Screw Thread Calculator
Determines the clamping force a threaded fastener generates from applied torque, accounting for friction. Essential for engineers and mechanics sizing bolts or designing assemblies where clamping load is critical.
About this calculator
When torque is applied to a bolt, only a fraction converts to clamping force — the rest overcomes thread and bearing friction. The axial force (clamping load) is derived from: F = (T × 2π × TPI) / (π × D × (1 + μ × π × D / TPI)), where T is applied torque (lb-in), TPI is threads per inch, D is the major diameter (inches), and μ is the coefficient of friction. The term 2π × TPI captures the mechanical advantage of the helical thread, while the denominator accounts for friction losses along the thread flanks. A higher TPI (finer thread) increases mechanical advantage but also raises friction sensitivity. Typical friction coefficients range from 0.10–0.20 for lubricated to dry steel threads.
How to use
Suppose you have a 0.5-inch diameter bolt with 13 TPI, applying 50 lb-in of torque, and a friction coefficient of 0.15. Plug into the formula: F = (50 × 2π × 13) / (π × 0.5 × (1 + 0.15 × π × 0.5 / 13)). Numerator: 50 × 81.68 = 4084. Denominator: 1.5708 × (1 + 0.0181) = 1.5992. Result: F ≈ 4084 / 1.5992 ≈ 2554 lb of clamping force. This tells you the bolt generates roughly 2,554 lbf of clamp load under those conditions.
Frequently asked questions
How does thread pitch affect the clamping force of a bolt?
A finer thread (higher TPI) increases the mechanical advantage of the screw, meaning more of the applied torque is converted to axial clamping force. However, finer threads also have a shallower helix angle, which can increase sensitivity to friction variations. In practice, fine-thread bolts achieve higher clamping loads for the same torque compared to coarse-thread bolts of the same diameter. Engineers often prefer fine threads in precision or vibration-prone assemblies.
What is a typical coefficient of friction for threaded fasteners?
The coefficient of friction for threaded fasteners depends heavily on surface finish and lubrication. Dry, uncoated steel-on-steel threads typically have μ ≈ 0.15–0.20, while lubricated or zinc-plated threads fall around 0.10–0.15. Waxed or PTFE-coated fasteners can drop to μ ≈ 0.04–0.08. Using an inaccurate friction value is one of the most common sources of error in bolt torque calculations, so always verify the value for your specific fastener and lubricant combination.
Why does most of the torque applied to a bolt not become clamping force?
Research shows that roughly 50% of applied torque is consumed overcoming friction under the bolt head or nut, about 40% overcomes thread friction, and only about 10% actually produces clamping force in a dry assembly. This is why proper lubrication dramatically increases clamping efficiency — it reduces frictional losses and allows more torque to be converted to useful clamp load. The formula in this calculator captures thread friction specifically, which is why the coefficient of friction has such a large influence on the result.