Screw Torque Calculator
Calculates the torque needed to clamp a fastener to a target axial force, accounting for thread geometry and friction. Use it when tightening critical bolted joints to avoid under- or over-torquing.
Last updated: September 2026
Formula below · 2 sources (asme.org, Wikipedia) · Updated Sep 2026
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About this calculator
Tightening a screw converts applied torque into axial clamping force (bolt preload). The torque has three parts: advancing the thread up its helix, T_pitch = F × p / (2π); friction on the 60° thread flanks, T_thread = F × μ × r_m / cos 30°; and friction under the nut or bolt head, T_head = F × μ × r_head. Here F is the axial force (N), p the pitch (mm), r_m the mean (pitch) thread radius (mm), μ the friction coefficient (0.15 for dry steel is assumed for both thread and bearing face), and r_head the mean radius of the nut bearing face, taken as 0.625 × the nominal diameter for a standard hex nut, with the nominal diameter estimated as 2r_m + 0.65p. The formula used here is T = F × [p/(2π) + 0.15 × r_m / cos 30° + 0.15 × 0.625 × (2r_m + 0.65p)]. This is the standard torque–tension relationship (VDI 2230 / Shigley); it gives a nut factor K = T/(F·d) of about 0.2, the usual value for dry steel. With pitch and radius in mm the result is in N·mm; divide by 1,000 for N·m. Lubricated threads need much less torque for the same preload, so always use the friction value for your actual condition.
How to use
You need a bolt to generate 5,000 N of clamping force. The thread pitch is 1.5 mm and the mean thread radius is 4.5 mm (about an M10). Step 1 – Pitch torque: 5,000 × 1.5 / (2π) ≈ 1,194 N⋅mm. Step 2 – Thread friction: 5,000 × 0.15 × 4.5 / 0.866 ≈ 3,897 N⋅mm. Step 3 – Bearing-face friction: nominal diameter ≈ 2 × 4.5 + 0.65 × 1.5 = 9.97 mm, face radius 0.625 × 9.97 = 6.23 mm, so 5,000 × 0.15 × 6.23 ≈ 4,675 N⋅mm. Step 4 – Total torque ≈ 9,766 N⋅mm ≈ 9.8 N⋅m (nut factor 9,766 / (5,000 × 9.97) ≈ 0.196). The defaults (5,000 N, 1.5 mm pitch, 5 mm radius) give about 10,670 N⋅mm.
Frequently asked questions
Why does thread pitch affect the torque required to tighten a screw?
Thread pitch determines the mechanical advantage of the screw's helical ramp. A finer pitch (smaller value) means more thread turns are needed to advance the fastener by a given distance, but each turn requires less torque — and more of the applied torque converts into clamping force. A coarser pitch advances faster per turn but is less efficient at converting torque to preload. For precision clamping applications, fine-pitched threads are often preferred because they allow more accurate torque-to-preload relationships.
What happens if I apply too much or too little torque to a bolted joint?
Under-torquing leaves the joint with insufficient preload, allowing the joint faces to separate under load, which causes fatigue cracking, loosening, and potential leakage in sealed systems. Over-torquing can yield or fracture the bolt, strip the threads, or crush the clamped material — failures that are often sudden and catastrophic. Correct torque specification, combined with calibrated torque wrenches, is therefore essential for safety-critical assemblies such as engine heads, wheel hubs, and pressure flanges.
How does friction coefficient affect the accuracy of the torque-to-preload relationship?
Up to 90% of applied tightening torque is consumed by friction — roughly 40% under the nut face and 50% in the thread engagement — with only the remainder generating useful clamping force. Because the friction coefficient varies significantly with lubrication, plating, and surface finish, small changes in μ cause large changes in actual preload for a given torque. This is why lubricated fasteners require a different (lower) torque than dry ones to achieve the same preload, and why engineers specify both the torque value and the lubrication condition in assembly procedures.