Screw Thread Calculator
Compute the tensile load capacity of a metric screw thread based on nominal diameter, pitch, material strength, and safety factor. Use it when verifying bolt joint adequacy in structural or mechanical assemblies.
About this calculator
A screw thread's load-carrying capacity is governed by the stress area — the effective cross-sectional area at the thread root that resists axial tension. For metric threads, the tensile stress area is approximated using the formula: A_s = (π/4) × (d − 0.9743 × p)² — a close equivalent to the ISO formula using the constant 1.082532 × p in this calculator's implementation. The maximum tensile load capacity is then F = A_s × σ_UTS / SF, where σ_UTS is the ultimate tensile strength of the bolt material and SF is the safety factor. Material grade markings (e.g., 8.8, 10.9) indicate the minimum tensile strength. A higher pitch (coarser thread) reduces the stress area and therefore reduces load capacity for the same nominal diameter. This calculation is fundamental to bolted joint design.
How to use
Check an M12 bolt: Nominal diameter = 12 mm, Pitch = 1.75 mm, Tensile strength = 800 MPa (grade 8.8), Safety factor = 2. Step 1 — stress area diameter: 12 − 1.082532 × 1.75 = 12 − 1.8944 = 10.1056 mm. Step 2 — stress area: A_s = (π/4) × 10.1056² = 0.7854 × 102.12 = 80.2 mm². Step 3 — allowable load: F = 80.2 × 800 / 2 = 32,080 N = 32.1 kN. This means the M12 grade 8.8 bolt can safely carry approximately 32 kN axial tensile load with a safety factor of 2.
Frequently asked questions
What is the tensile stress area of a screw thread and why does it differ from the nominal diameter area?
The tensile stress area accounts for the reduced cross-section at the thread roots, where fracture would occur under tensile overload. It is smaller than the area calculated from the nominal (outer) diameter because the thread cuts into the shank. Using the nominal diameter area would significantly overestimate bolt strength. The ISO 898 standard defines the tensile stress area formula A_s = (π/4) × ((d₂ + d₃)/2)², based on the average of the pitch and minor diameters, which closely matches empirical test results.
How do metric bolt grade markings like 8.8 or 10.9 relate to tensile strength?
ISO metric bolt grades are expressed as two numbers separated by a point. The first number multiplied by 100 gives the minimum ultimate tensile strength in MPa — so a grade 8.8 bolt has at least 800 MPa UTS, and a grade 10.9 bolt has at least 1,000 MPa UTS. The second number multiplied by the first times 10 gives the proof load stress (e.g., 8 × 8 × 10 = 640 MPa for grade 8.8). Higher grades allow smaller bolt diameters for the same clamping force, but may be more susceptible to hydrogen embrittlement and require controlled tightening procedures.
When should I use a finer thread pitch instead of a coarse thread for a bolted joint?
Fine thread pitches have a larger tensile stress area than coarse pitches of the same nominal diameter, giving higher tensile and torsional strength per bolt. They are preferred when the joint material is thin, when precise preload control is needed (fine threads are less sensitive to torque scatter), or where vibration resistance is critical since the shallower helix angle resists self-loosening better. However, coarse threads are more tolerant of dirt, corrosion, and cross-threading, and are faster to assemble — making them the default choice for most general-purpose structural and mechanical fastening applications.