Calculate bolt root area, nominal diameter, or thread pitch from any two values in mm or inches, with results in metric or imperial units.
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Bolt Root Area Formula
The bolt root area is based on the minor, or root, diameter of the threaded section. This calculator uses the nominal diameter and thread pitch to estimate the root diameter, then calculates the circular area at that diameter.
Combined into one formula:
To solve for nominal diameter:
To solve for thread pitch:
- Ar = bolt root area
- dr = root diameter, also called minor diameter in this calculation
- D = nominal bolt diameter
- P = thread pitch
- pi = 3.14159265…
If you enter nominal diameter and thread pitch, the calculator finds the root area. If you enter root area and pitch, it rearranges the formula to find nominal diameter. If you enter nominal diameter and root area, it rearranges the formula to find thread pitch. Inch inputs are converted to millimeters before calculation, and area results can be returned in mm² or in².
Common Metric Coarse Thread Root Areas
The values below use the same formula as the calculator. They are useful for checking typical metric coarse thread inputs.
| Thread Size | Nominal Diameter | Pitch | Approx. Root Diameter | Approx. Root Area |
|---|---|---|---|---|
| M6 × 1.0 | 6 mm | 1.0 mm | 4.773 mm | 17.89 mm² |
| M8 × 1.25 | 8 mm | 1.25 mm | 6.466 mm | 32.84 mm² |
| M10 × 1.5 | 10 mm | 1.5 mm | 8.160 mm | 52.30 mm² |
| M12 × 1.75 | 12 mm | 1.75 mm | 9.853 mm | 76.25 mm² |
| M16 × 2.0 | 16 mm | 2.0 mm | 13.546 mm | 144.12 mm² |
| M20 × 2.5 | 20 mm | 2.5 mm | 16.933 mm | 225.19 mm² |
Unit Conversions Used
| Measurement | Conversion |
|---|---|
| Diameter | 1 in = 25.4 mm |
| Pitch | 1 in = 25.4 mm |
| Area | 1 in² = 645.16 mm² |
Example Calculations
Example 1: Find root area from diameter and pitch
For an M10 × 1.5 bolt:
- Nominal diameter = 10 mm
- Thread pitch = 1.5 mm
The root area is approximately 52.30 mm².
Example 2: Find nominal diameter from root area and pitch
Suppose the root area is 76.25 mm² and the thread pitch is 1.75 mm.
The nominal diameter is approximately 12 mm, matching an M12 × 1.75 thread.
FAQ
Is bolt root area the same as tensile stress area?
No. Root area is based on the root, or minor, diameter of the thread. Tensile stress area is a different standardized effective area used for bolt strength calculations. The tensile stress area is usually larger than the root area for standard threads.
Why does a larger thread pitch reduce the root area?
A larger pitch means deeper thread geometry for the same nominal diameter. Deeper threads reduce the root diameter, and since area depends on diameter squared, the root area also decreases.
Can this be used for inch threads?
Yes, if you enter the nominal diameter and pitch in inches. For inch threads, pitch is often given as threads per inch, or TPI. Convert TPI to pitch first using pitch = 1 / TPI. For example, a 1/2-13 thread has a pitch of 1/13 = 0.07692 in.
