Bolt Torque & Preload Calculator — Tightening Torque & Proof-Load Target
Estimate bolt preload from tightening torque, calculate required torque from preload, or target a selected percentage of bolt proof load using metric or Unified thread geometry and nut factor K.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Bolt geometry
Tightening torque
Preload force
Bolt proof-load target
Torque coefficient
Results
Calculation tools Save, export and manage your results
Save your calculation, export available results, or store a finalized engineering artifact in your account.
Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Bolt torque and preload equations
The calculator uses the simplified nut-factor relationship between tightening torque, bolt preload and nominal bolt diameter:
T = K · F · d
where:
- T — tightening torque [N·m]
- K — empirical nut factor [–]
- F — bolt preload force [N]
- d — nominal bolt diameter [m]
Torque → Preload
When tightening torque is known, the estimated preload is:
F = T / (K · d)
Preload → Torque
When the required preload is known, the corresponding tightening torque is:
T = K · F · d
Proof-load target
In proof-load target mode, the calculator first determines the tensile stress area of the threaded bolt.
ISO metric thread
As = π / 4 · (d − 0.9382 · p)2
where p is the metric thread pitch.
Unified thread
The Unified thread pitch is obtained from threads per inch:
P = 0.0254 / n
and the tensile stress area is:
As = π / 4 · (d − 0.9743 · P)2
where:
- As — tensile stress area [m²]
- p — metric thread pitch [m]
- P — Unified thread pitch [m]
- n — threads per inch, TPI [1/in]
The bolt proof load is then:
Fproof = As · Sp
where Sp is the entered bolt proof strength [Pa].
For a selected preload target r expressed as a percentage of proof load:
F = (r / 100) · Fproof
The corresponding tightening torque is:
T = K · F · d
The reported proof-load utilization is:
Proof-load utilization = F / Fproof · 100%
The calculation requires d > 0 and 0 < K ≤ 1. Metric proof-load calculations additionally require 0 < p < d. Unified calculations require a positive TPI value. The proof-load target must be greater than 0% and not greater than 100%.
When to use this calculator
When to use this calculator
Use this calculator when you need a simplified engineering estimate of the relationship between bolt tightening torque and axial preload.
- Estimate bolt preload from a known tightening torque, nominal bolt diameter and nut factor.
- Calculate the tightening torque required for a specified bolt preload.
- Set preload as a percentage of bolt proof load when proof strength and thread geometry are known.
- Calculate tensile stress area for ISO metric or Unified threads as part of the proof-load calculation.
- Compare the selected proof-load target with the calculated bolt proof load.
- Evaluate how a change in nut factor affects the torque or preload predicted by the simplified torque–tension model.
The nut factor K is an empirical torque coefficient. It should represent the actual fastener, thread, lubrication, coating and bearing-surface condition. A preset may be used when appropriate, or K may be entered directly when a validated value is available.
When this calculator is not sufficient
This calculator does not perform a complete bolted-joint design or verification. It does not calculate joint stiffness, external-load sharing, separation load, slip resistance, thread stripping, bearing pressure, fatigue life, preload loss, embedment, relaxation or thermal effects.
It also does not calculate separate thread and bearing friction coefficients, tightening scatter, torque-tool uncertainty, bolt stretch, tightening angle or combined tensile and torsional stress during installation.
For critical joints, the selected preload, proof strength, tightening method and torque specification should be verified against the applicable fastener specification, joint design procedure, manufacturer data and governing engineering requirements.
How to interpret the result
How to interpret the results
F — Preload force represents the bolt axial preload used by the simplified torque–preload model.
T — Tightening torque represents either the applied torque entered by the user or the torque calculated to produce the specified preload using the selected nut factor.
Torque → Preload mode
The entered tightening torque is retained as T and the calculator estimates preload from F = T / (K · d). Increasing torque increases the estimated preload. Increasing K or nominal bolt diameter decreases the calculated preload for the same applied torque.
Preload → Torque mode
The entered preload is retained as F and the calculator calculates T = K · F · d. Required tightening torque therefore increases directly with preload, nut factor and nominal bolt diameter.
Proof-load target mode
As — Tensile stress area is the effective threaded tensile area calculated from the selected metric or Unified thread geometry.
Fproof — Bolt proof load is calculated as As · Sp using the entered proof strength.
F/Fproof — Proof-load utilization reports the selected preload as a percentage of the calculated proof load. Because the target preload is defined directly from this percentage, the reported utilization corresponds to the selected target.
A proof-load target below 100% returns an informational result. A target of exactly 100% produces a warning because the calculated preload reaches the proof-load reference.
The calculator does not produce a PASS/FAIL safety verdict for the complete bolted joint. A calculated torque, preload or proof-load percentage does not by itself verify the joint against separation, slip, fatigue, thread failure, preload loss or other applicable design criteria.
Calculation example
Example — tightening torque from a proof-load target
An M12 × 1.75 metric bolt has an entered proof strength of 600 MPa. The target preload is 70% of proof load and the selected nut factor is K = 0.20. Calculate the target preload and estimated tightening torque.
Input data
- Nominal bolt diameter: d = 12 mm = 0.012 m
- Metric thread pitch: p = 1.75 mm = 0.00175 m
- Proof strength: Sp = 600 MPa = 600,000,000 Pa
- Target preload: 70% of proof load
- Nut factor: K = 0.20
Step 1 — Tensile stress area
As = π / 4 · (d − 0.9382 · p)2
As = π / 4 · (0.012 − 0.9382 · 0.00175)2
As ≈ 0.00008427 m² = 84.27 mm²
Step 2 — Bolt proof load
Fproof = As · Sp
Fproof = 0.00008427 · 600,000,000 ≈ 50,560 N = 50.56 kN
Step 3 — Target preload
F = 0.70 · Fproof
F ≈ 0.70 · 50.56 kN = 35.39 kN
Step 4 — Tightening torque
T = K · F · d
T = 0.20 · 35,391.9 · 0.012 ≈ 84.94 N·m
Result
The calculated tensile stress area is approximately 84.27 mm², the proof load is approximately 50.56 kN, the 70% target preload is approximately 35.39 kN, and the corresponding tightening torque is approximately 84.94 N·m.
This torque is an estimate based on the selected nut factor. The calculation does not model friction scatter or verify the complete bolted joint.
Assumptions and limitations
Assumptions and limitations
- The torque–preload relationship is modeled using the simplified empirical equation T = K · F · d.
- The nut factor K is treated as a single empirical coefficient. The calculator does not separately model thread friction and bearing-surface friction.
- The selected or entered K value is assumed to represent the actual fastener, lubrication, coating, surface finish and tightening condition.
- Nominal bolt diameter is used directly in the torque–preload equation.
- The calculator internally requires positive finite values for bolt diameter, torque or preload as applicable, with 0 < K ≤ 1.
- Metric proof-load calculations use As = π/4 · (d − 0.9382p)2 and require a positive thread pitch smaller than the nominal diameter.
- Unified proof-load calculations use As = π/4 · (d − 0.9743P)2, with P = 0.0254/n and a positive TPI value.
- Proof strength Sp is supplied as an input. The calculator does not determine proof strength from a bolt grade, material designation or manufacturer specification.
- The proof-load target is limited to values greater than 0% and not greater than 100%. A 100% target is accepted mathematically but is explicitly flagged with a warning.
- The model does not calculate tightening uncertainty or preload scatter caused by variation in friction, tool accuracy, surface condition or assembly procedure.
- Joint stiffness and the distribution of external load between the bolt and clamped members are not modeled.
- Joint separation, slip resistance, thread stripping, bearing pressure, bolt shear and member strength are not evaluated.
- Torsional stress generated during tightening and combined tensile–torsional yielding are not evaluated.
- Fatigue, vibration, self-loosening, embedment, relaxation, creep, corrosion and thermal preload changes are outside the implemented model.
- No safety factor is applied automatically to the entered proof strength or selected proof-load percentage.
- The calculation is not a code-compliance check. Final preload and tightening requirements should be verified using the applicable fastener specification, manufacturer data, assembly procedure and governing engineering requirements.