Bolt Pull Out Force Calculator estimates the anchor working tension limit from concrete breakout, threaded steel strength, evaluated pullout capacity, embedment, and safety factor.
How Bolt Pull-Out Force Is Calculated
This calculator checks three separate ways a bolted anchor connection can fail and reports whichever one produces the lowest capacity, since that’s the mode that actually governs. It compares the concrete’s breakout strength around the bolt, the steel’s tension strength through the threaded section, and the evaluated pullout capacity you enter from testing or a manufacturer’s rating. The lowest of the three, divided by your safety factor, becomes the working tension limit.
Concrete breakout capacity is calculated as:
$$N_b = k_c \sqrt{f’_c} \, h_{ef}^{1.5}$$
where $k_c$ is a coefficient you select (17 by default), $f’_c$ is concrete compressive strength, and $h_{ef}$ is the effective embedment depth. Because embedment depth is raised to the 1.5 power, going deeper has a much bigger effect on breakout capacity than a proportional increase in concrete strength does, since strength only enters as a square root.
Steel tension capacity depends on the thread root diameter, not the bolt’s nominal diameter, since that’s the smallest cross-section resisting the load. The calculator first finds the thread pitch: for UN threads you enter threads per inch (TPI) and it takes $p = 1/n$; for ISO threads you enter the pitch directly. It then finds the thread root diameter:
$$d_r = d – C_t \, p$$
where $C_t$ is 0.9743 for UN threads or 0.9382 for ISO threads. From there, the tensile stress area and steel capacity follow:
$$A_t = \frac{\pi}{4} d_r^2 \qquad N_{sa} = A_t \, f_u$$
where $f_u$ is the bolt’s ultimate tensile strength. The evaluated pullout capacity, $N_p$, isn’t calculated at all — it’s the value you enter directly, typically from a load test or an anchor’s rated capacity in a product evaluation report. The final working tension limit applies the safety factor $\Omega$ to whichever of the three is smallest:
$$N_{work} = \frac{\min(N_b,\, N_{sa},\, N_p)}{\Omega}$$
Worked Example
Take a 0.5 in bolt with a UN thread of 13 TPI, embedded 4.0 in into 3,000 psi concrete, with an ultimate tensile strength of 60,000 psi, a manufacturer-evaluated pullout capacity of 10,000 lbs, a concrete breakout coefficient $k_c$ of 17, and a safety factor of 4.0.
Thread pitch is $p = 1/13 = 0.0769$ in. Thread root diameter is $d_r = 0.5 – (0.9743 \times 0.0769) = 0.4251$ in. Tensile stress area is $A_t = \frac{\pi}{4}(0.4251)^2 = 0.1419$ sq in, giving a steel tension capacity of $N_{sa} = 0.1419 \times 60{,}000 = 8{,}513.91$ lbs.
Concrete breakout capacity is $N_b = 17 \times \sqrt{3{,}000} \times 4.0^{1.5} = 17 \times 54.77 \times 8 = 7{,}449.03$ lbs. The evaluated pullout capacity is the entered value, 10,000 lbs.
| Limit State | Key Inputs | Nominal Capacity |
|---|---|---|
| Basic Concrete Breakout | k_c = 17, f’c = 3,000 psi, h_ef = 4.0 in | 7,449.03 lbs |
| Steel Tension | thread root dia = 0.4251 in, f_u = 60,000 psi | 8,513.91 lbs |
| Evaluated Pullout | entered directly | 10,000.00 lbs |
Concrete breakout is the smallest of the three, so it governs. The working tension limit is $N_{work} = 7{,}449.03 / 4.0 = 1{,}862.26$ lbs. The next-closest limit state, steel tension, sits 1,064.88 lbs above the governing value — only about 1.14 times higher — while the evaluated pullout capacity is 1.34 times the governing value.
What the Result Means
Which of the three limit states governs tells you where the connection’s real weakness is. If concrete breakout governs, the embedment depth or concrete strength is what’s limiting the design, and a deeper embedment or stronger concrete raises the ceiling. If steel tension governs, the bolt itself would snap before the concrete or the tested anchor capacity comes into play, and a larger diameter or higher-grade bolt is what moves the number. If the evaluated pullout capacity governs, the anchor’s tested performance in that concrete is the limiting factor — increasing embedment or bolt strength won’t help until you use an anchor with a higher rated pullout value.
The ratio between the governing capacity and the next-closest one shows how much redundancy exists. A ratio close to 1.0 means two failure modes are nearly tied, so a small change in one input — a slightly weaker batch of concrete, a slightly undersized bolt — could shift which mode governs. A larger ratio means the governing mode has a comfortable lead over the next weakest path.
Area reduction shows how much cross-sectional area threading removes compared to the bolt’s smooth nominal diameter. In the worked example, threading cuts the load-bearing area by about 27.73%, which is why steel tension capacity is calculated from the thread root diameter rather than the full nominal diameter.
Embedment ratio ($h_{ef}/d$) is simply how deep the bolt is set relative to its own diameter — 8.0 in the worked example, meaning the embedment depth is eight times the nominal bolt diameter.
What Changes the Result
The $k_c$ coefficient scales concrete breakout capacity linearly — doubling it doubles $N_b$ directly, with no other effect on the calculation.
Embedment depth has an outsized effect because it’s raised to the 1.5 power in the breakout formula, while concrete strength only enters as a square root. A given percentage increase in embedment depth raises breakout capacity by more than the same percentage increase in concrete strength would.
Switching between UN and ISO thread standards changes the constant used to find thread root diameter — 0.9743 versus 0.9382 — which shifts the tensile stress area and, with it, steel tension capacity and the area-reduction percentage.
Thread pitch and nominal diameter have to be geometrically compatible. If the pitch is too coarse for the diameter entered, the thread root diameter comes out zero or negative, and the calculator halts with a warning instead of returning a result.
Concrete strength is restricted to 2,500–10,000 psi (17.24–68.95 MPa). Values outside that band stop the calculation rather than extrapolating beyond it.
The safety factor has a floor of 1.0 — it can be raised as high as you want, but it can’t go below unity. Raising it lowers the working tension limit proportionally without changing any of the three nominal capacities.
The evaluated pullout capacity you enter is a direct input, not a calculated value, so it caps the working tension limit outright whenever it’s lower than both the concrete and steel capacities.
Switching between imperial and metric units converts every field using fixed factors — 25.4 mm/in for length, 0.006894757293168 MPa/psi for stress, and 0.0044482216152605 kN/lb for force — but the underlying calculation always runs internally in inches, psi, and pounds regardless of which system is displayed.
FAQs
What formula does a bolt pull-out force calculator use for concrete breakout?
The concrete breakout capacity comes from $N_b = k_c \sqrt{f’_c} \, h_{ef}^{1.5}$, where $k_c$ is a coefficient (17 by default), $f’_c$ is concrete compressive strength, and $h_{ef}$ is embedment depth. Because embedment depth is raised to the 1.5 power, deepening a bolt has a much larger effect on breakout capacity than increasing its diameter does.
Why does the calculator show three different capacity numbers?
It’s checking three separate ways the connection can fail: the concrete can break out around the bolt, the bolt’s threaded section can fail in tension, or the anchor can pull out below its tested capacity. Whichever of the three produces the lowest number is the one that actually limits the connection, and that’s what the working tension limit is based on.
What safety factor should I use for anchor bolt pullout calculations?
The calculator requires a safety factor of at least 1.0 and defaults to 4.0, which divides the governing nominal capacity down to a working tension limit. A safety factor of 4.0 means the reported working load is 75% lower than the raw nominal capacity of whichever failure mode governs.
Why do I need to enter threads per inch (TPI) or thread pitch?
Thread pitch determines the thread root diameter, which is smaller than the bolt’s nominal diameter and is what actually resists tension in the threaded section. A finer thread pitch removes less material at the root, producing a slightly higher steel tension capacity than a coarser thread at the same nominal diameter.
What’s the difference between UN and ISO thread standards in this calculator?
UN threads use a root-diameter constant of 0.9743 and ISO threads use 0.9382, applied to the pitch when calculating thread root diameter. Because ISO’s constant is smaller, an ISO thread of the same nominal diameter and pitch leaves slightly more material at the root than a UN thread does.
Why did my calculation get halted with a warning?
The calculator only accepts concrete strengths between 2,500 and 10,000 psi (17.24 to 68.95 MPa) and a safety factor of 1.0 or higher; anything outside that range stops the calculation. It also checks that the entered thread pitch is physically possible for the nominal diameter you entered — a pitch too coarse for a given diameter triggers the same halt.
What does the embedment ratio tell you?
Embedment ratio is embedment depth divided by nominal bolt diameter ($h_{ef}/d$). It’s a quick way to see how deep the bolt is set relative to how thick it is, without comparing the two numbers separately.
How does switching between imperial and metric units affect the result?
Switching units converts every entered value using fixed factors: diameter and depth by 25.4 mm/in, stresses by 0.006894757293168 MPa/psi, and force by 0.0044482216152605 kN/lb. The underlying calculation always runs in inches, psi, and pounds internally, then converts the output back to whichever system is currently selected.