KasperCalc: External Thread Stress Calculator

External Thread Stress Calculator | AS8879 / UNC / UNF / Metric

For bolts, screws and studs. For the threads of a nut or tapped hole, use the Internal Thread Stress Calculator.

Inputs

1. Thread Selection

Thread Standard

Thread Size

Major Dia d (in)

TPI

Enter the external thread’s major diameter and TPI. The pitch diameter and stress area are calculated for you.

Extra custom threads – override the calculated values

Pitch Dia d_m (in)

Stress Area (in²)

Thread Half Angle β (°)

Leave a box blank to use the calculated value (30° for the half angle). Fill one in for Acme, buttress, rolled, or any thread that is not a basic 60° form.

3. Applied Torque

Applied Torque T_applied (in-lb)

Prevailing & seal drag torque

Prevailing / Run-in Torque T_prevailing (in-lb)

O-Ring / Seal Drag Torque T_drag (in-lb)

Net torque available for preload = T_applied − T_prevailing − T_drag

5. Material Properties

Material Preset

F_tu – Ultimate (ksi)

F_ty – Yield (ksi)

F_tu (ksi)

F_ty (ksi)

2. Friction & Bearing Geometry

Friction Coefficient Preset (Src: Engineering Toolbox)

Friction Coefficient μ₁

Collar / bearing face & collar friction

Collar OD D_H (in)

Collar ID D_h (in)

Collar Friction μ₂ – blank uses μ₁

Collar dims = bearing contact surface under bolt head or nut face. A separate μ₂ covers a lubricated thread under a dry face, or a washer of a different finish.

4. Pressure Load – Proof / Burst (Optional)

Proof Pressure (psig)

Burst Pressure (psig)

Pressure Acting Area (in²) – defaults to stress area if 0

Joint Stiffness Factor C = k_b/(k_b + k_m) – 1.0 is conservative

Leave pressures at 0 for pure torque analysis.

6. Joint Checks – Shear / Tension & Pull-Out (Optional)

Fitting Factor (applied to the joint-check loads)

Combined shear & tension (NASA-TM-2012-217454)

Shear Load P_s (lb)

Tension P_t (lb) – blank = worst case

Shear Plane Passes Through

F_su – Shear Ultimate (ksi)

Shank Dia (in) – blank = major d

Thread pull-out from a tapped hole (NASA-RP-1228)

Engagement Length L (in)

Tapped-Material F_s (ksi)

Thread Mismatch Factor h

Mean Dia d_M (in) – blank = d_m

F_s is the shear strength of the weaker member, usually the tapped part (27 ksi / 186 MPa ≈ 6061-T6, 48 ksi / 331 MPa ≈ 7075-T6). The load is the worst axial case above.

Results

Fill in inputs on the left and click Calculate.

Margins of Safety

Load Case	Total Axial Force (lb)	Thread Stress σ (psi)	MS Yield	MS Ultimate

Where the Torque Goes

Only the “bolt stretch” share, F·(d_m/2)·tan α, does work on the joint. The rest is friction, which is why the preload is so sensitive to lubrication.

Joint Checks

Check	Load	Allowable	Interaction / Detail	MS

Intermediate Values ▶

Parametric: MS vs Friction Coefficient (at T_applied)

Preload and margins swept across μ₁ values. Selected μ₁ highlighted ◀

μ₁	K₁ (in)	K₂ (in)	F_preload (lb)	σ_preload (psi)	MS Yield	MS Ult

Critical Torque Limits

Maximum torque before yielding or fracture, computed by back-solving from the allowable thread stress. Includes T_prevailing and T_drag. Additional pressure load is not included here.

Method & Equations

Overview

This page analyses the external thread, the bolt, screw or stud. The internal thread of a nut or tapped hole is checked on the Internal Thread Stress Calculator, which uses the same thread tables and materials.

When a threaded fastener is torqued, the applied torque is resisted by two mechanisms: friction on the thread faces and friction on the bearing (collar) surface under the nut or bolt head. Only the remaining torque — after overcoming thread helix and both friction components — is converted into axial clamping preload. This calculator implements the standard torque–preload relationship derived from inclined-plane and collar-friction mechanics, consistent with ASME B1.1, Shigley's Mechanical Engineering Design, and aerospace thread stress practices per AS8879.

Torque Balance

The total applied torque must be balanced by thread torque, collar torque, and any drag/prevailing torques:

Torque balance $$T_\text{applied} = T_1 + T_2 + T_\text{prevailing} + T_\text{drag}$$

Rearranging for the net torque available to generate preload:

Net torque $$T_\text{net} = T_\text{applied} - T_\text{prevailing} - T_\text{drag}$$

Thread Torque Coefficient K₁

Fig. 1 — Flank angle β and lead angle α (click to enlarge)

$T_1 = K_1 \cdot F$, where $K_1$ is the thread torque nut factor derived from inclined-plane mechanics with Coulomb friction on the thread helix:

Thread torque coefficient K₁ $$K_1 = \frac{d_m}{2} \cdot \frac{\tan\alpha + \mu_1 \sec\beta}{1 - \mu_1 \tan\alpha \sec\beta}$$

where:

$d_m$ = thread pitch diameter (in)
$\alpha$ = thread lead angle (helix angle): $\tan\alpha = \dfrac{1}{\pi \, d_m \cdot \text{TPI}}$
$\beta$ = thread half-angle = 30° for 60° unified (UN/UNJ/Metric) threads
$\mu_1$ = coefficient of friction on thread faces
$\sec\beta = 1/\cos\beta$ — accounts for the inclined thread flank projecting the normal force

The $\sec\beta$ term distinguishes a V-thread from a square thread: the inclined flanks increase the normal (and therefore frictional) force compared to a flat-faced square thread with the same lead angle.

Collar Torque Coefficient K₂ & Preload Force

$T_2 = K_2 \cdot F$, where $K_2$ is derived by integrating the friction moment over the contact annulus under the bolt head or nut face:

Collar torque coefficient K₂ $$K_2 = \frac{\mu_1}{3} \cdot \frac{D_H^3 - D_h^3}{D_H^2 - D_h^2}$$

where $D_H$ = outer diameter and $D_h$ = inner diameter of the collar contact surface.

The resulting preload force:

Preload force $$F_\text{preload} = \frac{T_\text{net}}{K_1 + K_2}$$

Bolt joint section and top view: torque applied to the bolt head, the bolt face annulus bearing on the top plate, thread engagement in the base, and the annulus contact area A = (pi/4)(OD^2 - ID^2)

Fig. 2 — Bolt Face Annulus (Collar Contact) & Applied Torque (click to enlarge)

Thread Tensile Stress & Margin of Safety

Thread tensile stress $$\sigma_t = \frac{F_\text{total}}{A_s}$$

where $F_\text{total} = F_\text{preload} + F_\text{pressure}$ and $A_s$ is the tensile stress area from ASME B1.1 / AS8879 / ISO 898.

Margin of safety $$MS_\text{yield} = \frac{F_{ty}}{\sigma_t} - 1 \qquad MS_\text{ultimate} = \frac{F_{tu}}{\sigma_t} - 1$$

A positive MS indicates adequate design margin. A negative MS indicates failure under the applied load.

Critical Torque (Back-Solved)

The maximum torque before yielding or fracture is found by back-solving from the material allowable stress:

Critical torque — back-solve $$F_\text{allow} = F_{ty} \text{ (or } F_{tu}\text{)} \cdot A_s$$ $$T_\text{critical} = F_\text{allow} \cdot (K_1 + K_2) + T_\text{prevailing} + T_\text{drag}$$

AS8879 Thread Note

AS8879 (formerly MIL-S-8879) specifies UNJ (coarse) and UNJF (fine) aerospace threads. These differ from standard UN threads by having a controlled radius root on the external thread, which significantly improves fatigue life by reducing stress concentration at the thread root. AS8879 threads are the preferred aerospace thread form for structural fasteners per NAS and military standards.

Combined Shear & Tension (NASA-TM-2012-217454)

A fastener carrying shear and tension together fails before either load alone would break it. NASA-TM-2012-217454 tested this and fitted separate interaction curves depending on whether the shear plane cuts the full-diameter shank or the threads:

Load ratios $$R_s = \frac{P_s}{P_{su}}, \qquad R_t = \frac{P_t}{P_{tu}}$$

Interaction curves $$\text{shank: } R_s^{2.5} + R_t^{1.5} = 1 \qquad \text{threads: } R_s^{1.2} + R_t^{2} = 1$$

P_su = F_su·πd²/4 for a shank and F_su·A_s for threads in the shear plane (the stress area standing in for the root area); P_tu = F_tu·A_s. The margin is radial: the factor that scales both loads together until the point reaches the curve, less one. Threads in the shear plane give the more punishing curve, which is one more reason to keep them out of it.

The tension used is the worst axial case from the margins table (preload, or preload plus pressure) unless a value is entered. Where the joint stays clamped, the bolt tension under external load sits near the preload, so the preload is the right figure; where it separates, enter the external tension.

Source: NASA-TM-2012-217454, the interaction equations (PDF, 5.6 MB), a public-domain NASA report mirrored here.

Thread Pull-Out from a Tapped Hole (NASA-RP-1228)

Bolt threaded into a tapped part, with the internal thread stripping along a cylinder at the mean diameter over the engaged length L under the pull P

Fig. 3 — The shear cylinder of a stripped tapped hole (click to enlarge)

A steel bolt in a tapped aluminum part usually strips the softer internal thread before the bolt breaks. NASA-RP-1228 (Fastener Design Manual) sizes the engagement from the shear area of the internal thread:

Allowable pull-out load $$P_\text{allow} = h\,\pi\,d_M\,F_s\,L$$

with d_M the mean diameter of the tapped hole (the pitch diameter is used if blank), F_s the shear strength of the weaker material, L the length of engagement, and h an empirical factor for thread mismatch. If the threads mated perfectly h would be 1/2, the cylinder of the hole split equally between the two thread forms; the manual recommends 1/3 to allow for the mismatch of real threads.

The page also reports the engagement needed for the internal thread to match the full bolt ultimate, $L = F_{tu} A_s / (h \pi d_M F_s)$, the usual way the depth of a tapped hole is chosen.

That one empirical factor stands in for the thread geometry. To size the stripping areas of both the internal and the external thread from the thread form and the percent thread of the tapped hole, and see which one strips first, use the Internal Thread Stress Calculator.

Source: NASA-RP-1228, Fastener Design Manual, the pull-out formula (PDF, 5.1 MB), a public-domain NASA report mirrored here.

External Load and Joint Stiffness

A preloaded bolt does not feel an external tension load one-for-one. The bolt and the clamped parts act as two springs in parallel: an external load P_ext stretches the bolt a little further and unloads the clamped parts by most of the rest. While the joint stays closed, only a fraction C of the load reaches the bolt:

Bolt load in a clamped joint $$F_b = F_\text{preload} + C\,P_\text{ext}, \qquad C = \frac{k_b}{k_b + k_m}$$

k_b is the bolt’s axial stiffness and k_m the stiffness of the clamped members. For a steel bolt clamping steel or aluminum plates, C is typically 0.15–0.35. The joint opens when the clamped parts are fully unloaded:

Separation load $$P_\text{sep} = \frac{F_\text{preload}}{1 - C}$$

Beyond that the bolt carries the whole external load, and a seal or a fatigue-sensitive bolt is in trouble. Leaving C at 1.0, the default, adds the whole pressure load to the preload, which is conservative for bolt stress but hides the separation check. Enter a C from your joint stiffness calculation (Shigley ch. 8, or VDI 2230) to see both; the margins table marks any case where the joint has opened.

Choosing a Preload

Higher preload is almost always better: it keeps the joint closed under external load, reduces the alternating stress the bolt sees in fatigue, and resists loosening. Common targets, as a fraction of the bolt’s proof load F_p = A_sS_p:

0.75 F_p for joints that will be taken apart and reused (Shigley, eq. 8-31).
0.90 F_p for permanent joints.
Aerospace practice often specifies the torque table of the fastener standard (NASM, NAS) rather than a preload, which lands at roughly 50–70% of the bolt’s yield load for typical lubrication.

Torque is a poor proxy for preload. With the friction coefficient known only to ±20–30%, a torque-controlled bolt has a preload scatter of about ±25% (Bickford), which is why the parametric table on this page sweeps μ. Where preload matters, control it directly: turn-of-nut, load-indicating washers, ultrasonic or strain-gauged bolts. Size the torque so that the low-friction end of the scatter does not yield the bolt, using the critical-torque results above.

Worked Example: A 3/8″ A-286 Bolt

A 3/8-24 UNJF A-286 bolt (F_tu = 145 ksi, F_ty = 95 ksi in the presets) is torqued to 250 in-lb with light oil, μ = 0.15 on both the threads and the head. The head bears on a 0.5625″ OD, 0.390″ ID annulus. The joint also carries 1,000 lb of shear through the full-diameter shank, and the bolt threads 9/16″ (1.5D) into a 6061-T6 part. Load this example into the calculator.

Step 1 — torque coefficients $$\tan\alpha = \frac{1}{\pi d_m n} = \frac{1}{\pi(0.3479)(24)} = 0.03812, \qquad K_1 = \frac{d_m}{2}\,\frac{\tan\alpha + \mu\sec\beta}{1 - \mu\tan\alpha\sec\beta} = 0.03700\ \text{in}$$ $$K_2 = \frac{\mu}{3}\,\frac{D_H^3 - D_h^3}{D_H^2 - D_h^2} = 0.03611\ \text{in}$$

Step 2 — preload and stress $$F = \frac{250}{0.03700 + 0.03611} = 3{,}419\ \text{lb}, \qquad \sigma = \frac{3{,}419}{0.0875} = 39.1\ \text{ksi}$$ $$MS_{yield} = \frac{95}{39.1} - 1 = +1.43, \qquad MS_{ult} = \frac{145}{39.1} - 1 = +2.71$$

Step 3 — where the torque went $$T_{pitch} = F\,\frac{d_m}{2}\tan\alpha = 22.7, \qquad T_{thread\ friction} = 103.9, \qquad T_{collar} = 123.5\ \text{in-lb}$$

Only 9% of the wrench torque stretches the bolt; 42% is lost in the threads and 49% under the head. That is why lubrication changes the preload so much. The same torque with μ = 0.10 would give 44% more preload. The equivalent nut factor is K = (K₁ + K₂)/d = 0.195, close to the familiar 0.2.

Step 4 — critical torques $$T_{yield} = F_{ty}A_s(K_1+K_2) = 608\ \text{in-lb}, \qquad T_{ult} = 928\ \text{in-lb}$$

Step 5 — combined shear and tension, shank $$R_s = \frac{1{,}000}{0.6(145{,}000)\,\pi(0.375)^2/4} = 0.104, \qquad R_t = \frac{3{,}419}{145{,}000(0.0875)} = 0.270, \qquad R_s^{2.5} + R_t^{1.5} = 0.143 \;\Rightarrow\; MS = +2.51$$

Step 6 — thread pull-out of the aluminum $$P_{allow} = \tfrac{1}{3}\,\pi(0.3479)(27{,}000)(0.5625) = 5{,}533\ \text{lb} \;\Rightarrow\; MS = +0.62, \qquad L_{full} = \frac{F_{tu}A_s}{h\pi d_M F_s} = 1.29\ \text{in}$$

The aluminum threads hold the preload comfortably but would strip long before the bolt broke: matching the bolt’s ultimate needs 1.29″ of engagement, 3.4 diameters. In practice that is the case for a helical or key-locked insert, which moves the shear cylinder out to a larger diameter.

Verification

The joint checks (js/fastener-math.js) run in automated tests against hand calculations from the two NASA reports:

Case	By hand	This page
Shank, P_s 12,000 / P_t 15,000 lb, allowables 30,000 lb, factor 1.15	k such that (kR_s)^2.5 + (kR_t)^1.5 = 1	MS +0.359
Threads, same loads	(kR_s)^1.2 + (kR_t)² = 1	MS +0.226
Pull-out, ½″ mean dia, 0.25″ engagement, F_s 63 ksi	⅓·π·0.5·63,000·0.25 = 8,247 lb	8,247 lb

The interaction margin is the exact root of the NASA-TM-2012-217454 curve along the load line, not a reading off a plotted chart.

Friction Coefficient Reference

Friction Coefficients for Common Fastener Material Pairs

The friction coefficient $\mu_1$ has a dominant effect on the torque–preload relationship. Values below are sourced from Engineering Toolbox, Shigley's (Table 8-15), and Bickford's Bolted Joints.

Material 1	Material 2	Condition / Lubricant	μ static	μ kinetic	Fastener Relevance
PTFE / Solid Film / Graphite Lubricants
PTFE (Teflon)	PTFE	Dry or greased	0.04	0.04	PTFE-coated fasteners; extreme low-friction baseline
Steel	Steel	Graphite lubricant	—	0.058	Graphite-lubricated threads (kinetic)
Carbon (hard)	Carbon	Dry	0.16	—	Carbon-coated contact surfaces
Graphite	Steel	Dry	0.10	—	Graphite-coated steel threads
Greased / Well-Lubricated Metal Pairs
Cadmium	Cadmium	Greased	0.05	—	Cad-plated fasteners, greased
Copper	Copper	Greased	0.08	—	Copper-alloy thread inserts, greased
Steel	Steel	Greased ★	0.16	—	Typical value for lubricated steel/SS threaded fasteners
Nickel	Mild Steel	Greased	—	0.178	Nickel-alloy into mild steel, greased
Lightly Lubricated / Oiled
Steel	Steel	Light mineral oil (static)	0.23	—	Lightly oiled threads (use static for install)
Steel	Steel	Castor oil (kinetic)	0.15	0.081	Castor-oil lubricated threads
Copper	Steel	Oleic acid / light oil	—	0.18	Copper anti-seize / light oil on steel
Dry / Unlubricated Metal Pairs
Chromium	Chromium	Dry	0.41	—	Chrome-plated fasteners, dry
Brass	Steel	Dry (static)	0.51	0.44	Brass nut on steel bolt, dry
Cast Iron	Steel	Dry (static)	0.40	0.23	CI nut on steel, dry
Aluminum	Mild Steel	Dry (static)	0.61	0.47	Aluminum fastener into mild steel, dry
Steel	Steel	Dry (static)	0.5–0.8	0.42	Steel fasteners, unlubricated — large scatter, do not rely on
Nickel	Nickel	Dry (static)	0.7–1.1	0.53	Nickel-alloy fasteners, unlubricated — galling risk

References & Important Notices

NASA-TM-2012-217454 — Steeve, B. E. and Wingate, R. J. (2012). Aerospace Threaded Fastener Strength in Combined Shear and Tension Loading. The shank and thread interaction curves. Download PDF (5.6 MB).
NASA-RP-1228 — Barrett, R. T. (1990). Fastener Design Manual. Torque-preload, thread pull-out, combined loading. Download PDF (5.1 MB).
ASME B1.1 — Unified Inch Screw Threads. Defines UN, UNC, UNF thread geometry and tensile stress areas.
AS8879 (SAE) — Screw Threads — UNJ Profile, Inch Controlled Radius Root with Increased Minor Diameter. Aerospace UNJ/UNJF thread standard.
ISO 898-1 — Mechanical Properties of Fasteners Made of Carbon Steel and Alloy Steel. Metric thread stress areas and property classes.
Shigley, J.E. & Mischke, C.R. — Mechanical Engineering Design, 10th Ed. McGraw-Hill. Torque-preload equations, Chapter 8.
Bickford, J.H. — An Introduction to the Design and Behavior of Bolted Joints, 3rd Ed. Marcel Dekker.
MMPDS-10 / MMPDS-13 — Metallic Materials Properties Development and Standardization. Material properties for aerospace alloys.
Engineering Toolbox — Friction Coefficients for various Materials. engineeringtoolbox.com
NASM8846 — Insert, Screw Thread, Helical Coil. Prevailing torque values for helicoil inserts.
Friction coefficient uncertainty. The friction coefficient μ₁ has a dominant and highly variable effect on predicted preload. It is sensitive to surface finish, lubricant type and quantity, plating condition, coating wear, and assembly speed. The scatter in dry steel-on-steel values alone spans 0.5–0.8 (static). For flight-critical or pressure-boundary fasteners, torque-tension testing on representative hardware under production assembly conditions is strongly recommended.
Torsional stress not included. This calculator computes tensile (axial) thread stress only. During installation, the fastener also experiences torsional shear stress from thread and collar friction. The combined von Mises stress is approximately 10–15% higher than the tensile stress shown. Conservative practice per Shigley's applies a proof-strength check on the combined stress; this calculator is appropriate for comparative margin analysis but should not replace a full combined-stress check for critical applications.
For informational use only. This calculator is provided as an engineering aid. Results must be verified by a qualified engineer before use in any safety-critical or flight application. KasperCalc assumes no liability for design decisions made using these results.

External Thread Stress and Bolt Preload Calculator — AS8879 / UNC / UNF / Metric