How much does a solid gold oak tree weigh?

[moonfly7]

Through shenanigans my party accidentally turned a oak tree into solid gold. I decided each leaf equaled 1 gold coin and took the average number of leaves online for that. What I need now is a way to convert an average oak trees weight into its weight if it were gold. Since gold is heavier an equal amount if gold to wood ratio would weigh more. Which would effect how much it's worth using 5e prices. Issue is, I don't know how to find the weight. Can anyone help me?

[Galithar]

My rough calculations put the weight of the gold at 25 times the weight of Oak (American White Oak was my basis at .77 g/cm3 compared to gold at 19.3 g/cm3.

The same species of tree with an ~ 18 inch diameter and 40 feet tall would weigh around 4,000 pounds.

So you'd be looking at roughly 100,000 lbs of gold. Multiply by 50 coins per pound and you're looking at roughly 5 million gold.

Edit: For additional reference I found that a 100 year old tree of the same species would average 38-50 inches in diameter and be as much as 100 feet tall.

[Knaight]

Oak wood density runs from about 600 to 900 kg/m3,which is to be expected given that it floats and water is about 1000. Gold density is a bit trickier, pure elemental gold is 19300 kg/m3 but coins, jewelry, and the like generally aren't made of elemental gold. Depending on karat you'd expect anywhere from 13000 to 16000 kg/m3. The oak wood is also part of a living tree and can be assumed to be denser because of that, as it'll hold on to more water content. So, using the upper oak figure and the middle gold figure we have 14,500/900 for the ratio of densities, which gets about 16.

I assume you already have a weight picked out for your particular tree, so just multiply that by 16 and call it a day. For future reference the way you find this information is generally by looking up "[material] density". A bunch of sites will have that information, I favor Engineering Toolbox when possible, Sigma Aldritch failing that, or for simple things (e.g. pure elements) just using the google number. You will want to at least do a common sense check, so you'll want to know some numbers off hand. Water is 1 g/cm3 or 1000 kg/m3, plastics run from about 0.8 (800) to 2 (2000), stone runs from about 2 (2000) to 5 (5000), most metals run from about 5 (5000) to 10 (10000), really dense metals run from about 10 (10000) to 20 (20000), most organic liquids (e.g. oils, alcohols) end up somewhere in the 0.5 (500) to 1.5 (1500) range, woods are usually about 0.5 (500) to 1 (1000). Gases are complicated, but at standard conditions you'll generally see .001 (1) to .004 (4), though you probably want to just bust out the ideal gas law and molecular weight at that point.

There are exceptions to all of these; porous rocks less dense than water, really light metals, the very heaviest metals that breach the 20 by a bit, weird alloys, oddly high density organic fluids, etc. As a rule of thumb though they're decent ranges to keep in mind, and a lot of times you expect the exceptions - yeah, aluminum and titanium end up light, that's what they're known for, yeah, gneiss has a really low density, it feels lighter than you'd expect when picking up a rock, and yeah, that one plastic that felt really heavy when lifted turns out to have a high density*. Then there's the occasional really weird thing that defies categorization but can still be intuitively fit to that scale. Aerogel is a solid with a density that looks like what you'd expect from a gas, but if you know anything about aerogel those are not surprising numbers.

*Actual plastic specifics are a long post in their own.

[Zhorn]

The answer will change depending on what standard you want to use.

You can go by pure real world gold density (give above)
You can use an alloy (also given above) though then you're not actually dealing in gold, which if we're to take the term 'gold' in the books at face value, then coins/tradebars and the like are pure gold and not an alloy.

Alternatively you can use the game's own standard of gold's density.
5e DMG p20: A 5-pound gold bar is worth 250gp and is about 5 inches long, 2 inches wide, and 1/2 inch thick.
This gives us a density of 5 lb./in3 (138.4 g/cm3)

Much heavier than our real world 0.698 lb./in3 (19.32 g/cm3)

Alternatively going by the 3.5e Dracocomicon p278, gave coins a size of 1 inch diameter & 1/10th thickness. Using a standard coin weight of 0.02 pounds this gives us a density of 0.253165 lb/in3 (7.01 g/cm3)

Any case, once you have your final weight for your solid gold tree, those other posts above have it right in just weight * 50 for the total coinage.

[Knaight]

You can use an alloy (also given above) though then you're not actually dealing in gold, which if we're to take the term 'gold' in the books at face value, then coins/tradebars and the like are pure gold and not an alloy.


Of course, the obvious reason not to do that is that historically gold coins have always been alloys of some sort, and even high carat but impure gold is often a lot less dense.


Alternatively you can use the game's own standard of gold's density.
5e DMG p20: A 5-pound gold bar is worth 250gp and is about 5 inches long, 2 inches wide, and 1/2 inch thick.
This on the other hand is a perfect example of why I don't trust most RPG writers with actual units. Even if I'm being generous and assuming that these are maximum dimensions and that you have the standard pyramid-segment structure for gold bars (tapering on both ends) an actual pyramid that fits those dimensions is still 5/3 cubic inches, which should only weigh 1.16 lbs using pure gold density.

[dancrilis]

Through shenanigans my party accidentally turned a oak tree into solid gold. I decided each leaf equaled 1 gold coin and took the average number of leaves online for that. What I need now is a way to convert an average oak trees weight into its weight if it were gold. Since gold is heavier an equal amount if gold to wood ratio would weigh more. Which would effect how much it's worth using 5e prices. Issue is, I don't know how to find the weight. Can anyone help me?

This depends on how much the oak tree weighed before being turned to gold, a factor of age etc.
It also depends on much a gold coin weighs in your setting - and how much a leaf weighted prior to being made gold, and how the leaf to gold ratio has worked.

If for example each leaf can on average be exchanged for 1gp based on weight then if each leaf weights 9grams before being turned to gold (to take a fairly random figure as leaves can vary) and if a gold coin weighs for instance lets say a about a third of an ounce then the weight remains fairly consistant.
If on the other hand the average leaf weights only 4.5 grams then the oak tree would double in weight.

Very rough figures all around - the question you might want to ask is how much gold you want to give your PCs and work back from that.

Effectively you have created a standard of 'One Leaf Weight = 1gp', everything else you need can be determined from that.

[hamishspence]

Alternatively you can use the game's own standard of gold's density.
5e DMG p20: A 5-pound gold bar is worth 250gp and is about 5 inches long, 2 inches wide, and 1/2 inch thick.



Even if I'm being generous and assuming that these are maximum dimensions and that you have the standard pyramid-segment structure for gold bars (tapering on both ends) an actual pyramid that fits those dimensions is still 5/3 cubic inches, which should only weigh 1.16 lbs using pure gold density.
How about a squared-off gold brick with those dimensions? Doing the whole thing in cm:


1.27 cm x 5.08 cm x 12.7 cm = 81.935 cubic cm. Gold has a density of 19.3 grams per cubic cm = this object will weigh 1.581 kg = 3.49 pounds.

Still a little on the low side.

But if, by "about 1/2 inch, 2 inch, and 5 inch" allows for it to be slightly more - each of these being rounded down - you can get a lot closer.

1.9 cm (just short of 0.75 inches), 5.71 cm (just short of 2.25 inches) and 13.3 cm (just short of 5.25 inches) = 144.29 cubic cm - (much more than the previously obtained volume): 2.784 kg: 6.139 pounds.

So, 5 pounds is quite compatible with a brick-shaped bar, as long as all 3 dimensions are slightly low - rounded down rather than exact - to the nearest half-inch in all 3 cases.

[moonfly7]

Oak wood density runs from about 600 to 900 kg/m3,which is to be expected given that it floats and water is about 1000. Gold density is a bit trickier, pure elemental gold is 19300 kg/m3 but coins, jewelry, and the like generally aren't made of elemental gold. Depending on karat you'd expect anywhere from 13000 to 16000 kg/m3. The oak wood is also part of a living tree and can be assumed to be denser because of that, as it'll hold on to more water content. So, using the upper oak figure and the middle gold figure we have 14,500/900 for the ratio of densities, which gets about 16.

I assume you already have a weight picked out for your particular tree, so just multiply that by 16 and call it a day. For future reference the way you find this information is generally by looking up "[material] density". A bunch of sites will have that information, I favor Engineering Toolbox when possible, Sigma Aldritch failing that, or for simple things (e.g. pure elements) just using the google number. You will want to at least do a common sense check, so you'll want to know some numbers off hand. Water is 1 g/cm3 or 1000 kg/m3, plastics run from about 0.8 (800) to 2 (2000), stone runs from about 2 (2000) to 5 (5000), most metals run from about 5 (5000) to 10 (10000), really dense metals run from about 10 (10000) to 20 (20000), most organic liquids (e.g. oils, alcohols) end up somewhere in the 0.5 (500) to 1.5 (1500) range, woods are usually about 0.5 (500) to 1 (1000). Gases are complicated, but at standard conditions you'll generally see .001 (1) to .004 (4), though you probably want to just bust out the ideal gas law and molecular weight at that point.

There are exceptions to all of these; porous rocks less dense than water, really light metals, the very heaviest metals that breach the 20 by a bit, weird alloys, oddly high density organic fluids, etc. As a rule of thumb though they're decent ranges to keep in mind, and a lot of times you expect the exceptions - yeah, aluminum and titanium end up light, that's what they're known for, yeah, gneiss has a really low density, it feels lighter than you'd expect when picking up a rock, and yeah, that one plastic that felt really heavy when lifted turns out to have a high density*. Then there's the occasional really weird thing that defies categorization but can still be intuitively fit to that scale. Aerogel is a solid with a density that looks like what you'd expect from a gas, but if you know anything about aerogel those are not surprising numbers.

*Actual plastic specifics are a long post in their own.

Thank you every one, I'll use this one because it's simplest. Thank you.

[mindstalk]

Wikipedia says the Roman aureus was typically more than 99% pure gold. The Byzantine solidus seems to have been pretty pure, too, though that page says more like 95.8% gold due to refining limits. Got debased after 1000 AD

1800s European coins were 22 karat, ~92% gold.

Medieval Florins started out extremely pure, 98% or better, though German ones got debased down.

I see little wrong in assuming that gold and silver pieces are essentially pure. Debasement seems to have been more common for silver coins, but Athenian drachmae and English sterling stayed pretty pure. The later Roman emperors really ran down the denarius but it had been fairly stable under the Republic.

[Isikyus]

How about a squared-off gold brick with those dimensions? Doing the whole thing in cm:


1.27 cm x 5.08 cm x 12.7 cm = 81.935 cubic cm. Gold has a density of 19.3 grams per cubic cm = this object will weigh 1.581 kg = 3.49 pounds.

Still a little on the low side.


I wonder if the DMG authors may have got two different kinds of pound mixed up.

The normal US unit you'd expect in the DMG is the avoirdupois pound (about 0.45 kg), but gold's usually measured in troy pounds (~0.37 kg).
The DMG writers might easily have found figures for a 5-troy-pound gold bar and assumed the unit they were more familiar with.

1.581 kg is about 4.23 troy pounds, which is still a bit too low, but it is closer — especially if the measurements are rounded down as you suggest.

[Zhorn]

eh, it's fantasy gold measured in fantasy pounds on a fantasy world with fantasy gravity... blame those alien wizard gods.

It would have been neat if the numbers given in each of the editions matched up to real world values, but I'm fine with the numbers being fudged for the convenience of a game, be that the 3.5e coin measurements, or the 5e trade-bar dimensions.

Same thing for the purity of metals. Real world currencies and jewellery being made of alloys makes sense, but for games why add that layer of complication? Trade goods say gold is worth 50 gp per pounds. Coins are 50 to a pound. 50 gold coins have the same weight and value as one pound of gold. Seems pretty easy to just say those gold coins are pure gold and call it a day.

[moonfly7]

eh, it's fantasy gold measured in fantasy pounds on a fantasy world with fantasy gravity... blame those alien wizard gods.

It would have been neat if the numbers given in each of the editions matched up to real world values, but I'm fine with the numbers being fudged for the convenience of a game, be that the 3.5e coin measurements, or the 5e trade-bar dimensions.

Same thing for the purity of metals. Real world currencies and jewellery being made of alloys makes sense, but for games why add that layer of complication? Trade goods say gold is worth 50 gp per pounds. Coins are 50 to a pound. 50 gold coins have the same weight and value as one pound of gold. Seems pretty easy to just say those gold coins are pure gold and call it a day.

My thoughts exactly

[mindstalk]

If I ever run a game it'll be 100 coins to a pound. Even easier, and gives 4.5 gram coins, same as the drachma or denarius.

[Zhorn]

If I ever run a game it'll be 100 coins to a pound. Even easier, and gives 4.5 gram coins, same as the drachma or denarius.

Bit of trivia for you: While the PHB and DMG reference a 50 coin per pound standard, Waterdeep Dungeon of the Mad Mage has 1 lb. gold ingots valued at 100 gp. Guessing the writer of that one was prepping for your standard on that one :smallbiggrin:

[Vinyadan]

Did you convert the whole tree? At school they said that trees go as deep in the ground as they stand tall above it.

[AdAstra]

Did you convert the whole tree? At school they said that trees go as deep in the ground as they stand tall above it.

A quick google search suggests that the majority of an oak’s root system resides around 18 inches underground, so pretty shallow, while the taproot extends around a yard/meter. Past a certain point the soil’s just too dense/rocky to be worth growing down instead of out. However, the root system of an oak can horizontally extend four to seven times the width of the crown (the part with leaves).

I do wonder if a solid gold oak would be heavy enough to sink into the ground and/or collapse under its own weight. Gold isn’t exactly known for its high strength to weight ratio. All the branches would bend for sure.

[Zhorn]

I do wonder if a solid gold oak would be heavy enough to sink into the ground and/or collapse under its own weight. Gold isnÂ’t exactly known for its high strength to weight ratio. All the branches would bend for sure.
Assuming a mostly even distribution of weight and no lopsided growth trajectory, the core trunk of the gold tree should be able to stay upright, and with a root system wide enough there shouldn't be any drastic sinking into the soil. You can expect a little, but it should be anchored well enough.
The longer branches growing out to the sides would start to bend and bow downwards under their weight. Gold is a soft metal, but it's not so weak as to just collapse like a mound of jelly, it still has some strength to it, just not as much as more idea materials.
Rather than an immediate collapse, you're more likely to expect the tree to go from looking like a proper oak to more of a sad approximation of a weeping willow.
However, if there was a noticeable tilt in the main trunk, or a V-like split, the load bearing capacity of the gold tree would be compromised enough bending over in the weight baring direction could be a given.

[Knaight]

1800s European coins were 22 karat, ~92% gold.

Which is enough to drop from 19.3 g/mL to 15.6 g/mL, just for reference. Assuming copper as the other 8% (which is iffy, but does give a relatively low density companion metal among things likely to be used) you'd expect a density of 18.5 g/mL if mixing effects were negligible. That they clearly aren't suggests that a lot of the decrease in density comes from the metal lattice being disrupted, and that sort of thing can kick in at exceedingly low impurities. Even allowing for these 98% pure coins (which, if lattice impurities do kick in early could easily be much more rigid, the same way that 2% carbon in elemental iron makes a pretty rigid steel and not a soft metal) the 19.3 figure is potentially really high.

[Galithar]

Which is enough to drop from 19.3 g/mL to 15.6 g/mL, just for reference. Assuming copper as the other 8% (which is iffy, but does give a relatively low density companion metal among things likely to be used) you'd expect a density of 18.5 g/mL if mixing effects were negligible. That they clearly aren't suggests that a lot of the decrease in density comes from the metal lattice being disrupted, and that sort of thing can kick in at exceedingly low impurities. Even allowing for these 98% pure coins (which, if lattice impurities do kick in early could easily be much more rigid, the same way that 2% carbon in elemental iron makes a pretty rigid steel and not a soft metal) the 19.3 figure is potentially really high.

While the density of different CuAu alloys aren't completely linear, the drop off you are describing is way too extreme. A 92% CuAu alloys is going to have a density pretty close to 18 gcm-3.

Source (https://www.google.com/url?sa=t&source=web&rct=j&url=https://link.springer.com/content/pdf/10.1007/BF03216580.pdf&ved=2ahUKEwiXpoSu24XqAhU8SjABHRTNB6cQFjAAegQIAhAC&usg=AOvVaw31DBuxRXe-R6z828STuctp)

It's not a linear drop in density, but it also isn't a crazy drop. If you look at figure 3 in the paper that I linked (The graph is labeled as CuAg, but if you read the text and look at the 100% density values it's clearly CuAu) you'll see a gentle exponential curve between the two values. Slightly off from what you would expect but nothing insane.

Now another metal that can't form a decent lattice with Gold might be different, but Silver and Copper can. They are also the two metals I would most expect to be mixed with Gold if the process was intentional and not just from impurities and imperfections in the process.

[mindstalk]

If you somehow replaced 8% of the gold with pure distributed vacuum, you'd still have a density of 17.48

[Kami2awa]

Fun fact I learned at a biophysics conference: As a tree trunk branches into smaller and smaller twigs, the cross-sectional area of all the branches added up remains constant (approximately), due to the need for water flow through the whole thing. If you assume the trunk is circular in cross-section, you can closely approximate the tree's volume as a cylinder of the same diameter as the trunk and the same height as the tree itself.