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.
Last updated: September 2026
Formula below · 2 sources (asme.org, Wikipedia) · Updated Sep 2026
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About this calculator
When torque is applied to a bolt, only a small fraction (about 10–15% for dry steel) becomes clamping force; the rest overcomes friction in the threads and under the nut or head. The torque–tension relationship (VDI 2230 / Shigley) is T = F × [p/(2π) + μ × r_t / cos 30° + μ × r_n], so the axial force is F = T / [p/(2π) + μ r_t / cos 30° + μ r_n], where T is the applied torque (lb-in), p = 1/TPI is the pitch (in), r_t = (D − 0.6495p)/2 is the thread pitch radius, r_n = 0.625 × D is the mean radius of a standard hex nut bearing face, D is the major diameter (in), and μ is the friction coefficient, assumed the same in the threads and under the nut. The result corresponds to a nut factor K = T/(F·D) of about 0.2 for μ = 0.15. Typical friction coefficients range from 0.10–0.12 for lubricated to 0.15–0.20 for dry steel threads.
How to use
Suppose you have a 1/2-13 bolt, applying 50 lb-in of torque, with a friction coefficient of 0.15. Pitch p = 1/13 = 0.0769 in. Terms: p/(2π) = 0.01224 in; thread friction 0.15 × 0.2250 / 0.866 = 0.03898 in (r_t = (0.5 − 0.6495 × 0.0769)/2 = 0.2250 in); nut-face friction 0.15 × 0.625 × 0.5 = 0.04688 in. Sum = 0.0981 in. F = 50 / 0.0981 ≈ 510 lb of clamping force, a nut factor of 50 / (510 × 0.5) ≈ 0.196. A lubricated bolt (μ = 0.10) would reach about 720 lb with the same torque.
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?
Roughly 50% of applied torque is consumed by friction under the nut or bolt head, about 40% by thread friction, and only about 10% produces clamping force in a dry assembly. This calculator includes both friction terms (and the small pitch term), which is why the clamp force per unit torque is modest and why lubrication, which lowers μ, raises clamp force noticeably for the same torque.
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