Enter the AWG gauge size and choose the fraction precision into the calculator to determine the wire diameter in decimal inches, millimeters, and the nearest inch fraction.
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Gauge to Fraction Formula
American Wire Gauge is defined so that wire diameters follow a geometric progression. The following formulas are used to calculate the decimal diameter in inches, convert it to millimeters, and round it to a practical inch fraction.
d_{in} = 0.005 \times 92^{\frac{36-n}{39}}d_{mm} = d_{in} \times 25.4f \approx \frac{round(d_{in} \times D)}{D}Variables:
- din is the wire diameter in inches
- dmm is the wire diameter in millimeters
- n is the AWG gauge number
- D is the chosen fraction denominator, such as 16, 32, or 64
- f is the rounded fractional inch value
To calculate the gauge to fraction conversion, first determine the wire diameter in inches using the standard AWG equation. Then convert the inch value to millimeters and round the inch diameter to the nearest selected fraction such as 1/16, 1/32, or 1/64 of an inch.
What is Gauge to Fraction Conversion?
Gauge to fraction conversion is the process of taking an American Wire Gauge size and expressing the wire diameter in more familiar forms, including decimal inches, millimeters, and fractional inches. This is useful when comparing wire sizes with drawings, drill references, shop measurements, and general specifications that use inch fractions instead of AWG numbers.
Because AWG sizes are based on a geometric scale, each step in gauge changes the wire diameter by a constant ratio rather than by a fixed linear amount. Once the decimal diameter is known, it can be rounded to a practical inch fraction for quick reference.
How to Calculate Gauge to Fraction?
The following steps outline how to calculate the gauge to fraction conversion.
- First, determine the AWG gauge number n.
- Next, calculate the wire diameter in inches using d (in) = 0.005 × 92(36 − n)/39.
- Convert the result to millimeters by multiplying the inch diameter by 25.4.
- Choose a fraction denominator such as 16, 32, or 64.
- Finally, round the decimal inch value to the nearest fraction using round(d × D) / D.
- After calculating the result, check your answer with the calculator above.
Example Problem:
Use the following values as an example problem to test your knowledge.
Gauge (AWG) = 12
Fraction Denominator (D) = 64
Diameter in Inches ≈ 0.0808
Diameter in Millimeters ≈ 2.0523
Nearest Fraction ≈ 5/64 in
Gauge to Fraction Conversion Table
The table below lists common AWG sizes, their approximate diameters in inches and millimeters, and the nearest inch fraction when rounded to the nearest 1/64 inch.
| Gauge (AWG) | Diameter (in) | Diameter (mm) | Nearest Inch Fraction (1/64 in) |
|---|---|---|---|
| 10 | 0.102 | 2.59 | 7/64 in |
| 12 | 0.081 | 2.05 | 5/64 in |
| 14 | 0.064 | 1.63 | 1/16 in |
| 16 | 0.051 | 1.29 | 3/64 in |
| 18 | 0.040 | 1.02 | 3/64 in |
In practice, engineers, technicians, and fabricators often move between decimal inches, millimeters, and fractional inches when reading specifications and comparing component sizes. Converting AWG to a fractional inch format makes those references easier to interpret in everyday use.