Bolt Torque & Preload

Tightening torque and clamping preload for threaded fasteners using T = K·F·d. Computes tensile stress area, proof load, target preload, required torque, and bolt tensile stress.


ISO 898-1 · VDI 2230

Bolt & Grade

Parameters

mm
mm
MPa
MPa

Torque & Preload

218.08N·m
Tightening torque
68 × 10³N
Target preload
156.67mm²
Stress area At
91 × 10³N
Proof load

Bolt Stress

435.0MPa
Tensile stress
68.0 %
of yield

About Bolt Torque & Preload Calculator

The bolt torque and preload calculator determines the tightening torque needed to develop a target clamping preload in a threaded fastener, using the widely used short-form torque equation T = K·F·d. It first computes the tensile stress area At from the ISO metric thread geometry, then the proof load Fp = At·Sp and the target preload as a chosen fraction of that proof load (typically 75 %).

Select an ISO metric bolt size and property class, or enter the diameter, pitch, proof strength, and yield strength directly. Choose a nut factor K that reflects the thread and under-head friction condition (about 0.20 plain, 0.16 lubricated, 0.12 with anti-seize). The tool returns the tensile stress area, target preload, required torque, and the resulting bolt tensile stress expressed as a percentage of yield.

How It Works

  1. Select a bolt size (sets diameter d and pitch p) and a property class (sets proof strength Sp and yield Sy), or override the values directly.
  2. Pick a preload target as a fraction of proof load (0.75 is common for reusable joints) and a nut factor K for the friction condition.
  3. The calculator computes the tensile stress area At = (π/4)(d − 0.9382·p)², the proof load Fp = At·Sp, and the target preload F = fraction·Fp.
  4. It applies the short-form torque equation T = K·F·d (with d in metres) and reports the bolt tensile stress σ = F/At and its ratio to yield strength.

Worked Example

An M16 class 8.8 bolt (d = 16 mm, pitch p = 2.0 mm, Sp = 580 MPa, Sy = 640 MPa) is tightened to 75 % of proof load with a plain nut factor K = 0.20. The tensile stress area is At = (π/4)(16 − 0.9382·2.0)² = (π/4)(14.124)² = 156.7 mm². The proof load Fp = 156.7·580 = 90,870 N, and the target preload F = 0.75·90,870 = 68,150 N. The required torque T = K·F·d = 0.20·68,150·0.016 = 218.1 N·m. The bolt tensile stress σ = F/At = 68,150/156.7 = 435 MPa, which is 0.75·Sp and about 68 % of the 640 MPa yield strength.

Formulas

Tensile stress area (ISO 898-1)
At = (pi / 4) * (d - 0.9382 * p)^2
Proof load and target preload
Fp = At * Sp ; F = fraction * Fp
Short-form tightening torque
T = K * F * d
Bolt tensile stress
sigma = F / At

Standards & References

  • ISO 898-1 (mechanical properties of fasteners, property classes)
  • VDI 2230 (systematic calculation of bolted joints)
  • Shigley’s Mechanical Engineering Design (torque–preload relation)

Frequently Asked Questions

What is the nut factor K and what value should I use?

The nut factor K is an empirical torque coefficient that lumps thread friction and under-head bearing friction into a single number in the relation T = K·F·d. Typical values are about 0.20 for plain as-received steel, 0.16 to 0.18 lubricated, and 0.10 to 0.12 with anti-seize or wax. Lower friction means more of the torque becomes preload.

Why target 75 % of proof load?

Tightening to about 75 % of proof load develops a high, stable clamping force while leaving margin below the proof and yield strengths, which keeps the joint tight under service loads without yielding the bolt. Permanent (single-use) joints are sometimes taken to 85–90 % of proof, and critical joints may use angle-of-turn or bolt-stretch control instead of torque.

How accurate is the T = K·F·d torque method?

The short-form torque equation is convenient but the achieved preload typically scatters by ±25–35 % because the nut factor K is sensitive to surface finish, lubrication, and seating. For tighter preload control use measured bolt elongation, turn-of-nut, or a calibrated tensioner, and follow VDI 2230 for a full joint analysis.

Why use the tensile stress area instead of the nominal area?

Threads remove material, so a bolt fails through the thread region at an effective area smaller than the shank. The tensile stress area At = (π/4)(d − 0.9382·p)² uses a diameter between the pitch and minor diameters and correlates with measured tensile strength, giving a realistic stress and preload basis.