Screw Pull-Out Strength Calculator

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 specific gravity to the 1.5 power, so a hardwood like maple holds far more than a softwood like cedar for the identical screw. Embedment depth 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 the estimated ultimate withdrawal load in both pounds and Newtons, plus suggested working loads after a safety factor.

The NDS Withdrawal Equation

The holding force comes from the withdrawal relationship used in the National Design Specification for Wood Construction (NDS), fit to years of pull tests across many species. Written per screw, it is:

In this expression, $F$ is the ultimate withdrawal load in pounds, $G$ is the specific gravity of the wood, $D$ is the nominal screw diameter in inches, and $L$ is the length of thread embedded in inches. The constant 1380 rolls the empirical test data into one coefficient, and the 1.5 exponent on specific gravity is why density dominates the result. One assumption is baked in: the screw is driven into side grain, so the threads bite across the wood fibers. Drive it into end grain — straight into the cut ends of the fibers — and real withdrawal can drop by a third or more, which the formula does not capture.

The calculator converts your metric inputs to inches before applying the formula. After obtaining $F$ in pounds, it converts the result to Newtons by multiplying by $4.44822$. Treat the number as a ballpark: pilot-hole size, moisture, thread profile, and whether every buried turn is actually gripping all shift the real value.

Specific Gravity by Wood Species

The table lists approximate specific gravity values for common North American woods. Entering these numbers into the calculator lets you compare withdrawal strength across species. For instance, a 5 mm screw embedded 40 mm into cedar (G = 0.35) yields a lower withdrawal force than the same screw in maple (G = 0.72). Because the formula raises G to the 1.5 power, that swap multiplies the density term by roughly 2.9 — nearly triple 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.

Worked Example: A 4 mm Screw in Pine

Consider a screw with a 4 mm diameter embedded 30 mm into pine, which has a specific gravity of approximately 0.42. Converting to inches gives $D=0.157$ and $L=1.18$. Plugging into the NDS equation:

That works out to an ultimate withdrawal load of about 70 pounds, or roughly 311 Newtons — the value the calculator returns for these inputs. It is a failure estimate, not a load you should plan around; divide it down by a safety factor before trusting a joint to it. The arithmetic also shows how sensitive the answer is to wood choice: bump the pine up to oak (G = 0.67) and the same screw clears 140 pounds, while dropping to cedar cuts the grip roughly in half.

From Ultimate Load to a Safe Working Load

The 70-pound figure is where the wood lets go, not where you should load the joint. A safety factor closes the gap between that failure point and 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. Dividing the ultimate load by four is a common woodworking rule of thumb, which turns our 70 pounds into a working load closer to 17 pounds. The calculator does this for you, listing allowable loads at safety factors of three and four once you run it.

Direction matters as much as the number. Threads driven into end grain — into the cut ends of the fibers rather than across them — hold far less than the side-grain case the formula assumes, 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. A pilot hole sized to the screw and a controlled final torque keep 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.

Where the Simple Formula Runs Out

The equation was fit to plain straight-shank 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, and reputable brands publish their own tested pull-out values — use those when you have them. 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. The 1380 coefficient assumes 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.

Measuring Your Three Inputs

Two of the inputs you can read off a caliper. Screw diameter is the nominal shank diameter across the threads — the number you already know from the box, or measure at the widest point of the thread. Embedment depth is only the threaded length actually buried in the receiving piece: subtract any smooth shank near the head and anything poking out the far side, since only gripping threads count. Enter both in millimeters. 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 millimeters to inches (dividing by 25.4), runs the withdrawal equation, and reports the ultimate load in both pounds and Newtons along with a small table of allowable loads at safety factors of three and four. 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.