Bolt Elongation Calculator

Mechanical elongation assumes linear elasticity:

δ_mech = (F · L) / (A · E)

Thermal elongation is optional:

δ_th = α · ΔT · L

Total elongation sums both contributions:

δ_total = δ_mech + δ_th

Stress and strain are:

σ = F / A,    ε = δ / L

Stiffness is:

k = (A · E) / L

Area estimation (when A is not entered)

For metric threads, tensile stress area is estimated by:

A_s ≈ (π/4) · (d − 0.9382·p)²

For unified threads, tensile stress area is estimated by:

A_s ≈ (π/4) · (d − 0.9743/n)²

d is diameter, p is pitch, and n is threads-per-inch.

1. Enter the bolt axial force and effective length.
2. Provide tensile area, or enter diameter for estimates.
3. Select a material preset, then verify E and α.
4. Optional: add temperature change for thermal effects.
5. Optional: enter yield strength to get safety factor.
6. Press Calculate to view results above the form.
7. Download CSV or PDF for documentation.

1) What bolt stretch controls

Bolt elongation is the elastic stretch that produces clamp force in a joint. Stable stretch helps resist vibration, gasket relaxation, and embedment. If stretch is too small, clamp load can vary wildly. If stretch is too large, threads can yield and preload repeatability drops.

2) Mechanical elongation from axial force

This calculator uses δ = F·L/(A·E). Elongation rises with higher force and longer effective length. It falls with larger tensile area and higher elastic modulus. When you stay below yield, the relationship is nearly linear, so scaling inputs gives predictable elongation changes.

3) Picking an effective length (L)

Effective length is the portion of the fastener that actually stretches. It is often close to grip length plus a fraction of engaged threads. Longer effective length makes the bolt “springier,” improving preload stability after seating or creep. Short, stiff bolts lose preload faster.

4) Tensile stress area versus shank area

Threads reduce the load-carrying section, so tensile stress area is smaller than shank area. Using tensile area gives higher stress and more elongation for the same force. If you do not know A, the tool can estimate it from diameter and pitch (metric) or TPI (unified).

5) Stress, strain, and a quick safety check

Stress is σ = F/A and mechanical strain is ε = δ/L. If you provide yield strength, the calculator reports Sy/σ as a simple safety factor against yielding. It is not a fatigue or joint-separation model, but it helps flag loads that are too aggressive.

6) Thermal elongation for temperature swings

Thermal growth is δth = α·ΔT·L. A steel fastener with α≈12×10⁻⁶/°C gains about 0.03 mm over 50 mm for a 50°C rise. Real clamp change also depends on joint materials and constraints, so treat δth as bolt-only expansion.

7) Using bolt stiffness output

Bolt stiffness k = A·E/L shows how much force changes per unit stretch. Higher stiffness means small elongation differences create large force differences. This is useful for estimating preload loss from settlement: a small seating displacement can remove more force when k is high.

8) Practical input ranges and unit discipline

Typical steel modulus is near 200 GPa, while yield strength varies widely by grade. Preload targets often fall around 60–80% of proof capacity when using controlled methods. Keep units consistent, verify the chosen area, and compare stress to your allowable limits for final verification.

1) What is bolt elongation?

Bolt elongation is the axial stretch of a fastener under tensile load. In the elastic range, that stretch behaves like a spring and generates clamp force that holds joint members together.

2) Which force should I enter?

Enter the axial bolt force you expect in service, commonly the preload. If you only have torque, estimate preload using your torque method first, then use that force here.

3) What if I do not know tensile stress area?

Leave area blank and enter diameter. The calculator can estimate tensile area using metric pitch or unified TPI. For critical designs, confirm area from the relevant fastener standard table.

4) Why does effective length matter so much?

Elongation is proportional to L. Longer bolts stretch more for the same force, which generally improves preload stability after embedment or creep. Very short bolts are more sensitive to small seating losses.

5) Does thermal elongation equal preload change?

No. The tool reports bolt-only expansion using α·ΔT·L. Preload change also depends on how the clamped parts expand, joint stiffness, and whether components are constrained.

6) What does bolt stiffness mean?

Stiffness k shows force per unit elongation. A higher k means a small additional stretch corresponds to a larger force change. It is useful when combining bolt and joint stiffness in clamp-load models.

7) Is the safety factor a full design approval?

No. Sy/σ is a quick check against yielding under the entered force. It does not cover fatigue, thread stripping, joint separation, relaxation, or installation scatter. Use your engineering standard for final approval.