Almighty Calculator

Bolt Stress Area, Proof Load, and Torque Calculator

Tensile stress area is 0.7854 × (D − 0.9743 ÷ TPI)², proof load is that area times proof strength, and torque ≈ K × diameter × preload.

Estimate only. Results are estimates. Verify against the applicable code and manufacturer specifications before relying on them for safety-related work.

in
Grade 5 proof strength applies up to 1 in; Grade 8 up to 1-1/2 in.
TPI
1/2 in coarse is 13; fine is 20.
%
Your engineering choice; joints that will be reused are usually loaded lower than permanent ones.
Typical values; K varies a lot with plating, lubricant, and surface.
Proof load
12,061lbf
Tensile stress area0.1419 in²
Target preload9,046 lbf
Estimated tightening torque75.4 lb·ft

Show the math

Stress area = 0.7854 × (0.5 − 0.9743 ÷ 13)² = 0.1419 in²
Proof load = 0.1419 in² × 85 ksi = 12,061 lbf
Preload = 12,061 × 75% = 9,046 lbf
Torque = K × D × preload = 0.2 × 0.5 in × 9,046 lbf ÷ 12 = 75.4 lb·ft

Rounded the same way as the result above.

How it works

A threaded fastener carries tension over its tensile stress area, which is a little less than the shank area because of the threads. The proof load is the largest tension it can carry without permanent stretch: the stress area times the grade’s proof strength.

Tightening a bolt stretches it and clamps the joint; the stretch tension is the preload. Torque relates to preload through T = K × D × F, where K, the nut factor, lumps together all the thread and under-head friction. Because K varies widely, torque is only an estimate of preload.

A_t = 0.7854 × (D − 0.9743 ÷ n)² Proof load = A_t × proof strength Torque = K × D × F

Worked example

A 1/2-13 Grade 5 bolt tightened to 75% of proof, dry:

  1. Stress area = 0.7854 × (0.5 − 0.9743 ÷ 13)² = 0.1419 in²
  2. Proof load = 0.1419 in² × 85 ksi = 12,061 lbf
  3. Preload = 12,061 × 75% = 9,046 lbf
  4. Torque = K × D × preload = 0.2 × 0.5 in × 9,046 lbf ÷ 12 = 75.4 lb·ft
InputValue
Bolt gradeSAE Grade 5 (85 ksi proof)
Nominal diameter0.5 in
Threads per inch13 TPI
Target preload, % of proof load75 %
Thread condition (nut factor K)Dry, plain steel (K = 0.20)
ResultValue
Tensile stress area0.1419 in²
Proof load12,061 lbf
Target preload9,046 lbf
Estimated tightening torque75.4 lb·ft

Assumptions and limits

  • Inch UNC and UNF threads only, and SAE Grade 5 and Grade 8 proof strengths from SAE J429. Metric and other grades differ.
  • K values are typical. Plating, lubricant, thread condition, and surface finish change K by tens of percent, so torque gives an uncertain preload.
  • Tension only. Shear, fatigue, embedment, and joint stiffness are not evaluated.

Common questions

What is the proof load of a 1/2-13 Grade 5 bolt?

About 12,000 lbf: 0.1419 in² × 85,000 psi.

How do I torque a bolt to a preload?

Use T = K × D × F. Select a nut factor for your thread condition, then check the result against the joint designer’s specified torque.

Should I lubricate the bolt?

Lubrication lowers K, so the same torque produces a larger preload. Use torque values specified for the condition you have.

What is the tensile stress area?

The effective cross-section that carries tension, smaller than the nominal shank because of the thread roots: 0.7854 × (D − 0.9743 ÷ n)².

Sources

  • Machinery’s Handbook thread stress area: A_t = 0.7854 (D − 0.9743 ÷ n)² for unified threads.
  • SAE J429 proof loads (Grade 5 up to 1 in: 85 ksi; Grade 8 up to 1-1/2 in: 120 ksi), as tabulated by Engineering ToolBox.
  • Short-form torque equation T = K D F and typical nut factors (dry 0.20, lightly oiled 0.15, hot-dip galvanized 0.18, moly grease 0.10).
  • Read them: Engineering ToolBox: U.S. bolts tensile and proof load

Updated 2026-09-30