# Shotgun Bore Diameter Math

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## Introduction

Figure 1: Relative Bore Diameters of Shotgun Gauges. (Source)

I have been doing some metalwork lately that involves using units of "gauge". You will find the term gauge used in the measurement of wire, metal thickness, and pipe bore diameter. This quaint, but confusing, measurement system is slowly falling out of favor (example, sheet metal thickness gauge).

One area where I do not see gauge measurements going away is in the specification of shotgun bore diameters. I was talking to friends recently about their recent hunting adventures, and the subject of shotgun gauges came up. During this conversation, I mentioned that in my youth I hunted using my grandfather's 10 gauge shotgun  – he called it his "goose gun". I was surprised to hear that some folks consider the 10 gauge shotgun obsolete (example). Their arguments were based on old 10 gauge guns only supporting limited chamber pressures compared to newer 12 gauge shotguns.

As we talked, I realized that I did not know how to convert between shotgun gauge and bore diameter. This post examines the derivation of a formula that relates shotgun gauge to bore diameter.

## Analysis

The Wikipedia defines shotgun gauge as

An n-gauge diameter means that a ball of lead (density 11.34 g/cm3 or 0.4097 lb/in3) with that diameter has a mass equal to 1/n part of the mass of the international avoirdupois pound (approx. 454 grams), that is, that n such lead balls could be cast from a pound weight of lead.

This means that a 10 gauge shotgun bore has the same diameter as a 1/10 pound ball of lead. The gauge number and the bore diameter are related by Equation 1.

 Eq. 1 $\displaystyle {{d}_{G}}\left( {{{n}_{{Gauge}}}} \right)=\frac{{1.67049}}{{n_{{Gauge}}^{{\frac{1}{3}}}}}\cdot \text{in}$

where

• dG is bore diameter of a shotgun of gauge nGauge
• nGauge is gauge of the shotgun in question.

Using Mathcad, we can derive Equation 1 as follows.

Figure 2: Derivation of Equation 1.

## Example Calculations

We can use Equation 1 to compute some common shotgun bore diameters. I will also compare my computed diameters with the diameters listed on a popular website. I will also compute the equivalent gauge of a 410 caliber shotgun.

Figure 3: Simple Calculation Examples Using Equation 1.

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### 3 Responses to Shotgun Bore Diameter Math

1. Filip says:

This is interesting I was not aware that people also used Gauge for the bore diameter of shotguns. I always believed that Gauge was only used for representing the diameter of needles. However, although both are called Gauge the equation for needle Gauge is different: Unit which expresses the external diameter of the object, in a range
from 8 to 30, corresponding respectively to 4 and 0.3mm.

• mathscinotes says:

Hi Filip,

I was unaware of gauge being used for needles! I encounter gauge units all the time in many areas. I find them frustrating because they all seem to have a historical basis that is no longer relevant.

mark

2. Filip says:

Dear Mark, I can only confirm your frustration. It would be a tremendous benefit if we would all use the same units all over the world...