how big is stuff, and how much does it weigh?

March 11th, 2014 by paul

The PCs ask: "Can I lift the life-sized gold statue?" "How much food will fit in the castle's cellars?" "How many books in the library?" "Can I carry the boat on my back?" "How many coins fit in my backpack?" Dammit, now you have to do calculations.

Here are six numbers that you can learn to make a ballpark estimate on nearly any weight/volume question. These are useful for quick plausibility calculations when the players try something you didn't expect. We want memorable numbers, accurate within 20% or so.

The First Number: Density of water: The first fact you need to know is that a cubic foot of water weighs around 60 pounds. Water is good because the density of the human body is virtually identical to that of water, and we all have a good intuition about how big, say, a 180# person is compared to a 120# person.

Numbers two through six: Density of Everything Else: There are basically six materials that are useful for D&D. Their weights are given in multiples of water.

60# cubic foot of water
2/3x Things that float
2x Dirt
3x Stone
10x Most metal
20x Gold and platinum

Now the details:

Water: Lots of things are around the same density as water, especially things that are mostly water: wine, ice, people, orcs, dragons, and raw meat. Also leather (a meat byproduct), vellum (a leather byproduct) and paper (a vellum competitor) are around the same weight as water.

Everything that floats: If it floats, and you can use it in D&D, it's probably around 2/3 the density of water: 40# per cubic foot. Oil, wood, cloth, and common medieval foods like wheat, beans, vegetables, and dried meat are all around this weight. The few lighter substances (sawdust, snow, feathers) don't come up that much in D&D.

Dirt: Dirt includes clay (and its byproduct bricks), sand (and its byproduct glass) and soil.

Stone: If you're stoned by a medusa, your weight is multiplied by 3.

Most metal: Metal weight varies: steel is around 8x the density of water; copper and silver are around 9x; lead is 11x. 10x is a convenient and memorable average.

Gold and platinum: The really valuable metals are around 20x the density of water (gold 19x; platinum 21x).

Loose packing: Keep in mind that these densities are for solid, or relatively solid, materials. If something is crated, barreled, shelved, packed with straw, loosely piled, or stacked, multiply its volume by x2. If you need aisles, such as in a storeroom or library, multiply by another x2.

Examples: From these six numbers, and the loose-packing estimates, you can easily calculate the following:

  • Statues: That life-sized statue of a 200# man is 130# in wood, 600# in stone, 2000# in iron, and 4000# in gold. In 3e, you'd need a strength of 25 to drag the gold statue.
  • Storage: Let's say your castle has a 50x50x10 cellar. You could theoretically pack 25k square feet or 1 million pounds of food in there. At a ration of one pound per day, that would feed 5000 people for six months. But your food is probably stored in aisles of barrels and crates, so you can probably only feed 800 people for six months.
  • Wooden stuff: An oak table, 12"x4" and 1 inch thick, would be about 4 cubic feet of wood, or 160#. A boat with the same dimensions would use a little more wood for the sides and maybe weigh 200#.
  • Books: A cubic foot of paper (60#) would make 12 5-pound tomes. Shelved and in aisles (/4), that's, like, 3 books per cubic foot. Doesn't sound like much, but a 20"x20" library with 5" shelves holds 6000 books.
  • Treasure: Let's say you have a cubic foot of space in your backpack. By volume, you could fit 1200# of solid gold or maybe 600# of loose coinage. That's 30,000 GP. Of course, your backpack would break under the weight, even if you could lift it.

    References:

    http://www.engineeringtoolbox.com/specific-gravity-solids-metals-d_293.html

    http://www.engineeringtoolbox.com/density-materials-d_1652.html

    http://go.key.net/rs/key/images/Bulk%20Density%20Averages%20100630.pdf

    http://www.loc.gov/today/pr/2002/02-164a.html

  • 14 Responses to “how big is stuff, and how much does it weigh?”

    1. Roger GS says:

      We need more posts like this, if we are going to expect “old-school” style GMs to make rulings on the fly about the material world (or new school ones to recognizes when their meticulous simulation rules part company with reality).

    2. This should be included in every DMG. =)

    3. Jeff says:

      Makes me think of a puzzle where a player in the party has to voluntarily petrify themselves to solve a see-saw balance puzzle. Or maybe bait an angry, large, and dumb monster into the right spot to use them as a counter weight.

    4. PeterD says:

      Very useful stuff, thanks. I’ve had more complicated measures for weight by density and size, but this is more immediately game useful even if it’s just close rather than exact.

    5. Roger GS says:

      You know what would really rock? A similar system resolving conflicts of force (number of small/big/huge people pushing/bashing/kicking) versus resistance (to bending/breaking/lifting/pushing) (of objects by material and weight/thickness).

    6. Charles says:

      This is very nicely put together.

    7. I also agree this should be in every game manual. And love Jeff’s idea about using it for a puzzle!

    8. kaloo says:

      This is very neat, especially since it can fit in a little tiny card or the like.

    9. Of course, we could know the meaning of density and use a website like SI Metric.

    10. paul paul says:

      Sure, but I don’t like using websites while I DM.

    11. Rhenium says:

      Regarding statues, very few of them would be solid. Even the wonderful bronzes from Greece to the present day are all hollow, and ring akin to a bell if struck.

    12. Sully says:

      Super useful, thanks for sharing.

    13. Ben Bennett says:

      A DM screen with this and all of the other handy tables and “X on a business card” you’ve made would be the bomb.

    14. paul says:

      I’ve got an idea for just such a thing! It’s in the works!

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