# How Many Candles in a Barrel?

In a current Pathfinder game I'm running the PCs have decided to take multiple wagons full of mundane items to outposts/remote villages/etc., both as bribes and for business purposes. They are frequently asking me questions such as "how many candles can I fit in a standard barrel?" and "if we buy cabbages, apples, walnuts, and pumpkins, how many can we fit in our wagon?"

Since this is apparently the theme they've settled on, I'm going to let them run with it until they devise some other method of... whatever they're doing. My players do genuinely want this kind of detail. In all fairness, I do as well; I like low-magic campaigns, and in those, logistics like this become increasingly important. However, I'm getting stretched trying to ad-hoc reasonable responses to these, and am looking for a sensible approach without a lot of math each time, while keeping to a relative level of consistency.

Is there a ratio relating the listed weights to volume that I can use to help answer these questions? If there's a ratio, then I could take the CRB's given weights for items and multiply by the ratio to obtain a rough idea of the amount of space an item occupies.

Yes, I know everything varies, and a ton of feathers clearly isn't the same as a ton of bricks, etc., etc. I don't want real-world accuracy, I want a reasonably fast, gameable method so I can ensure consistency during play without taking up lots of time. We're mostly dealing with produce, or the standard trade goods listed in most rule sources, so big density differences are not likely to be an issue that needs to intrude on gameability.

What I'm hoping for is a rough decimal/fraction/percentage comparing weight to volume, so I can just plug in "X pounds of item" and then divide into the given container volumes.

I also don't want to keep guesstimating since that has been, from experience, neither fast nor sufficiently consistent. It's a waste of my time as GM.

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"One candle per barrel, but it's a big one." – Trevel Jan 7 at 21:00

While Pathfinder is great at letting the player know what's on his character's body and how much all of that weighs, it's not so good at measuring freight or determining weight and value of household goods. These are better off abstracted into just gp values and raw weights instead of individual fruits and vegetables.

That is, if the players want to spend their table time with their characters haggling over every pumpkin and where the pumpkin will go in their cart and how much the pumpkin weighs and how long until the pumpkin spoils and whether the pumpkin's organically or magically grown or whatever—seriously, if the players want to play Pathfinder: Farmers' Market—the game's not really going to support them very well. Pathfinder's a game of heroic magical adventure, and that sort of agronomical detail is better left to other game systems. No one game is supposed to accommodate all interests, after all.

But, if the players are nonetheless trying to make this work, I suggest abstracting the crap out of this to speed play. For instance, here's a really basic system to get you started that you can repurpose for your campaign:

• Measure everything in creature-size crates (Fine, Diminutive, Tiny, Small, Medium, etc.). That solves the volume problem.
• A Medium crate of anything weighs 100 lbs. Multiply or divide that weight by 10 for every size category bigger or littler, respectively.
• Multiply that weight by ×½ for light goods or by ×2 for heavy goods, creating higher or lower additional categories if needed.
• A Medium crate of anything has a value of 1 gp. Multiply or divide the value by 10 for every size category bigger or littler, respectively.
• Multiply that value by ×½ for cheap goods or by ×2 for expensive goods, creating higher or lower additional categories if needed.

There you go. Medium crate of expensive goods? 2 gp and 100 lbs. Small box of cheap goods? 1 cp and 10 lbs. Colossal crate of heavy expensive goods? 2,000 gp and 1,000 tons. Easy, quick, playable, and you don't have to count cabbages.

Your players may balk at the minuscule sums their characters earn through such efforts, and they should: being a commoner sucks, and they're doing commoner work, so they're earning commoner wages. They want real money? Go kill some monsters and take their stuff.

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Perfect. If they want the greater income, I can point them to @RobertF 's answer below, and they're welcome to do that math themselves. Thank you. – YttriumDervish Jan 7 at 20:24
As you say: Commoners work! Another approach would be the economic approach: Doing the work of a normal tradesman should earn them the same as a normal tradesman. If they are taking a dangerous route they will earn how much a tradesman and some mercenaries for protection earn alltogether. By calculating these numbers you can easily infer how much profit they can make with "a wagon full" and you don't break economics by calculating wrong and letting them make 100 GP profit with a barrel full of candles. – Falco Jan 8 at 10:23
@Falco If it were solely a function of profit I would. It isn't uncommon for then to give a barrel of candles to a guard outpost, to try and earn the Quartermaster's favor. Plus, they want to know as near exact a number as I'm willing to tell them. I get the feeling they're plotting against me when I'm not around, but I don't mind; at least then they have a plan and aren't, as HICC put it, playing Pathfinder: Farmer's Market. – YttriumDervish Jan 8 at 14:17
@YttriumDervish In my experience from both sides of the screen, players are usually colluding out of earshot of the GM. But it's also been my experience that plans from such collusion usually resolve themselves in unexpected ways because the DM isn't able to adjust the campaign for them. I urge you to ask the players what they're up to then either nixing it or getting on board... so you can stop worrying about this stuff and start doing instead what the game's good at doing. – Hey I Can Chan Jan 8 at 14:35

Assuming the candles are cylindrical, they'll pack together in a hexagonal pattern.

Given the dimensions of the candles and the barrels (which we'll assume are also cylindrical), see here for a formula approximating the # of hexagons which can be fit inside a circle. Multiple this number by the ratio of the barrel height/candle length and you should have a good ballpark estimate.

When loading spherical shaped objects like fruit and nuts, there are sphere-packing formulas available for calculating the density of spheres in a given volume.

In reality goods like fruit are very squishable - for simplicity's sake the objects are considered incompressible for the above calculations. Perhaps there are partitions inside the barrels to prevent cargo getting damaged?

In the spirit of Jekowl's suggestion for using Fermi estimation in the question comments, another option is sampling. Find a cardboard box of known dimensions and pack it with various items from around your home (candles, apples, etc.) equivalent in size & shape to the goods being traded by the PCs. Then extrapolate the # of items you successfully packed to a much larger container like a barrel or a wagon. This estimation method may work especially well with irregularly shaped things, like shovels.

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This is close to what I'm looking for, and perfect for times when I need a more exact figure, i.e. items of great value. It's a bit much for general use. And no partitions; nominal loss is mitigated by general rounding. – YttriumDervish Jan 7 at 19:46
@YttriumDervish - I think it's reasonable to outsource the math to the players in this case - it shouldn't be too hard to set up an Excel spreadsheet. I'm sure medieval merchants trading in quantity had to perform similar calculations, why not make the PCs do so as well? At any rate, you only need to do the calculations once for each type of good. After that it's simple math finding the # of items which can be packed in a given volume. – RobertF Jan 7 at 19:54
Valid point. Maybe then they'll move on to adventuring if I'm not having to shoulder this work for them. Or not, but either way they can handle it. – YttriumDervish Jan 7 at 20:05
@YttriumDervish - Also, as the players gain skill at making these calculations, other merchants may take notice & come to the players for help. The PCs can set up an accounting shop! :) – RobertF Jan 7 at 20:12

I would abstract the whole thing into weight and not worry about details at all to make sure this does not impact on gameplay greatly.

By the rules a barrel contains 650 lbs, costs 2 GP and weighs 30 lbs. Thus a medium wagon can carry 2000 lbs or ~2.9 full barrels of anything. The weight of the goods is ~1890 lbs and the cost of the barrels is 5 GP + 8 SP.

If this seems unrealistic (it does to me), include a "packing" factor for non liquid items (being less dense and taking a bit of packing space). I reversed the calculation for a medium wagon load.

I.e. I think a medium wagon should hold 6 barrels and can carry a total of 2000 lbs. So 2000/6 = 333 lbs / barrel. This the contents of each barrel is 300 lbs. This seems like a nice packing rule and makes calculating the number of barrels easy. So each barrel can handle 300lbs of anything.

So the generalised packing costs are then:

Liquids packed weight: weight+4%

Liquids packed cost: weight * 0.289 CP

Normal item packed weight: weight + 9%

Normal item packed cost: weight * 0.6 CP

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As an aside, the packing factor allows you to get your "packmaster" to role a skill check to reduce the cost of packing the items. e.g. roll a Profession(Carter) DC 20 to halve the cost of packing the items. – Nat Jan 7 at 22:57
This isn't terrible either; I might present it to them as a second option. I'm going to roll with the answer selected for now, particularly since I do want them adventuring at some point; at the rate they're on now, they're not going to be out of 4 for several RL months, and I'm trying to save the whole "monsters steal your loot" bit until they have something of real value. You've given them a good middle; I can do it HICC's way for next-to-no income, they can do RobertF's way if they want maximum profit (and work), or they can split the difference with yours. Thank you! – YttriumDervish Jan 8 at 1:11