About

Incorrect bolt torque is the leading cause of joint failure in mechanical assemblies. Under-torquing allows fatigue loosening and joint separation under cyclic loads. Over-torquing exceeds the bolt's proof load, causing yielding, hydrogen embrittlement in high-strength fasteners, or outright shank fracture. This calculator computes the required tightening torque T from the bolt's nominal diameter d, the target preload F, and the nut factor K. Preload is derived from the tensile stress area A_t and proof strength S_p per SAE J429, ASTM A307/A325, and ISO 898-1 standards. The tool assumes elastic tightening within the bolt's proof load range.

Roughly 90% of applied torque is consumed by friction in the threads and under the bolt head. The K-factor encapsulates these friction losses. A dry steel-on-steel joint uses K ≈ 0.20, while anti-seize compounds drop it to ≈ 0.12. Misidentifying the surface condition can shift actual preload by 40% or more. This tool provides standard K-factor values but does not account for prevailing-torque locknuts, thread-locking adhesives, or angular tightening methods. For safety-critical joints (pressure vessels, structural steel), always cross-reference with the fastener manufacturer's specifications and applicable code (AISC, ASME PCC-1).

Formulas

The fundamental short-form torque equation for threaded fasteners relates applied wrench torque to the resulting bolt preload (clamp force):

T = K × d × F

Where T = tightening torque (lb⋅ft or N⋅m), K = nut factor (dimensionless friction coefficient, typically 0.10 - 0.22), d = nominal bolt diameter (in or mm), F = desired preload / clamp force (lbf or N).

The target preload is calculated from the bolt's tensile stress area and proof strength:

F = C_p × A_t × S_p

Where C_p = preload fraction (0.75 for reusable joints, 0.90 for permanent joints), A_t = tensile stress area of the bolt (in² or mm²), S_p = proof strength of the bolt material (psi or MPa).

For UNC/UNF threads, the tensile stress area is computed from the nominal diameter d and thread pitch n (threads per inch):

A_t = π4 × (d − 0.9743n)²

For metric threads with pitch P (mm):

A_t = π4 × (d − 0.9382 × P1)²

The bolt stress under preload is verified against proof strength: σ = FA_t. If σ > S_p, the bolt is overloaded and may yield.

Reference Data

Standard	Grade / Class	Material	Proof Strength S_p	Tensile Strength S_ut	Yield Strength S_y	Size Range
SAE J429	Grade 1	Low/Med Carbon Steel	33 ksi	60 ksi	36 ksi	¼ - 1½ in
SAE J429	Grade 2	Low/Med Carbon Steel	55 ksi	74 ksi	57 ksi	¼ - ¾ in
SAE J429	Grade 5	Med Carbon Steel, Q&T	85 ksi	120 ksi	92 ksi	¼ - 1 in
SAE J429	Grade 5 (lg)	Med Carbon Steel, Q&T	74 ksi	105 ksi	81 ksi	1⅛ - 1½ in
SAE J429	Grade 8	Med Carbon Alloy, Q&T	120 ksi	150 ksi	130 ksi	¼ - 1½ in
ISO 898-1	Class 4.6	Low/Med Carbon Steel	225 MPa	400 MPa	240 MPa	M5 - M36
ISO 898-1	Class 4.8	Low/Med Carbon Steel	310 MPa	420 MPa	340 MPa	M1.6 - M16
ISO 898-1	Class 5.8	Low/Med Carbon Steel	380 MPa	520 MPa	420 MPa	M5 - M24
ISO 898-1	Class 8.8	Med Carbon Steel, Q&T	600 MPa	830 MPa	660 MPa	M16 - M36
ISO 898-1	Class 8.8 (sm)	Med Carbon Steel, Q&T	580 MPa	800 MPa	640 MPa	M1.6 - M16
ISO 898-1	Class 9.8	Med Carbon Steel, Q&T	650 MPa	900 MPa	720 MPa	M1.6 - M16
ISO 898-1	Class 10.9	Alloy Steel, Q&T	830 MPa	1040 MPa	940 MPa	M5 - M36
ISO 898-1	Class 12.9	Alloy Steel, Q&T	970 MPa	1220 MPa	1100 MPa	M1.6 - M36
ASTM A307	Grade A	Low Carbon Steel	33 ksi	60 ksi	36 ksi	¼ - 4 in
ASTM A325	Type 1	Med Carbon Steel, Q&T	85 ksi	120 ksi	92 ksi	½ - 1½ in
ASTM A490	Type 1	Alloy Steel, Q&T	120 ksi	150 ksi	130 ksi	½ - 1½ in
Common K-Factor Reference
Condition		K Factor		Notes
Black Oxide (Dry)		0.20		Baseline; as-received steel
Zinc Plated (Dry)		0.20		Electroplated, no oil
Zinc Plated (Lubed)		0.17		Waxed or oiled after plating
Cadmium Plated (Dry)		0.16		Military / aerospace spec
Cadmium Plated (Lubed)		0.11		With MoS₂ grease
Moly Paste (MoS₂)		0.13		Anti-seize compound
Anti-Seize (Copper)		0.12		Copper-based paste
Anti-Seize (Nickel)		0.13		Nickel-based paste
Machine Oil		0.15		Light machine oil applied
Waxed		0.14		Paraffin wax coating
PTFE Coated		0.12		Teflon® dry film
Phosphate & Oil		0.15		Manganese phosphate + oil

Frequently Asked Questions

The K-factor (nut factor) is a dimensionless coefficient that accounts for all friction losses in the joint - thread friction, under-head friction, and thread geometry. A K-factor change from 0.20 (dry) to 0.12 (anti-seize) reduces the required torque by 40% for the same preload. This means applying "dry" torque values to a lubricated bolt will over-stress it by 40%, risking yield or fracture. Always verify the actual surface condition before selecting a K-factor.

The preload fraction C_p determines how close to the bolt's proof load you tighten. A value of 0.75 loads the bolt to 75% of proof load - standard for reusable connections that will be disassembled and re-torqued. A value of 0.90 is used for permanent, non-reusable joints (e.g., structural steel per AISC) where maximum clamp force is critical and the bolt is replaced after removal. Using 0.90 on a bolt you intend to reuse risks fatigue failure after several cycles.

UNF (fine pitch) threads have a larger tensile stress area A_t than UNC (coarse pitch) threads at the same nominal diameter, because the minor diameter is larger. A ½-20 UNF bolt has A_t = 0.1599 in² versus 0.1419 in² for ½-13 UNC. The larger stress area means higher preload at the same proof strength, which results in higher required torque. Fine threads also have a mechanical advantage that reduces the torque needed per unit preload, but the net effect of higher preload usually dominates.

This calculator's built-in grade tables cover carbon and alloy steel per SAE J429 and ISO 898-1. Stainless steel fasteners (A2-70, A4-80 per ISO 3506) have different proof strengths - A2-70 has S_p ≈ 450 MPa and A4-80 has S_p ≈ 600 MPa. You can use the "Custom" input mode to enter these values manually. Note that stainless steel is prone to galling, making lubrication (K ≈ 0.12 - 0.15) essential to prevent thread seizure during tightening.

The short-form equation T = K × d × F is an empirical simplification that lumps thread pitch, thread friction coefficient μ_t, and bearing friction coefficient μ_b into a single K-factor. The long-form (Motosh equation) separates these variables and typically agrees within ±5% when using published K-values. For most industrial applications, the short-form is standard practice (per Fastenal, Nord-Lock, and Boltscience guidelines). The dominant source of error is K-factor uncertainty (±25%), not the equation form.

Non-standard bolt diameters are uncommon in production hardware but occur in custom machined studs. This calculator requires you to select a standard size from the dropdown, which ensures the tensile stress area A_t matches published thread data. If you have a non-standard fastener, use "Custom" mode and enter the known A_t from the machining drawing. Interpolating A_t between standard sizes is not recommended because stress area depends non-linearly on both diameter and thread pitch.