Enter the bolt diameter (in) and the threads per inch into the Bolt Area Calculator. The calculator will evaluate the Bolt Area.
- All Construction Calculators
- All Area Calculators
- Bolt Length Calculator
- Bolt Pull Out Force Calculator
- Flange Bolt Torque Calculator
- Bolt Preload Calculator
Bolt Area Formula
The calculator uses one of three formulas depending on the mode you select.
Unified inch threads (tensile stress area):
At = (π/4) × (D − 0.9743/n)²
- At = tensile stress area (in²)
- D = nominal major diameter (in)
- n = threads per inch (TPI)
Metric (ISO) threads (tensile stress area):
As = (π/4) × (d − 0.9382p)²
- As = tensile stress area (mm²)
- d = nominal major diameter (mm)
- p = thread pitch (mm)
Plain round shank (unthreaded cross-section):
A = π × d² / 4
- A = cross-sectional area
- d = bolt or shank diameter
The Unified and ISO formulas approximate the area at the mean of the pitch and minor diameters. They apply to standard 60-degree thread profiles and are the values used in most strength calculations for tensile loading. For shear strength on the threaded portion, use a slightly smaller minor-diameter area.
Reference Tables
Tensile stress areas for common Unified coarse threads:
| Size | D (in) | TPI | At (in²) |
|---|---|---|---|
| 1/4-20 UNC | 0.250 | 20 | 0.0318 |
| 5/16-18 UNC | 0.3125 | 18 | 0.0524 |
| 3/8-16 UNC | 0.375 | 16 | 0.0775 |
| 1/2-13 UNC | 0.500 | 13 | 0.1419 |
| 5/8-11 UNC | 0.625 | 11 | 0.2260 |
| 3/4-10 UNC | 0.750 | 10 | 0.3340 |
| 1-8 UNC | 1.000 | 8 | 0.6060 |
Tensile stress areas for common ISO metric coarse threads:
| Size | d (mm) | p (mm) | As (mm²) |
|---|---|---|---|
| M5 | 5 | 0.8 | 14.2 |
| M6 | 6 | 1.0 | 20.1 |
| M8 | 8 | 1.25 | 36.6 |
| M10 | 10 | 1.5 | 58.0 |
| M12 | 12 | 1.75 | 84.3 |
| M16 | 16 | 2.0 | 157 |
| M20 | 20 | 2.5 | 245 |
| M24 | 24 | 3.0 | 353 |
Worked Example and FAQ
Example: 1/2-13 UNC bolt. D = 0.500 in, n = 13 TPI. Effective diameter = 0.500 − 0.9743/13 = 0.4251 in. At = (π/4) × 0.4251² = 0.1419 in². Multiply by the bolt’s allowable tensile stress to get its working load.
Which area should you use for tensile load? Use the tensile stress area (At or As). The plain shank area overstates capacity because the threads reduce the effective cross-section.
Which area for shear? If the shear plane goes through the threads, use the minor-diameter area, which is smaller than At. If the shear plane is on the unthreaded shank, use the plain round area.
Why 0.9743 and 0.9382? These constants come from the 60-degree thread geometry of Unified and ISO profiles. They place the diameter used in the area formula between the pitch and minor diameters.
Does coating change the area? No. Plating and coatings do not affect the structural cross-section used in strength calculations.
