# Bolt Torque Calculator

## Calculate required bolt torque

The relation between applied torque and axial force - or load - in a bolt can be calculated as

*T = K F d (1 - l/100) (1)*

*where *

*T = wrench torque (Nm, lb _{f} ft)*

*K = constant that depends on the bolt material and size *

*d = nominal bolt diameter (m, ft)*

*F = axial bolt force (N, lb _{f})*

*l = fubrication factor (%)*

Typical values for K with mild-steel bolts in range 1/4" to 1":

- normal dry:
*K = 0.2* - nonplated black finish:
*K = 0.3* - zinc-plated:
*K = 0.2* - slightly lubricated:
*K = 0.18* - cadmium-plated:
*K = 0.16*

**Note! **- be aware that this is a rough calculation - in addition the accuracy of a torque wrench is normally no better than +-25%.

### Bolt Torque Calculator

The calculator below can be used to calculate the torque required to achieve a given axial bolt force or load. The calculator is generic an can used for imperial and metric units as long as the use of units are consistent.

*K -* *constant*

* d - diameter of bolt (m, ft)*

* F - axial bolt force or load (N, lb _{f})*

* torque reduction due to lubrication (%)*

Note that standard dry torques are normally calculated to produce a tensile stress - or axial force or clamp load - in the bolt that equals to 70% of minimum tensile strength or 75% of proof strength.

### Example - Required torque for tightening a Imperial bolt

The required bolt clamping force for a joint is *20000 lbs*. The torque required for a *3/4"* dry steel bolt with *0%* lubrication to achieve this tension can be calculated as

*T _{dry} = (0.2) (20000 lb) (0.75 in) (1/12 ft/in) (1 - (0%) / (100%))*

* = 250 (lb _{f} ft)*

### Example - Required torque for tightening a Metric bolt to proof load

The proof load for a *M30* metric bolt grad 8.8 is *337000 N*. The torque required to achieve this tension with a dry bolt with *0%* lubrication can be calculated as

*T _{dry} = (0.2) (337000 N) (30 mm) (10^{-3} m/mm) *

* = 2022 (Nm)*

Lubricating the bolt with SAE 30 oil reduces the torque required to achieve the same tension with approximately 40%. The reduced torque can be calculated

*T _{SAE30} = (2022 Nm) (1 - (40%) / (100%))*

* = 1213 Nm*

### Bolt Force vs. Torque

Eq. 1 can be rearranged to express bolt force as

*F = T / (K d (1 - l / 100)) (1a)*

#### Example - Dry vs. Lubricated Bolt

The proof load for a *M30* metric bolt grad 8.8 is *337000 N*. The torque required to achieve this force with a **dry bolt** is calculated to * 2022 Nm*.

By failure the bolt is **lubricated** and tightened with the same torque *2022 Nm*. The force acting in the lubricated bolt can be calculated as

*F _{lubricated} = (2022 Nm) / (0.2 (0.03 m) (1 - (40%) / (100%))) *

* = 561667 N*

This is way above what the bolt can handle and **fatal failure** is likely.

### Bolt Force Calculator

This calculator can be used to calculate the force acting in a bolt.

*T - torque (Nm, lb _{f} ft)*

* K - constant*

* d - diameter bolt (m, ft)*

* torque reduction due to lubrication (%)*

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