Why Torque Matters
Proper bolt tightening creates sufficient preload (clamping force) to hold joints together under operating loads. Too little torque — joint leaks or separates. Too much torque — bolt yields, strips threads, or fractures.
The relationship between torque and preload depends on thread friction, under-head friction, thread pitch, and bolt diameter.
Torque-Tension Relationship
The standard short-form equation:
Where:
- T = torque (N·m)
- K = nut factor (dimensionless, accounts for friction)
- D = nominal bolt diameter (m or mm — use consistent units)
- F = preload/bolt tension (N or kN)
Detailed Torque Formula (Long Form)
For more accuracy, break torque into three components:
Where:
- P = thread pitch (mm/rev)
- µt = thread coefficient of friction (0.10-0.20 for lubricated; 0.15-0.25 dry)
- rt = effective thread radius ≈ (D − P/2)/2
- α/2 = half thread angle (30° for standard 60° threads)
- µc = collar/nut face friction coefficient
- rc = mean collar radius ≈ 1.25 × D/2 for standard hex nuts
For 60° threads (UNC/UNF/ISO metric): cos(30°) = 0.866
Thread and Collar Friction Coefficients
| Surface Condition | Thread µt | Collar µc | Effective K |
|---|---|---|---|
| As-received, clean, dry | 0.15-0.25 | 0.15-0.25 | 0.30 |
| Lightly oiled | 0.10-0.15 | 0.10-0.15 | 0.20 |
| Molybdenum disulfide (moly) | 0.08-0.12 | 0.06-0.10 | 0.15 |
| Zinc-plated | 0.12-0.18 | 0.10-0.15 | 0.22 |
| Hot-dip galvanized | 0.25-0.35 | 0.30-0.40 | 0.40 |
| Cadmium-plated | 0.08-0.12 | 0.08-0.12 | 0.16 |
Friction is the dominant term: it consumes roughly 80-90% of the applied torque. Only 10-20% of torque actually stretches the bolt and creates preload.
Bolt Grades and Strength
| Metric Grade | Property Class | Proof Strength (MPa) | Ultimate (MPa) | SAE/Imperial |
|---|---|---|---|---|
| Low carbon | 4.6 | 225 | 400 | Grade 2 |
| Medium carbon | 5.8 | 420 | 520 | Grade 2 (higher) |
| High strength | 8.8 | 600 | 800 | Grade 5 |
| Alloy steel | 10.9 | 900 | 1000 | Grade 8 |
| High alloy | 12.9 | 1080 | 1200 | Grade 8 (higher) |
Preload Target
Typical preload is 75% of bolt proof load for permanent connections:
Tensile stress area for metric bolts (ISO 898-1):
| Diameter | Pitch | Stress Area (mm²) |
|---|---|---|
| M8 | 1.25 | 39.7 |
| M10 | 1.5 | 64.1 |
| M12 | 1.75 | 92.1 |
| M16 | 2.0 | 167 |
| M20 | 2.5 | 258 |
| M24 | 3.0 | 369 |
| M30 | 3.5 | 580 |
| M36 | 4.0 | 840 |
Unit Conversion Reference
| Quantity | Convert From | Multiply By | To Get |
|---|---|---|---|
| Torque | lb·ft | 1.3558 | N·m |
| Torque | N·m | 0.7376 | lb·ft |
| Torque | lb·in | 0.1130 | N·m |
| Torque | N·m | 8.8507 | lb·in |
| Force | kN | 224.8 | lbf |
| Force | lbf | 4.448 | N |
| Stress | MPa | 0.1450 | ksi |
| Stress | ksi | 6.895 | MPa |
| Length | mm | 0.03937 | in |
Example: 300 N·m = 300 × 0.7376 = 221 lb·ft. An M16 grade 8.8 bolt at 210 N·m (from the chart below) = 210 × 0.7376 = 155 lb·ft.
Standard Torque Values (Metric, K=0.20 Lubricated)
| Bolt | 8.8 (N·m) | 10.9 (N·m) | 12.9 (N·m) |
|---|---|---|---|
| M8 | 25 | 37 | 44 |
| M10 | 49 | 73 | 88 |
| M12 | 85 | 127 | 152 |
| M16 | 210 | 315 | 378 |
| M20 | 425 | 630 | 755 |
| M24 | 725 | 1100 | 1320 |
| M30 | 1450 | 2100 | 2520 |
| M36 | 2530 | 3780 | 4540 |
Worked Example — M20 Grade 8.8
- M20 bolt, stress area As = 258 mm²
- 8.8 grade proof strength = 600 MPa
- Target F = 0.75 × 600 × 258 = 116,100 N = 116 kN
- Lubricated (K = 0.20): T = 0.20 × 0.020 × 116,000 = 464 N·m
- Dry (K = 0.30): T = 0.30 × 0.020 × 116,000 = 696 N·m
Same bolt, same preload, different torque values depending on K.
Worked Example — Flange Bolt Torque (ASME B16.5)
A DN150 Class 150 RF flange uses 8 × M20 bolts. For a spiral-wound gasket with target seating stress of 70 MPa on a 3.2mm wide gasket at a mean gasket diameter of 190mm:
- Gasket seating load: Fg = π × 190 × 3.2 × 70 = 133.7 kN
- Required preload per bolt: F = 133.7 / 8 = 16.7 kN
- Check bolt stress: σ = F / As = 16,700 / 258 = 64.7 MPa (comfortably below 8.8 proof = 600 MPa)
- Torque per bolt (lubricated, K = 0.20): T = 0.20 × 0.020 × 16,700 = 67 N·m
This is why real flange torques are much lower than the bolt capacity table values — the gasket seating load, not bolt strength, sets the target.
Related Calculator
Rotating machinery torque and power are linked by P = T × ω — use the Pump Power Calculator for pump and driver torque-power checks, and the Motor Power Calculator for motor sizing at the target speed. For bolted flange and fastener weight estimates during material takeoffs, see the Steel Weight Calculator.
Tightening Methods
| Method | Accuracy | Cost | Applications |
|---|---|---|---|
| Torque wrench | ±25-35% | Low | General purpose |
| Calibrated torque wrench | ±15-25% | Medium | Most industrial |
| Turn-of-nut (angle) | ±10-15% | Low | Structural bolts |
| Hydraulic tensioner | ±5-10% | High | Critical flanges, large bolts |
| Bolt elongation (ultrasonic) | ±1-5% | Very high | Turbines, pressure vessels |
| Direct tension indicator (DTI) | ±10% | Medium | Structural steel |
Tightening Sequence (Flanges)
For flange joints, tighten bolts in a crisscross (star) pattern in at least three passes:
- First pass: 30% of target torque
- Second pass: 60% of target torque
- Third pass: 100% of target torque
- Optional final pass: clockwise around flange at 100%
This ensures even gasket compression and prevents flange bowing or leaks. Follow ASME PCC-1 guidelines.
Bolt Torque for Pressure Vessels and Flanges
For ASME B16.5 flange joints per ASME PCC-1:
- Calculate required gasket seating stress (from gasket manufacturer)
- Determine total bolt load to seat gasket and resist internal pressure
- Select torque that achieves target bolt stress
- Apply in crisscross pattern per PCC-1
For spiral-wound gaskets: target gasket stress ≈ 50-70 MPa (7-10 ksi), which sets the bolt load.
See the Flange Rating Standards guide for flange class ratings and the Pressure Vessel Design guide for vessel nozzle and flange loads.
Bolt Relaxation and Re-Torquing
- Embedding: Bolts and gaskets relax in the first 24 hours; re-torque hot bolts after heat cycle
- Gasket creep: Spiral wound and compressed fiber gaskets relax; some specs require re-torquing
- Thermal effects: Different thermal expansion between bolt and flange changes preload
Common Mistakes
- Using same torque value regardless of lubrication
- Not calibrating torque wrenches (should be calibrated annually)
- Tightening in a circle instead of crisscross pattern
- Using impact wrenches for final torque (no control, causes overload)
- Ignoring bolt material differences (Grade 5 vs Grade 8 torque values differ)
- Overlooking thread condition (dirty/rusty threads = high friction = low preload)
- Mixing bolt grades in same joint (uneven load sharing)
Frequently Asked Questions
What is the formula for bolt torque? The standard formula is T = K × D × F, where T = torque (N·m), K = nut factor (0.20 lubricated, 0.30 dry), D = nominal bolt diameter (m), and F = desired preload (N). For a more accurate result use the long form with thread pitch and friction coefficients.
How do I convert N·m to lb·ft? Multiply N·m by 0.7376 to get lb·ft. For example, 464 N·m × 0.7376 = 342 lb·ft. To convert lb·ft to N·m, multiply by 1.3558.
What torque should I use for an M10 bolt? For an M10 grade 8.8 bolt, lubricated (K = 0.20), use about 49 N·m (36 lb·ft); for grade 10.9 use 73 N·m (54 lb·ft); for grade 12.9 use 88 N·m (65 lb·ft). Dry conditions require roughly 50% more torque.
How much torque is 30 N·m in lb·ft? 30 N·m × 0.7376 = 22.1 lb·ft. As a reference, 30 N·m is close to the standard lubricated torque for an M8 grade 8.8 bolt (25 N·m) and below the M10 grade 8.8 value (49 N·m). Always check the bolt grade chart for the exact size and grade.
What is the recommended preload for a bolt? For permanent connections, use 75% of the bolt proof load. For 8.8 grade M20: F = 0.75 × 600 MPa × 258 mm² = 116 kN. This ensures the joint stays tight under operating loads without yielding the bolt.
What is a bolt torque chart used for? A bolt torque chart gives pre-calculated torque values by bolt size and grade for a stated K factor and preload percentage. Charts assume specific friction conditions — verify the lubrication and coating assumption before use.
Summary
Use T = K × D × F for bolt torque, with K = 0.20 lubricated or K = 0.30 dry. Target preload at 75% of proof load. Standard metric torque tables assume K = 0.20 — adjust for actual lubrication. Friction dominates (80-90% of torque), so control surface condition and lubrication. Always tighten in crisscross pattern per ASME PCC-1 for flanges. For critical joints (pressure vessels, large flanges), use hydraulic tensioners or ultrasonic measurement instead of torque-only control.