Stud and Nut Preload Calculator and Equations

Bolt and Nut Preload Force Calculator

Engineering Calculators
ANSI Hardware Guide
ISO Hardware Guide
Torque Engineering and Design
Strength of Materials

The following calculator will determine the preload engineering data of a stud and nut installation or other fastener under the load of torque. All engineering units must be entered consistent.

Equations used:

Bolt Preload Equation 1

Bolt Preload Equation 3

Input Number Displayed in BOLD, Results in RED, All units in N, mm, degrees
Description	Input
Number of bolts
Young's modulus of bolt
Poisson ratio of bolt
Young's modulus of flange
Poisson ratio of flange
Upper flange thickness
Lower flange thickness
Total resulting effective flange thickness
Bolt diameter
Bolt thread root diameter
Bolt clearance hole
Bolt head diameter
Nut thickness (enter 0 if threaded into flange)
Thickness of bolt head
Bolt length assumed equal total effective flange thickness + nut
Cone angle
Preload force applied to a bolt
Maximum bolt stress
% of max stress used by bolt preload
Description	Stiffness Results
Tensile stiffness of a bolt shaft
Shear stiffness of a bolt head
Shear stiffness of a nut
Total stiffness of all bolts
Compressive stiffness of top flange in series with bottom flange
Shear stiffness of top flange in series with bottom flange
Total stiffness of all flange elements under all bolts
Ratio flange-to-bolt stiffness
total joint stiffness
Description	Force Results
Maximum allowable force on a bolt
Total force that can be applied to joint till joint preload is lost
Force added to each bolt preload force by leak
Total force on a bolt when the joint starts to leak
Force on joint at which bolts break
Preload stress in a bolt (based on thread root diameter)
Total stress in a bolt when joint begins to leak
% of max stress used by total bolt load
Fbreak/Fleak: resulting safety factor
Preload
Description	Joint stiffness
Joint stiffness pressure (N/mm/mm²)
Diameter of stress cone at center of flange (joint)
Area of stress cone at flange joint
Area under bolt head
Joint stiffness under bolt head
Joint stiffness flange-to-flange