TAHA Engineering Toolsby TAHA Knowledge Lab

Mechanical Engineering

Bolt Tightening Torque Estimator

Tightening torque from preload (T = K·F·d), preload from torque, or a preload target from proof strength.

Inputs

Calculate from
A bolt with a head and a nut clamping two plates together, torque T applied to the nut and preload arrows on the bolt.TFd
Turning the nut with torque T stretches the bolt and clamps the plates with preload F. Most of the torque is used to overcome friction in the threads and under the nut, which is why the nut factor K varies so much. Diagram not to scale.

Depends strongly on surface finish and lubrication. 0.2 is a widely used general value for unlubricated steel; lubricated or coated fasteners can be much lower. Use the fastener or lubricant supplier’s value when available.

Result

Tightening torque
50
Torque if K is ±25% different
37.5 to 62.5 N·m (K from 0.15 to 0.25)
Working
T = K × F × d = 0.2 × 25 kN × 10 mm = 50 N·m

Tighten to about 50 N·m. Because friction varies, the actual preload may differ widely from this estimate.

Educational estimate — check the assumptions below.

About this calculator

A bolt works by being stretched to a preload that clamps the joint together. In the workshop, preload is usually set indirectly by tightening torque. The short-form torque equation T = K × F × d links the two through the nut factor K, which lumps together thread and under-head friction. K changes a lot with finish and lubrication, so this tool is an estimate and lets you choose K yourself.

The third mode sets a target preload as a percentage of the bolt’s proof load, using the standard tensile stress area of the thread.

Formula

Torque from preload

T = K × Fi × d

T = tightening torque, K = nut factor, Fi = preload, d = nominal diameter.

Preload from torque

Fi = T ÷ (K × d)

T = tightening torque, K = nut factor, d = nominal diameter.

Preload target from proof strength

At = π/4 × (d − 0.9382 P)² (metric)    At = π/4 × (d − 0.9743 ÷ n)² (Unified)

Fi = (% ÷ 100) × At × Sp    T = K × Fi × d

At = tensile stress area, P = pitch, n = threads per inch, Sp = proof strength of the bolt grade.

Worked example

M10 × 1.5 bolt, property class 8.8 (proof strength 580 MPa in ISO 898-1), target 75% of proof load, K = 0.2:

  • At = π/4 × (10 − 0.9382 × 1.5)² = 57.99 mm² (the standard value is 58.0 mm²)
  • Preload = 0.75 × 57.99 × 580 = 25.2 kN
  • Torque = 0.2 × 25 225 N × 0.010 m = 50.5 N·m — but with K anywhere from 0.15 to 0.25 it would be 37.8 to 63.1 N·m.

Assumptions and limitations

  • The short-form torque equation is an approximation. Typical torque tightening gives a preload scatter of about ±25% or more, even with a calibrated wrench.
  • K, proof strength and the target percentage are your inputs. Where the manufacturer, a design code or a drawing gives a tightening torque, use that instead.
  • Gaskets, soft joints, plated or stainless fasteners (galling), and re-used fasteners can behave very differently. Critical joints may need tension-control methods (angle tightening, direct-tension indicators, ultrasonic measurement).

Safety note

Over-tightening can break bolts or strip threads; under-tightening can let joints loosen. For pressure, lifting, structural and safety-critical joints, follow the specified procedure and torque.

References

  • Short-form torque–preload relation T = K F d (e.g. Shigley’s Mechanical Engineering Design, chapter on screws and fasteners).
  • Tensile stress area: ISO 898-1 (metric), ASME B1.1 (Unified).
  • VDI 2230 (systematic calculation of highly stressed bolted joints).