About this calculator
This is the simplest and quickest of the bolted-joint tools on this site: it evaluates the axial load capacity of a metric bolt cross-section. Choose a thread size (M6–M42 coarse) and an EN ISO 898-1 strength class, set the initial tensile stress as a fraction α of the yield strength, and read off the preload Fi, the load at which the bolt reaches yield F0.2, and the reserve between the two. No friction or torsion is involved — the calculation looks purely at the tension side of the problem, which makes it the right first check when sizing a bolt for a required clamping force.
Theory and equations
A threaded fastener under axial load fails through a cross-section that is larger than the thread root circle, because the material between roots participates in carrying load. EN ISO 898-1 captures this with the tensile stress area:
where d is the nominal diameter and P the pitch. The term d − 0.938194 P is the mean of the pitch diameter d2 and the minor diameter d3 from ISO 724. With the stress area established, the outputs follow directly:
The load reserve Pb is the extra axial force the bolt can absorb beyond its preload before the nominal stress reaches the 0.2% proof strength. In a real joint only a fraction of any external load reaches the bolt (the rest unloads the clamped parts) — the joint diagram calculator shows exactly how that split works.
Strength classes per EN ISO 898-1
The class designation encodes the material properties: the first number is the nominal tensile strength in hundreds of MPa, the second the yield-to-tensile ratio in tenths. So class 8.8 means Rm = 800 MPa and Rp0.2 = 0.8 × 800 = 640 MPa; class 12.9 means Rm = 1200 MPa and Rp0.2 = 1080 MPa. The calculator covers classes 3.6 through 12.9 with their nominal values.
Worked example: M16, class 8.8, 90% preload
- Stress area: M16 coarse has P = 2 mm, so At = (π/4)(16 − 0.938194 × 2)² = 156.67 mm² (published value 157 mm²).
- Tensile stress: σt = 0.90 × 640 = 576 MPa.
- Preload: Fi = 576 × 156.67 = 90.2 kN.
- Load at yield: F0.2 = 640 × 156.67 = 100.3 kN.
- Load reserve: Pb = 100.3 − 90.2 = 10.0 kN — the additional bolt force available before nominal yielding.
Interpretation: preloaded to 90%, this M16 bolt clamps with just over 90 kN, and an external load path could add roughly 10 kN of bolt force before yield. Whether 90% preload is actually reachable with a torque wrench is a separate question involving thread friction — check it with the tightening torque calculator.
Assumptions and limitations
- Nominal EN ISO 898-1 properties; actual certified batch values may differ slightly (for some classes, sizes above M16 have adjusted guaranteed values).
- Static, purely axial loading of the threaded section; no bending, shear, or torsion.
- Coarse-pitch ISO metric threads; fine pitches have slightly larger stress areas.
- The reserve is measured to first nominal yield, not to fracture.
Frequently asked questions
What is the tensile stress area of a bolt?
The effective cross-section for converting bolt stress to force: At = (π/4)(d − 0.938194 P)², based on the mean of pitch and minor diameters. For M12 coarse it is 84.3 mm² — noticeably less than the 113 mm² of the plain 12 mm shank.
What preload fraction should I choose?
Typically 60–90% of Rp0.2. Higher preload helps fatigue life and prevents separation and slip, but leaves less reserve to yield — and when tightening by torque, friction-induced torsion usually caps the achievable preload near 70% of yield.
What does a strength class like 8.8 mean?
First number: tensile strength in hundreds of MPa. Second: yield-to-tensile ratio in tenths. 8.8 ⇒ Rm = 800 MPa, Rp0.2 = 640 MPa; 10.9 ⇒ Rm = 1000 MPa, Rp0.2 = 900 MPa.
Why doesn’t this calculator ask for friction or torque?
It intentionally isolates the axial capacity of the cross-section. Friction only matters when converting torque to preload — that conversion, including the torsional stress it adds, lives in the tightening torque calculator.