Fastener Torque–Tension Calculator
Bolt Torque & Preload
Enter torque to find preload, or enter target preload to find the required torque. Uses T = K × D × F with adjustable nut factor for surface condition.
Solve For
Thread System
Thread Series
Locknuts, thread inserts, or Loctite — subtracted before preload calc
Total clamped thickness — used to estimate bolt stretch under load
Torque Unit
75% of proof load is standard practice for most joints
Select a bolt size and enter a value
Torque Reference — SAE Grade 5 & 8
Dry (K = 0.20), 75% of proof load. For lubricated joints, reduce torque by 25–30%.
| Bolt Size | Grade 5 (ft·lbf) | Grade 5 (N·m) | Grade 8 (ft·lbf) | Grade 8 (N·m) |
|---|
The Math Behind the Torque
The governing equation
T = K × D × F
T is torque, K is the nut factor (dimensionless friction coefficient), D is nominal bolt diameter, F is axial preload (clamp force). This is the "short form" torque equation — it lumps thread pitch, thread friction, and bearing friction into a single K factor.
What each variable does
T = applied torque (in·lbf)
The wrench input. Internally this calculator works in in·lbf; conversions happen at input/output.K = nut factor (0.10 – 0.25 typical)
Accounts for all friction: thread helix, thread flanks, and nut bearing face.
~90% of your torque goes to overcoming friction — only ~10% generates clamp force.
This is why lubrication matters so much: changing K from 0.20 to 0.15 increases
preload by 33% at the same wrench torque.D = nominal bolt diameter (in)
Major diameter of the thread. Larger bolts need more torque for the same stress
because the moment arm is longer.F = preload / clamp force (lbf)
The axial tension in the bolt that creates the clamping force between parts.
This is what actually holds the joint together — not the torque.Proof load and tensile area
Aₜ = (π/4) × (D − c × P)²
Tensile stress area. D is nominal major diameter, P is pitch (1/TPI for
inch threads). The constant c differs by standard: 0.9743 for ASME B1.1
(UN threads, flat root minor diameter) and 0.9382 for ISO 898-1 (metric
threads, rounded root minor diameter). The ~1.3% difference matters if
you're comparing against published tensile areas from bolt catalogs.F_proof = Sp × Aₜ
Proof load: the max force the bolt can sustain without permanent deformation.
Target preload is typically 75% of proof load — enough to maintain clamp force
under service loads without risking yield.Why 75%?
At 75% of proof load, you have a 25% margin above your preload before the bolt
takes a permanent set. This margin absorbs torque scatter from wrench accuracy (±25%
for hand torque wrenches), embedding relaxation, and elastic interactions during
tightening sequences. Go higher and you're gambling on your torque wrench calibration.K factor values by surface condition
| Condition | K Factor | Notes |
|---|---|---|
| Black oxide, dry | 0.20 – 0.22 | As-received from the box. Most published torque specs assume this. |
| Zinc plated, dry | 0.17 – 0.20 | Common hardware store finish. K varies with plating thickness. |
| Cadmium plated | 0.14 – 0.18 | Military/aerospace spec. Consistent K but cadmium is toxic — being phased out. |
| Machine oil | 0.14 – 0.16 | Light oil on threads and bearing face. Cheap, effective, but messy. |
| Moly paste (MoS₂) | 0.12 – 0.14 | Heavy-duty anti-friction. Common on structural bolts and high-temp joints. |
| Anti-seize (copper/nickel) | 0.11 – 0.13 | Prevents galling on stainless, prevents seizing on dissimilar metals. Reduce torque spec ~30%. |
| PTFE / wax coatings | 0.09 – 0.12 | Lowest friction. Used on prevailing-torque locknuts. Very sensitive to K — small torque changes → big preload swings. |
When torque-to-value isn't enough: torque-angle method
Why torque alone is unreliable
The T = K×D×F equation assumes a constant K, but K varies ±25–30%
from friction scatter alone. Two identical bolts torqued to the same value can
have preloads that differ by 2:1. For non-critical joints this scatter is
acceptable. For cylinder head bolts, connecting rods, and structural steel
it's not.Torque-angle tightening
Snug the bolt to a low "threshold" torque (usually 20–30% of final), then
turn a specified additional angle (e.g., 90° or 180°). The angle portion
stretches the bolt by a known geometric amount regardless of friction,
so the final preload depends on bolt stiffness rather than surface condition.
Scatter drops from ±25% to ±5–10%.Where it's used
Automotive head bolts (torque + 90° + 90° is common), connecting rod bolts,
main bearing cap bolts, AISC structural steel (turn-of-nut method per RCSC
specification), and any joint where the consequence of under- or over-clamping
justifies the extra procedure.Limitation
Torque-angle only works if the bolt is in its elastic range during the angle
turn. If the bolt yields, the preload plateaus and more angle just causes
permanent stretch. Yield-controlled tightening intentionally takes the bolt
just past yield — that's a third method, common on TTY (torque-to-yield) head bolts.Proof stresses per SAE J429 (inch grades), ISO 898-1 (metric classes), and ISO 3506-1 (stainless classes). Tensile areas per ASME B1.1 (inch) and ISO 898-1 (metric). The T = K × D × F equation is an approximation — actual preload varies ±25% or more due to friction scatter. For critical joints, use direct tension indicators (DTIs) or ultrasonic bolt measurement.