Torque Calculator
Calculate the rotational force (torque) produced when a force is applied at a distance from a pivot point. Use it for bolt tightening, lever design, motor sizing, and any mechanical analysis involving rotational force.
Last updated: May 2026
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About this calculator
The formula is: torque (N·m) = force (N) × distance (m), where force is the applied perpendicular force and distance is the perpendicular distance from the pivot (the "moment arm" or "lever arm"). Edge cases: zero force or zero distance produces zero torque; force applied along the lever (parallel to it) produces zero useful torque because there's no perpendicular component. Torque is a vector quantity (with direction by right-hand rule), but most engineering applications focus on magnitude. Common units: N·m (SI metric); kgf·m (older metric); lbf·ft (imperial pound-foot, common in US automotive and aerospace); lbf·in (imperial pound-inch, for small fasteners). Conversions: 1 lbf·ft = 1.356 N·m; 1 lbf·in = 0.113 N·m; 1 kgf·m = 9.807 N·m. Bolt torque specifications come from the fastener's grade and intended preload (clamping force on the joint). Common automotive applications: lug nuts 80–120 lbf·ft (108–163 N·m); cylinder head bolts 50–80 lbf·ft (68–108 N·m), often with torque-then-angle protocol; oil pan bolts 8–14 lbf·ft (11–19 N·m). For machinery, manufacturers publish bolt torque tables for each fastener size and material grade. The grade 5 (SAE) or 8.8 (metric) standard bolts have published preload values; high-strength fasteners (grade 8 / 10.9 / 12.9) require higher torques and more careful application. Important context: torque is not preload directly — torque produces preload through friction (typically 90% of applied torque becomes friction; only 10% becomes actual clamping force). This is why "torque-to-angle" methods are increasingly preferred over pure torque for critical applications — they bypass the friction variability.
How to use
Example 1 — Lug nut tightening. Apply 80 lbf force to a torque wrench with a 1-foot handle effective length. Force = 80 × 4.448 = 356 N; distance = 1 × 0.3048 = 0.3048 m. Enter force 356, distance 0.3048. Result: 356 × 0.3048 ≈ 108 N·m = 80 lbf·ft. ✓ Correct lug nut torque for most passenger cars (manufacturer-specific; verify in owner's manual). Use a calibrated torque wrench (clicker, beam, or digital); avoid impact wrench for final tightening as it can over-torque dramatically. Tighten in star pattern across the wheel to seat evenly. Example 2 — Cylinder head bolt. M12 head bolt torqued to 90 N·m using a torque wrench with handle pivot 400mm (0.4m) from the bolt. Required hand force = 90/0.4 = 225 N ≈ 50 lbf. Enter force 225, distance 0.4. Result: 225 × 0.4 = 90 N·m. ✓ Cylinder head bolts often follow a sequence: tighten to 30 N·m → 60 N·m → 90 N·m, then turn an additional 90° rotation. The angle-turn step ensures consistent preload by stretching the bolt to a defined extension rather than relying on friction-dependent torque alone. Cylinder head fasteners are typically single-use; replace with new bolts on re-assembly.
Frequently asked questions
What is the difference between torque and preload?
Torque is the applied rotational force; preload is the actual clamping force (axial tension) on the bolt and joint after tightening. They are related but not identical. The relationship: applied torque × bolt nut factor (K) × bolt diameter = preload tension. Typical K values: dry steel-on-steel 0.20; oiled steel 0.18; thread-lockers (Loctite) 0.16; anti-seize 0.10–0.13; copper-based anti-seize 0.10. The "torque-tension" relationship has significant variability: even with controlled lubrication, scatter is typically ±25–30% on actual preload at a given torque. This is why critical applications (cylinder heads, connecting rods, structural bolts in airplanes and ships) increasingly use "torque-to-angle" protocols: first tighten to a low torque (clear thread friction and seat the joint), then rotate the bolt by a specific angle (typically 60°–120° depending on bolt grade and length). The angle directly stretches the bolt to a predictable tension, bypassing friction uncertainty. The "torque-then-yield" method takes this further — tighten until the bolt approaches its yield strength, which produces highly reproducible preload but consumes the bolt (single-use). For most non-critical applications, simple torque method is adequate; for critical fasteners (cylinder heads, suspension), use the manufacturer's specified procedure exactly.
How accurate is my torque wrench?
Depends on type, condition, and use. Click-type torque wrenches: typically ±4% of full scale when new and calibrated; degrades over time, especially if dropped or stored loaded. Beam-type (mechanical needle): typically ±3% accuracy and very stable; reads by visual indicator on a scale. Digital torque wrenches: typically ±2% accuracy with electronic readout; some include angle measurement for torque-to-angle work. Hydraulic torque wrenches (industrial): typically ±3–5% accuracy with much higher torque capacity. Storage and handling affects accuracy: 1) Always relax click-type wrenches to the lowest setting before storage; storing loaded over-stresses the spring and shifts calibration. 2) Do not use as breaker bars or for loosening fasteners (unless designed bidirectionally); shock loading degrades accuracy. 3) Get torque wrenches calibrated annually for production use; many garages calibrate every 5,000 cycles. 4) Use at the wrench's middle range (20–80% of capacity); accuracy degrades at extreme ranges. 5) Apply force smoothly at the handle's designated grip area; squeezing different positions changes the effective lever arm. 6) Replace wrenches that have been over-loaded or dropped from heights; internal damage may not be visible. For occasional DIY use, even a $50 click-type wrench provides better accuracy than no torque measurement. For professional or critical work, invest in $200–500 digital units with calibration certificates.
When should I use torque-to-angle instead of pure torque?
For applications requiring consistent preload: cylinder head bolts, connecting rod bolts, main bearing caps, suspension fasteners on modern vehicles, high-strength structural fasteners in critical assemblies. The reason: friction variability between fasteners can cause ±25–30% preload variation at the same torque; angle-turn methods produce much more consistent preload (±5–10%). Modern automotive engine fasteners almost universally use torque-then-angle protocols specified by the manufacturer. Aerospace fasteners often use torque-then-angle or direct tension measurement. The methodology: 1) Lubricate threads as specified by the manufacturer (some specify oil, some specify dry, some specify thread sealant). 2) Tighten to the snug torque (typically 25–50% of "full" torque) to seat the joint and remove gross slack. 3) Mark the bolt head and surrounding surface so you can see the start position. 4) Rotate the bolt the specified additional angle (typically 60°, 90°, or 120°). Some applications specify two stages (e.g., 30° then another 60°). 5) Verify the final position with the marks made. For DIY work, the angle method works without a torque wrench at all once you reach snug — use a protractor angle gauge or just a protractor mark on the head. Many service manuals now specify angle turn rather than final torque for critical fasteners.
What are the most common torque application mistakes?
The biggest is using the wrong torque specification for your specific application; manufacturer-specified torques are critical, not interchangeable across designs. Always check the service manual for your exact application. The second is mixing lubricated and dry torque specs; lubricated thread torque can produce 30–50% higher preload than the dry torque value would imply. Follow the specification's lubrication condition exactly. The third is impact wrenches set too aggressively, far over-torquing fasteners and stretching them beyond yield. Use torque wrenches for final tightening, not impacts. The fourth is using cheater bars (pipes over wrench handles) for additional leverage; this exceeds tool ratings and produces unknown actual torque. The fifth is failing to use thread sealants on tapered pipe threads when specified; the seal mechanics depend on the sealant. The sixth is leaving click-type wrenches set to high torque in storage; relax to lowest setting after each use. The seventh is tightening fasteners in random order rather than the specified sequence; head bolts and gasketed joints have specific patterns that distribute load evenly. The eighth is reusing torque-to-yield bolts (cylinder head, connecting rod); these have stretched beyond elastic limit and lose preload capacity. The ninth is over-torquing soft-material fasteners (brass, aluminum, plastic threaded into metal); the threads strip easily. Use lower torques specified for these materials. The tenth is failing to verify wrench accuracy; especially with cheaper wrenches, calibration drift over time produces wrong torque without warning.
When should I not use this calculator?
Skip it for non-fastener applications where torque is a power-transmission quantity (motor torque, shaft torque) rather than tightening torque; use power transmission calculators with motor characteristics. It is the wrong tool for very small fasteners (M2, M3 in electronics) where torque is measured in cN·m (centi-newton-meters) and specialized inch-pound wrenches or torque drivers are needed; standard torque wrenches don't apply to these scales. Do not use it for plastic-threaded fasteners (snap-fit connectors, plastic-to-metal threads in consumer electronics); plastic creep changes the joint behavior; follow manufacturer-specific guidance. For critical aerospace, nuclear, and pressure-vessel fasteners, follow detailed manufacturer and code specifications including torque sequence, lubrication, retorquing schedule, and inspection; the basic torque = F × d formula is correct but the specification is much more complex. For applications using ultrasonic bolt extension measurement (very high-end manufacturing), the direct measurement supersedes torque calculation. For broken or damaged fasteners requiring extraction, the torque required to remove (which may exceed yield strength) is not described by tightening torque math; use extractor tools and replace with new fasteners. And for torque sensors and instrumentation where the device measures torque directly (load cells in motor dynamometers, in-process torque transducers in manufacturing), use the measured value rather than calculation.