Pull Out Force Calculator: Formula & Examples

A pull out force calculator estimates the force needed to pull a fastener, anchor, or connector out of a material, or the force a magnetic or adhesive assembly can resist before separation. You enter the relevant dimensions and material properties, and the calculator returns the maximum pull out force in your chosen unit (newtons, pounds-force, or kilograms-force). The exact formula depends on the application, so this guide covers the most common cases: threaded fasteners in metal, anchors in concrete, magnets, and adhesive bonds.

Formula

For a threaded fastener or a cylindrical rod embedded in a material, the pull out force is calculated using the shear area of the interface:

F = π × d × t × S_u

• F = pull out force (newtons, N)
• d = nominal diameter of the fastener (mm)
• t = engagement length (mm) – the depth the fastener is embedded
• S_u = ultimate tensile strength of the weaker material (MPa, N/mm²)

This assumes the failure occurs along the cylindrical interface between the fastener and the surrounding material. The result is in newtons; divide by 1000 to get kilonewtons (kN) or multiply by 0.2248 to get pounds-force (lbf).

Worked Example

Using the default values from the calculator above:

• Fastener diameter, d = 10 mm
• Engagement length, t = 20 mm
• Material ultimate tensile strength, S_u = 400 MPa

Step 1: Calculate the shear area:

A = π × 10 mm × 20 mm = 628.3 mm²

Step 2: Multiply by the tensile strength:

F = 628.3 mm² × 400 N/mm² = 251,327 N

Step 3: Convert to kN:

F = 251,327 N ÷ 1000 = 251.3 kN

So the pull out force is approximately 251.3 kN (about 56,500 lbf). This matches the calculator output for the default values.

When to Use This Calculator

This calculation is used in mechanical design, construction, and product engineering to verify that a connection will not fail under a pulling load. Common applications include:

• Selecting the length and diameter of a bolt or screw for a given load
• Checking the holding power of an anchor in concrete or masonry
• Designing threaded inserts in plastic or metal parts
• Estimating the force needed to extract a pin, rivet, or dowel
• Evaluating magnet or adhesive pull-off forces (with different formulas)

How to Choose the Right Formula

The formula above works for a solid cylindrical interface with full contact. For other situations, you need a different approach:

• Threaded fasteners in metal: Use the thread shear area formula, which accounts for thread geometry. A common approximation is F = A_s × S_u, where A_s is the tensile stress area of the thread.
• Concrete anchors: Concrete breakout strength depends on embedment depth, concrete strength, and edge distances. Use ACI 318 or similar design codes – the simple cylindrical formula is not accurate for concrete.
• Magnets: Pull force for a magnet depends on the magnetic circuit, gap, and material. Use the magnet’s rated pull force (often given by the manufacturer) or a magnetic circuit calculator.
• Adhesive bonds: The pull force is the shear strength of the adhesive (N/mm²) multiplied by the bonded area.

Common Mistakes and Misconceptions

One frequent error is using the tensile strength of the fastener material instead of the weaker of the two materials. If the surrounding material is softer, failure will occur there. Another mistake is confusing engagement length with total fastener length – the engagement is only the portion that is actually embedded in the material.

Unit mix-ups are also common. Tensile strength is often given in MPa (N/mm²), but sometimes in psi. If you use psi with mm dimensions, the result is off by a factor of about 1550. Always convert to consistent units (e.g., N/mm² with mm) before calculating.

This formula assumes a uniform stress distribution along the interface. In reality, stress is higher at the loaded end, so the actual pull out force may be lower, especially for long engagement lengths. For critical applications, use a safety factor of 2 to 4.

Limitations of the Formula

The cylindrical shear formula is a simplification. It does not account for:

• Stress concentration at the pull end
• Thread geometry (for threaded fasteners, use thread shear area)
• Material ductility or brittleness
• Temperature effects
• Dynamic or impact loads
• Edge effects in concrete anchors

For safety-critical applications, always verify with physical testing or consult a design standard. The calculator gives a theoretical estimate, not a certified design value.

Safety and Accuracy Notes

When using any pull out force calculation, always apply a safety factor. The theoretical maximum is the point of failure; in practice, you want the working load to be well below that. For permanent installations, consider environmental factors like corrosion, moisture, and temperature cycling, which can reduce holding power over time.

If you are designing a lifting point, a fall protection anchor, or any component that could cause injury if it fails, do not rely solely on this calculator. Use a certified engineer and follow applicable standards (e.g., ASME B30 for lifting, OSHA for fall protection).

Frequently Asked Questions

What is the difference between pull out force and pull off force?

Pull out force usually refers to a fastener or anchor being pulled out of a material along its axis. Pull off force is more often used for magnets or adhesive tapes – the force needed to separate two surfaces perpendicular to them. The formulas differ: pull out uses shear area, while pull off for magnets uses magnetic flux density and area.

How do I convert the result to pounds-force?

1 kN = 224.809 lbf. Multiply the kilonewton result by 224.8 to get pounds-force. For example, 251.3 kN × 224.8 = 56,500 lbf.

Does the formula work for wood screws?

Not directly. Wood screw pull out strength depends on the wood species, screw diameter, and depth of penetration. A common empirical formula is F = S_g × D × L, where S_g is the specific gravity of the wood, D is the screw diameter, and L is the penetration depth. The values are different from the metal formula.

What is a typical safety factor for pull out connections?

For static loads in non-critical applications, a safety factor of 2 to 3 is common. For dynamic loads, lifting, or human safety, use 5 or higher. When in doubt, consult a design standard for your specific industry.

Can I use this calculator for concrete anchors?

No, concrete anchor pull out strength is governed by concrete breakout, not pure shear of the interface. Use design codes like ACI 318 or manufacturer data. The cylindrical formula would overestimate the strength significantly.

Why does the calculator give a much higher force than a physical test?

Real-world factors – misalignment, uneven stress distribution, material defects, and the method of load application – reduce the actual capacity. Also, the formula assumes perfect bonding over the entire engagement length, which is rarely true. Always test a sample or use a conservative safety factor.

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in d | Fastener diameter | mm | 10 | 0
in t | Engagement length | mm | 20 | 0
in Su | Material ultimate tensile strength | MPa | 400 | 0
out F | Pull out force | kN | (pi * d * t * Su) / 1000 | 1
out F_lb | Pull out force | lbf | ((pi * d * t * Su) / 1000) * 224.809 | 0