How can you convert units of weight into units of length? You can if you're talking about old cannons.

Up until second half of XIX century cannon’s caliber was expressed in pounds. For example, 24-pounds cannon. You can often meet such things in historical books. Now, how modern person can imagine such cannon? Is it big or not? What is the 24-pounds cannon?

So, I decided to employ a little bit of logic and convert pounds to more familiar units used for gun’s calibers now – inches and millimeters.
(BTW, there are the tables of correspondence all over the Internet, so later I’ll use them to prove my calculations)

Here comes the deduction.

Pounds in caliber denote weight of cannon ball, which can be fired off this gun. Now caliber is measured as diameter of gun’s barrel, and expressed in inches, or millimeters, and we can imagine how big such gun is.

Let’s start from conversion of pounds to kilograms. Pounds are very different by nature , but, since I’m Russian, "Russian artillery pound", equals 494,414 gramms, looks very promising to me. And, surprisingly, it was used to measure weight of cannon balls.

After we have find weight of cannon ball, and since it is, well, spherical, we can find diameter of sphere. Cannon balls were made from cast iron. Density of cast iron, according to this handbook is 7000 kilograms per cubic meter. We have ball mass and density, so obviously, we can find volume. From the over hand, volume of sphere should be , and from this we can find radius, hence, diameter of cannon ball.

According to common sense, diameter of barrel should be slightly greater than diameter of cannon ball. But the gap should be as small as possible, so explosion impulse can be used at maximum.

Piter the Great (1672-1725) establish the standard, and according to it, cannon of 24 pounds or less should have gap between barrel and ball not greater than 1/29 of caliber, in other words, diameter of barrel is 29/29 and diameter of ball is 28/29. Cannons of greater calibers have separately defined gaps.

But even this is enough information for my further deduction. 1/29 for 24-pounds caliber is 5.2 millimeters. For greater calibers I’ll take 5 millimeters.

So, on final step I just add this gap (twice) to the diameter of ball. To get inches, I simply divide millimeters to 25.4 (one inch)

Online calculator below repeats these steps and outputs gun’s caliber in inches and millimeters given the cannon ball weight in pounds.

Now, I’ve compared my results with tables.
3 pounds - 76 millimeters (mine) - 77 millimeters (tables)
4 pounds - 88 millimeters (mine) - 84 millimeters (tables)
6 pounds - 95 millimeters (mine) - 97 millimeters (tables)
12 pounds - 120 millimeters (mine) - 122 millimeters (tables)
18 pounds - 137 millimeters (mine) – 139 millimeters (tables)
24 pounds - 152 millimeters (mine) – 153 millimeters (tables)
60 pounds - 195 millimeters (mine) – 206 millimeters (tables)

Well, pretty close, I’d say. Common sense with school knowledge of physics and math can yield you and answer :)