Bolt Torque Calculator

The relation between applied torque and axial force - or load - in a bolt can be calculated in this general equation 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 = lubrication 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 where the screw pitch is not included. Typical Metric and Imperial bolt torques are indicated in the links below:

• Metric Bolts - Tightening Torques

• US Bolts - Tightening Torques

Manufacturing data should always be checked before use.

In addition the accuracy of a torque wrench is normally no better than +-25%.

• Improvised Torque Wrench

Typical metric and imperial bolyt torques

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.

• Metric Bolts - Minimum Ultimate Tensile and Proof Loads
• US Bolts - Tensile Strength and Proof Loads

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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 (%)

• Calculate bolt stress

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm