What is bolt tightening torque?

Bolt tightening torque is the rotational force applied to a fastener to generate a controlled clamping preload in the joint. It is calculated using T = K × F_i × d, where K is the nut factor, F_i is the bolt preload, and d is the nominal diameter.

What is bolt preload and why does it matter?

Bolt preload is the tensile force generated in a bolt when it is tightened. It creates the clamping force that holds the joint together. Standard practice is to target 75–90% of proof load to ensure reliable joint performance without yielding the bolt.

What is the difference between ISO Class 8.8 and Class 10.9?

ISO Class 8.8 has a yield strength of 640 MPa and is the most common structural bolt. ISO Class 10.9 has a higher yield strength of 940 MPa and is used in high-strength joints. Class 12.9 is the strongest at 1080 MPa yield, used in critical applications.

Engineering DisclaimerEngineering calculations are provided for preliminary design and educational/reference purposes only. Users must verify all results according to applicable engineering standards, supplier data, manufacturing requirements, and professional engineering judgment.

ISO 898-1 / VDI 2230

Fastener Design

Bolt torque is the rotational force (N·m) required to tighten a fastener to a specific preload. Use the formula T = K × Fi × d where K = nut factor, Fi = preload force, d = nominal diameter. This calculator implements VDI 2230 method.

Bolt Torque Calculator

Calculate the recommended tightening torque, bolt preload clamp force, and tensile stress for metric (ISO) and imperial (UNC/UNF) fasteners using the verified nut-factor method per VDI 2230.

BOLT PRELOAD & TORQUE WORKBENCH PRO

VDI 2230 / ISO 16047

Preliminary assembly design solver with Motosh 3-term mechanics, decoupled stress audits & friction sensitivity

Workspace Mode:

Unsaved Configuration

Fastener Parameters

Calculation ModeISO / VDI

Assembly Sizing: Solves required wrench torque from clamp force / yield utilization.

Target Preload Input

Yield Utilization (ν)90%

Calculation EngineMethod

Fastener Size

Property Class / Grade

Proof S_p225

Yield S_y240

Area A_s1.70

Surface & LubricationFriction μ

μ_G = 0.18μ_K = 0.18K_eff = 0.234

Tightening Tool (Scatter Factor α_A)

Embedment Relaxation Compensation (+5%)VDI 2230 Table 5

Required Torque (M_A)

0.10N·m

0.1 ft·lb

Clamp Preload (F_M)

0.2kN

Scatter: 0.2 - 0.2 kN

VDI 2230 Stress Verdict

PASS90% Sy

σ_red = 216 MPa

VDI 2230 Stress Audit & Preload Scatter Analysis

Decoupled evaluation of von Mises yield stress (σ_red = √(σ_z² + 3τ_k²)) and axial proof stress (σ_z / S_p).

PASS — Elastic Range

Yield Utilization (σ_red / R_p0.2)90.0%

Limit: 100% (Yield: 240 MPa)Safe

Proof Utilization (σ_z / S_p)59.2%

Limit: 100% (Proof: 225 MPa)Safe

Axial Stress (σ_z)

133.2 MPa

From clamp tension elongation

Torsional Stress (τ_k)

98.2 MPa

From thread flank friction

von Mises (σ_red)

216.0 MPa

Combined 3D tightening stress

Assembly Clamp Band

0.2 - 0.2 kN

Tool scatter α_A = 1.50

Verification Summary

SAFE: Tightening stress state (216.0 MPa, 90.0% of yield; axial 59.2% of proof) is safely within permissible assembly limits.

Torque Reaction Component Breakdown (VDI 2230 / Motosh)

Over 85% of applied wrench torque is consumed by friction rather than stretching the fastener.

0.1 N·mTotal Torque

Pitch Stretch (T_p)13.2%

0.01 N·m

Useful elastic axial stretching work

Thread Flank (T_t)38.8%

0.04 N·m

Sliding friction on 60° thread flanks

Head Bearing (T_b)48.0%

0.05 N·m

Sliding friction on clamped bearing face

Friction Scatter Sensitivity Analysis (±20%)

Evaluates clamp load dispersion and stress shifts when actual shop floor friction deviates by ±20%.

Sensitivity Audit

High Friction (+20% μ)-14.8%

Contaminated / dry thread contact

0.2 kN

σ_red = 202 MPa (84.0% Sy)

⚠️ Risk: Under-clamping, joint gap separation, or fatigue bolt loosening.

Nominal Reference (μ)100% Target

Specified lubrication preset

0.2 kN

Target clamp force generated at nominal torque

✓ Benchmark design baseline.

Low Friction (-20% μ)+21.0%

Excessive anti-seize / moly lube

0.3 kN

σ_red = 238 MPa (99.1% Sy)

⚠️ Risk: Bolt overload and elevated plastic strain risk.

Note: This sensitivity analysis evaluates clamp load dispersion under a ±20% friction scatter assumption. It is an engineering sensitivity model and not a standardized test limit. Critical joints must be verified with physical torque-tension testing per ISO 16047.

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VDI 2230 / ISO 16047 Bolt Tightening Torque & Preload Report — Calculation Report

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Date: —

Standard: ISO 898-1 / VDI 2230 / ISO 16047 / ASME B1.1

VDI 2230 / ISO 16047 Bolt Tightening Torque & Preload Report

Design Inputs

Calculation Mode: Preload → Torque (Assembly Sizing)
Calculation Engine: VDI 2230 / DIN 946 (Full 3-Term Engine)
Bolt Size Selection: M1.8 × 0.35
Property Class / Grade: ISO Class 4.6
Lubrication / Thread Condition: Dry (Unlubricated Steel)
Tightening Tool (Scatter α_A): Calibrated Torque Wrench (Manual)
Target Preload Utilization Ratio: 90 % S_y
Tensile Stress Area (A_s): 1.70 mm²
Effective Nut Factor (K_eff): 0.234

Calculated Results

Assembly Preload Force (F_M):	0.2 kN
Min Assembly Preload (F_M,min):	0.2 kN
Target Wrench Torque (M_A):	0.10 N·m
Pitch Stretch Torque (M_P):	0.01 (13.2%)
Thread Flank Friction (M_G):	0.04 (38.8%)
Underhead Bearing Friction (M_K):	0.05 (48.0%)
Axial Tensile Stress (σ_z):	133.2 MPa
Proof Stress Utilization:	59.2%
von Mises Tightening Stress (σ_red):	216.0 MPa
Yield Strength Utilization:	90.0%
Yield Safety Audit Verdict:	PASS

Verification Steps

1. Thread Profile & Fastener Geometry (M1.8 × 0.35 Coarse):
- •Major nominal diameter (d) = 1.8 mm
- •Thread pitch (P) = 0.35 mm
- •Pitch diameter (d₂) = 1.573 mm [d - 0.649519 P]
- •Core minor diameter (d₃) = 1.371 mm [d - 1.226869 P]
- •Tensile stress area (A_s) = 1.70 mm² [ISO 898-1 / ASME B1.1]
- •Core polar modulus (W_p) = 0.51 mm³ [(π d₃³) / 16]
- •Mean bearing diameter (D_Km) = 2.25 mm [(d_w + d_h) / 2]
2. Material Strength Thresholds (class-4.6):
- •Proof load strength (S_p) = 225 MPa
- •Yield strength (R_p0.2 / S_y)= 240 MPa
- •Calculation Mode = Preload → Torque (90% of yield strength utilization)
3. Friction Coefficients & Tool Scatter (dry):
- •Thread friction coeff (μ_G) = 0.18
- •Bearing friction coeff (μ_K) = 0.18
- •Effective Nut Factor (K_eff) = 0.234
- •Tool scatter factor (α_A) = 1.50
4. Analytical 3-Term Torque Mechanics (Motosh / ISO 16047):
- •Pitch stretch torque (M_P) = 0.01 N·m (13.2%) [Elastic stretch climb]
- •Thread flank friction (M_G) = 0.04 N·m (38.8%) [Flank sliding drag]
- •Bearing face friction (M_K) = 0.05 N·m (48.0%) [Underhead washer drag]
- •Total Wrench Torque (M_A) = 0.10 N·m (100.0%)
5. Clamping Force & Tool Scatter Envelope (VDI 2230):
- •Nominal Clamping Preload (F_M) = 226.5 N
- •Maximum assembly preload (F_M,max) = 226.5 N
- •Minimum assembly preload (F_M,min) = 151.0 N [F_M / α_A]
6. Fastener Core Stress & Decoupled Yield/Proof Audits:
- •Axial tensile stress (σ_z) = 133.2 MPa
- •Proof stress utilization (σ_z/S_p) = 59.2% (Threshold: ≤ 100%)
- •Thread core torsional shear (τ_k) = 98.2 MPa
- •Combined von Mises (σ_red) = 216.0 MPa [√(σ_z² + 3 τ_k²)]
- •Yield utilization (σ_red/R_p0.2) = 90.0%
- •Verification Safety Verdict = PASS
7. Friction Sensitivity Analysis (±20% Scatter):
- •Low friction (-20% μ): F_M = 274.1 N (+21.0%), σ_red = 238.0 MPa (99.1% yield)
- •High friction (+20% μ): F_M = 193.0 N (-14.8%), σ_red = 201.5 MPa (84.0% yield)
8. Bolt Shear & Tension Capacity (AISC 360 / NBR 8800):
- •Nominal shear capacity (φRn) = 0.3 kN
- •Nominal tension capacity (φRn) = 0.4 kN
- •Note: φ = 0.75 (LRFD), threads excluded from shear plane

Engineering Disclaimer: Preliminary sizing based on Motosh/VDI 2230 analytical mechanics. Tightening tool scatter factor α_A defines the achievable minimum clamp load range. Final critical joints must be verified with physical torque-tension testing per ISO 16047 or full joint elasticity/relaxation analysis.

Domain of Validity

Valid for standard metric and imperial fasteners with coarse and fine threads. The VDI 2230 method applies to bolts from M1.6 to M100 (or 1/8" to 4"). Not valid for thread-rolled fasteners with unknown K-factors or non-standard lubricants.

Worked Example

M12 Grade 8.8 bolt, K = 0.20, preload = 55 kN, d = 12 mm: T = 0.20 x 55,000 x 0.012 = 132 N.m for 70% yield preload.

Verification

VDI 2230 Part 1:2014 verified formulas. ISO 16047 test data cross-checked. Last verified: August 2026.

Accuracy and Uncertainty

Torque-to-tension relationship has plus/minus 15% uncertainty due to friction scatter. K-factor variation of plus/minus 0.05 changes torque by plus/minus 25%.

Frequently Asked Questions

What is the VDI 2230 method?

VDI 2230 is a German standard that provides a systematic method for calculating bolt fastening torque based on friction coefficients, thread geometry, and preload requirements. It is the most widely used method for industrial bolted joint design.

What is a nut factor (K-factor)?

The K-factor (nut factor) is an empirically derived coefficient that accounts for friction in the threads and under the bolt head. Typical values: dry steel-on-steel K = 0.20-0.30, lubricated K = 0.12-0.18, stainless steel K = 0.25-0.35.

How much preload should I apply?

For steel bolts, typical preload is 70-80% of proof strength (0.7-0.8 x A_t x f_p). For critical joints, 85-90% may be used. Exceeding the proof load causes permanent elongation.

What is the difference between torque and tension?

Torque is the rotational force applied to tighten a bolt. Tension (preload) is the tensile force developed in the bolt as a result of tightening. The relationship is T = K x F_i x d, where most of the torque (up to 90%) overcomes friction.

ISO 898-1 vs ASME B18.2.1 - which standard?

ISO 898-1 covers metric hex bolts and defines property classes (8.8, 10.9, 12.9). ASME B18.2.1 covers inch-series hex bolts. The calculator supports both with appropriate unit selection.

Bolt Torque Calculator

BOLT PRELOAD & TORQUE WORKBENCH PRO

Bolt Preload & Tightening Torque PRO Workbench

VDI 2230 Stress Audit & Preload Scatter Analysis

Torque Reaction Component Breakdown (VDI 2230 / Motosh)

Friction Scatter Sensitivity Analysis (±20%)

VDI 2230 / ISO 16047 Bolt Tightening Torque & Preload Report — Calculation Report

VDI 2230 / ISO 16047 Bolt Tightening Torque & Preload Report

Design Inputs

Calculated Results

Verification Steps

Domain of Validity

Worked Example

Verification

Accuracy and Uncertainty

Frequently Asked Questions

What is the VDI 2230 method?

What is a nut factor (K-factor)?

How much preload should I apply?

What is the difference between torque and tension?

ISO 898-1 vs ASME B18.2.1 - which standard?

BOLT PRELOAD & TORQUE WORKBENCH PRO

Bolt Preload & Tightening Torque PRO Workbench

VDI 2230 Stress Audit & Preload Scatter Analysis

Torque Reaction Component Breakdown (VDI 2230 / Motosh)

Friction Scatter Sensitivity Analysis (±20%)

VDI 2230 / ISO 16047 Bolt Tightening Torque & Preload Report — Calculation Report

VDI 2230 / ISO 16047 Bolt Tightening Torque & Preload Report

Design Inputs

Calculated Results

Verification Steps