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.
About this calculator
Tightening a screw converts applied torque into an axial clamping force (bolt preload). The total torque has two main components: the torque needed to advance the thread (overcoming the thread's helical ramp) and the torque lost to friction under the nut or bolt head. The thread component is given by T_thread = F × p / (2π), where F is the axial force in N and p is the thread pitch in mm. The friction component is approximated as T_friction = F × r_m × μ, where r_m is the mean thread radius and μ is the thread friction coefficient (commonly taken as 0.15 for dry steel). The formula used here is T = (F × p / (2π)) + (F × r_m × 0.15), combining both effects. Note that units must be consistent: if pitch and radius are in mm, the resulting torque will be in N⋅mm; divide by 1,000 for N⋅m. Accurate torque specification is critical in structural, automotive, and pressure-vessel bolted joints.
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. Step 1 – Thread torque: T_thread = 5,000 × 1.5 / (2π) = 7,500 / 6.2832 ≈ 1,194 N⋅mm. Step 2 – Friction torque: T_friction = 5,000 × 4.5 × 0.15 = 3,375 N⋅mm. Step 3 – Total torque: T = 1,194 + 3,375 = 4,569 N⋅mm ≈ 4.57 N⋅m. Enter 1.5 in Thread Pitch, 5,000 in Axial Force, and 4.5 in Mean Thread Radius to confirm this result.
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.