Roymech engineering encyclopedia

Thread Tensile Stress Area Calculator




Solid Print 3D


Use this thread tensile stress area calculator to estimate the tensile stress area of an ISO metric screw thread from nominal diameter and pitch. The calculator can also calculate bolt tensile stress from an applied axial load using the thread stress area.

What does this calculator do?

This calculator determines the tensile stress area of an ISO metric thread using the nominal thread diameter and pitch. It then uses the calculated stress area to estimate axial tensile stress in the threaded section of a bolt or screw.

The calculator provides:

  • ISO metric thread tensile stress area
  • comparison with nominal shank area
  • axial tensile stress using thread stress area
  • design allowable stress
  • utilisation percentage
  • factor of safety
  • pass/fail result
  • worked calculation

This is useful where the threaded portion of the bolt is the critical section rather than the plain shank.

Engineering note: This calculator is intended for preliminary engineering calculations and educational use. It uses the common ISO metric tensile stress area approximation. Final fastener design should consider the relevant standard, thread tolerance, bolt grade, engagement length, fatigue, preload and joint conditions.

How to Use the Calculator

  1. Enter the nominal thread diameter, d. For example, enter 10 for an M10 thread.
  2. Enter the thread pitch, p. For example, a standard coarse M10 thread has a pitch of 1.5 mm.
  3. Enter the tensile load, Ft. This is optional in principle, but used by this calculator to calculate tensile stress.
  4. Select the force unit. Loads may be entered in newtons or kilonewtons.
  5. Enter the allowable or yield stress. This is the stress limit used for the utilisation check.
  6. Enter the safety factor. The calculator divides the allowable or yield stress by the safety factor to obtain the design allowable stress.
  7. Click calculate. The calculator gives thread stress area, tensile stress, utilisation and factor of safety.

Thread Tensile Stress Area Diagram

Thread tensile stress area calculator diagram showing ISO metric thread nominal diameter, pitch and tensile stress area
ISO metric thread geometry showing nominal diameter, pitch and tensile stress area used for bolt tensile stress calculations.

Formulae Used

Thread tensile stress area:

As = π4 (d - 0.9382p)2

Nominal shank area:

An = πd24

Tensile stress using thread stress area:

σ = FtAs

Design allowable stress:

σdesign = σallowSF

Utilisation:

Utilisation = σσdesign × 100%

Factor of safety:

FoS = σallowσ

Variables

Symbol Description Units
d Nominal thread diameter mm
p Thread pitch mm
As Thread tensile stress area mm²
An Nominal shank area mm²
Ft Axial tensile load N
σ Tensile stress using thread stress area N/mm²
σallow Allowable or yield stress N/mm²
SF Safety factor -

Common ISO Metric Coarse Pitches

Thread Coarse Pitch
M6 1.0 mm
M8 1.25 mm
M10 1.5 mm
M12 1.75 mm
M16 2.0 mm
M20 2.5 mm
M24 3.0 mm

Calculator Inputs

Results

Enter the thread diameter, pitch and tensile load, then click calculate.

Understanding the Results

Result Meaning
Thread tensile stress area The effective tensile area of the threaded section, normally smaller than the nominal shank area.
Nominal shank area The circular area based on the nominal diameter. This is usually larger than the thread stress area.
Area reduction The percentage reduction from nominal shank area to thread stress area.
Tensile stress The axial tensile load divided by the thread tensile stress area.
Utilisation The calculated tensile stress divided by the design allowable stress. A value below 100% passes this simplified check.
Factor of safety The entered allowable or yield stress divided by the calculated tensile stress.

Calculator Limitations

This calculator gives a simplified ISO metric thread tensile stress area and tensile stress check. It does not check all possible thread or joint failure modes.

This Calculator Includes This Calculator Does Not Include
ISO metric thread stress area approximation Thread stripping check
Comparison with nominal shank area Nut or tapped hole strength
Tensile stress from axial load Thread tolerance class effects
Utilisation and factor of safety Fatigue or fluctuating load checks
Worked calculation Prying action, preload or joint stiffness

For a simple tensile check using a chosen bolt diameter, use the Bolt Tensile Stress Calculator.

For combined tensile and shear stress, use the Bolt Combined Stress Calculator.

For estimating preload from torque, use the Bolt Preload Calculator.

Thread Tensile Stress Area Calculation Notes

The tensile stress area is used because the threaded portion of a bolt has a smaller effective tensile area than the plain shank. If the threaded section is the critical section, using the nominal shank area can underestimate the tensile stress.

For ISO metric threads, a commonly used approximation for tensile stress area is:

As = π4 (d - 0.9382p)2

where d is the nominal thread diameter and p is the pitch. Both should be entered in millimetres.

For further screw thread data, see the RoyMech reference pages: Screw Stress Areas and ISO Metric Thread Dimensions.

For the full calculator section, see: Bolted Joint Calculators.

Thread Tensile Stress Area Calculator FAQ

What is thread tensile stress area?

Thread tensile stress area is the effective area of the threaded section used for tensile stress calculations. It is smaller than the nominal shank area because the thread root reduces the effective section.

How do you calculate ISO metric thread stress area?

A common approximation for ISO metric thread tensile stress area is:

As = π4 (d - 0.9382p)2

where d is the nominal diameter and p is the thread pitch.

Why is thread stress area smaller than shank area?

The thread root reduces the effective cross-section of the bolt. This means the threaded section usually has a smaller tensile area than the plain shank.

Should I use nominal area or thread stress area?

Use the area at the critical section. If the plain shank is critical, nominal shank area may be suitable. If the threaded section is critical, use the thread tensile stress area.

Can this calculator be used for fine pitch threads?

Yes. Enter the actual pitch for the thread. Fine pitch threads generally have a larger tensile stress area than coarse pitch threads of the same nominal diameter.

Does this calculator check thread stripping?

No. This calculator checks tensile stress in the threaded section. Thread stripping, nut strength and tapped hole engagement require separate checks.

�