screw Straight Out

Screws resist two very different loads. Shear tries to slice the shank sideways, and withdrawal tries to pull it straight back out along its axis. Withdrawal is the one that surprises people: a screw that feels rock-solid to wiggle can still ease out of soft pine under a steady axial pull, because all that is holding it is the wood fiber wrapped between the threads. That grip is what fails when a heavy mirror tears off a wall or a ledger board sags away from a joist. This calculator estimates that axial holding force from three things you can measure at the bench — thread diameter, how much thread is buried in the wood, and how dense the wood is.

Density does most of the heavy lifting here, and the formula reflects that: it scales with the square of specific gravity, so a hardwood like maple holds several times more than a softwood like cedar for the identical screw. Thread penetration matters linearly — twice the buried thread roughly doubles the grip — and diameter helps because a fatter screw wraps more fiber per turn. Enter the three values and the tool returns two numbers in pounds and Newtons: the code-style reference design value and the far higher average ultimate at which threads actually tear out in testing.

Both numbers assume the same thing the code assumes: a cut-thread or rolled-thread wood screw turned into the side grain of seasoned wood, with the screw axis perpendicular to the fibers. Everything below — the worked example, the species chart, and the Withdrawal Rig practice bench under the calculator — is built on that one geometry.

The NDS Withdrawal Formula

The design-level holding force comes from Equation 12.2-2 of the National Design Specification for Wood Construction (NDS), fit to decades of pull tests across many species. The equation actually returns a unit value in pounds per inch of thread penetration, which NDS 12.2.2.2 then multiplies by the thread penetration to get the capacity of one screw:

In these expressions is the specific gravity of the wood on an oven-dry weight and volume basis, is the shank diameter of the screw in inches, and is the length of thread penetration into the receiving member in inches. The squared exponent on specific gravity is why density dominates the result. NDS Table 12.2B tabulates the same equation for specific gravities from 0.31 to 0.73 and screw numbers 6 through 24, and that is the range in which the coefficient was calibrated. Because the design value already carries a large reduction from failure-level testing, USDA Forest Products Laboratory data also gives an average ultimate — where the joint actually lets go on the test bench, typically after five to ten minutes of loading:

One assumption is baked into both: the screw is driven into side grain, so the threads bite across the wood fibers. Drive it into end grain instead — straight into the cut ends of the fibers — and the code stops you outright. NDS 12.2.2.3 states that wood screws shall not be loaded in withdrawal from end grain, an end-grain factor of . Wood Handbook test data is less absolute — end-grain withdrawal averages about 75% of the side-grain load when splitting is avoided — but it calls those results erratic, which is exactly why the code refuses to give them a design value.

The calculator converts your millimetre inputs to inches before applying the formulas, then converts pounds to Newtons by multiplying by . Treat the numbers as a ballpark: pilot-hole size, moisture, thread profile, and whether every buried turn is actually gripping all shift the real value.

Sources: the reference withdrawal design value W = 2850 G² D (lb per inch of thread penetration into side grain) is Equation 12.2-2 in Chapter 12 of the 2018 NDS for Wood Construction, Dowel-Type Fasteners (American Wood Council), with Table 12.2B giving the tabulated values and the 0.31–0.73 specific-gravity range. The average ultimate p = 15,700 G² D L lb is Equation 8-10b in the USDA Forest Products Laboratory Wood Handbook, Chapter 8: Fastenings (FPL-GTR-190), which also supplies the lead-hole guidance and the 75% end-grain observation. Adjustment factors for connections are in NDS Table 11.3.1. Conversions: 1 lb = 4.44822 N; 1 in = 25.4 mm. Last reviewed August 2026.

Specific Gravity by Wood Species

The table lists approximate specific gravity values for common North American woods alongside the unit withdrawal value the NDS equation produces for a #10 screw; the first four rows match NDS Table 12.2B exactly. Entering these numbers into the calculator lets you compare withdrawal strength across species. For instance, a 5 mm screw penetrating 40 mm of thread into cedar (G = 0.35) yields a far lower withdrawal force than the same screw in maple (G = 0.72). Because the formula squares G, that swap multiplies the density term by roughly 4.2 — more than quadruple the grip from wood choice alone. It is the reason a screw that anchors happily in fir can strip out of soft cedar under the same load. The species chart under the calculator draws this comparison automatically for whatever screw you enter.

Screw Gauge and Shank Diameter

Wood screws are sold by gauge number, not by diameter, and the NDS equation wants the shank diameter in inches. The two are related by a simple linear rule, inches, which reproduces the diameters behind NDS Table 12.2B:

Use the gauge dropdown in the calculator to fill the diameter field from this table, or measure the smooth shank with a caliper if you are working from an unmarked box. Note that this is the shank diameter, not the outside diameter across the threads — modern deck and structural screws often have threads that stand well proud of the shank, and using the thread diameter overstates the NDS result.

Worked Example: A 4 mm Screw in Pine

Consider a screw with a 4 mm shank diameter and 30 mm of thread buried in pine, which has a specific gravity of approximately 0.42. Converting to inches gives and . Plugging into the NDS design-value formula:

That works out to a reference design value of about 94 pounds (416 Newtons) — the code-style planning number the calculator returns for these inputs. Broken into NDS steps it is a unit value of W = 2850 × 0.42² × 0.157 = 79 lb per inch of thread, multiplied by 1.18 inches of penetration. The Wood Handbook average ultimate for the same screw is about 515 pounds (2,290 Newtons), roughly five and a half times higher, which is where the threads actually tear out on a test bench. That 15,700 ÷ 2850 = 5.5 ratio is fixed, so it holds for every screw and every species this calculator handles. The arithmetic also shows how sensitive both numbers are to wood choice: bump the pine up to oak (G = 0.67) and the design value climbs to about 238 pounds, while dropping to cedar roughly halves it.

From Design Value to a Safe Working Load

The 94-pound design value is the right starting point for planning, and the 515-pound ultimate explains where its margin comes from: the NDS reduction absorbs the messiness of a real installation — lumber that grades out weaker than the table, a screw driven slightly proud, moisture that softens the fibers, or a shelf that ends up carrying more than anyone planned. In actual code-checked design the reference value is then multiplied by the adjustment factors of NDS Table 11.3.1 — load duration , wet service , and temperature — so the working number can move in either direction. This calculator reports the unadjusted reference value only. Never plan around the ultimate figure; it is an average failure point with no margin at all, and half the test joints let go below it.

Two further ceilings sit above the formula. NDS 12.2.2.5 requires that the adjusted tensile strength of the screw at its root diameter is never exceeded, so in dense hardwoods a long screw simply snaps before the wood lets go — which is why the Wood Handbook calls the longest standard screws "superfluous in dense hardwoods." And direction matters as much as the number: threads driven into end grain get no design value at all under NDS 12.2.2.3, so back up end-grain joints with a bracket or glue block rather than counting on the raw estimate. Wet-dry cycling gradually works screws loose as the wood swells and shrinks around each thread. The Wood Handbook equation assumes a lead hole about 70% of the thread root diameter in softwoods and about 90% in hardwoods; a hole sized that way plus a controlled final torque keeps the threads intact so they grip the full depth you measured. Strip the hole while driving and the real withdrawal never reaches the calculated value.

Limitations: Where the Simple Formula Runs Out

The limitations follow from the assumptions: the equation was fit to plain straight-shank cut-thread and rolled-thread wood screws, so treat it as a floor rather than a spec for anything fancier. Structural and deck screws with aggressive deep threads, self-tapping tips, or high-low thread patterns often withdraw noticeably harder than the number suggests — the Wood Handbook puts plain sheet-metal tapping screws alone at 5% to 16% above comparable wood screws — and reputable brands publish their own tested pull-out values under an ICC-ES evaluation report. Use those when you have them. Outside the calibrated ranges the equation drifts: NDS Table 12.2B stops at G = 0.31 and G = 0.73 and at screw numbers 6 through 24, and the Wood Handbook notes that for lengths and gauges outside its own table the real values are likely to be lower than the equation predicts. The formula also says nothing about geometry off the screw itself. Set a screw too close to an edge or an end and the wood splits along the grain before the threads ever reach their rated grip, which is why edge distance and spacing rules exist in real connection design.

Moisture is the other big blind spot. Green or damp wood grips softer because the fibers deform instead of pinching the thread, and a joint made wet can lose holding power as it later dries and shrinks away from the shank — or occasionally gain a little, at the risk of splitting. Both coefficients assume ordinary dry, in-service conditions. For anything outdoors, in a bathroom, or exposed to weather, size up, choose corrosion-resistant fasteners, and expect the true capacity to wander over the seasons.

How to Use It: Measuring Your Three Inputs

Two of the inputs you can read off a caliper. Screw diameter is the smooth shank diameter, not the outside diameter across the threads — pick the gauge from the dropdown if you know the screw number, or measure the shank between the head and the start of the thread. Thread penetration is only the threaded length actually buried in the receiving piece: subtract the side member the screw passes through, any smooth shank near the head, and anything poking out the far side, since only gripping threads count. Enter both in millimetres. For specific gravity, pull the wood species from the table above, or measure a dry offcut by dividing its mass by its volume and again by the density of water.

Press Calculate Strength and the tool converts your millimetres to inches (dividing by 25.4), runs both withdrawal formulas, and reports the unit value W in pounds per inch of thread, the NDS design value, and the Wood Handbook ultimate in pounds and Newtons, along with a species comparison chart for the same screw. It also flags inputs that fall outside the ranges the coefficients were calibrated for. Reset inputs puts every field back to its starting value. You can pick a species from the dropdown to fill in its specific gravity automatically, and the Withdrawal Rig bench below the calculator lets you practise predicting the design value before the ram tears the screw out. Everything runs in your browser, so it works on a jobsite with no signal and never sends your numbers anywhere.

Sizing Screws for Shelves, Cabinets, and Brackets

The everyday use is a sanity check before you commit fasteners. Hanging a heavy shelf, a TV mount, or a coat rack? Estimate one screw’s withdrawal load, apply a safety factor, then divide the hanging weight (plus a generous allowance for someone leaning on it) by that allowable to see how many screws you actually need — and whether they should be longer or fatter to reach a deeper bite. In cabinet work the same logic sets how many screws tie a wall cabinet to the studs, or whether the short screws that came with a drawer slide will really hold a loaded drawer.

It is also a fast gut-check ahead of a proper structural calculation. A designer can rule out an obviously undersized fastener in seconds before opening the code book, and a contractor can hand a client a rough holding capacity to explain why a bracket needs three screws instead of one. Just remember the estimate stops where code compliance begins.

When Not to Rely on the Number

This is a planning estimate, not a guarantee, and a few situations push it well off. Off-axis or cyclic loads — a hinge that gets yanked at an angle, a fastener buzzed by vibration — loosen screws in ways a single static formula can’t see. Damaged or stripped threads, knots, checks, and low-grade lumber all undercut the assumed clean side-grain bite. And the formula only accounts for mechanical thread grip: if your joint leans on adhesive, friction, or clamping instead, the real capacity is a different problem entirely. For anything where failure is costly, pull-test a representative joint or bring in an engineer rather than trusting the printout.

Withdrawal questions woodworkers ask