I play a teleportation and extra dimensional sorcerer in my group and I'm getting close to obtaining the spell Gate which requires "a diamond worth at least 5,000 gp". How big would a diamond worth 5000 gp be?
My reason for asking is that I want to place the diamond on top of my legendary staff, and the size definitely dictates whether I can or can not do so.
Keep in mind that in real life (which may be compared to dnd only spuriously) qualities such as clarity, cut and sometimes even history can affect a diamond's value.
Now on to dnd 5th edition. In the Dungeon of the Mad Mage there is a 5000gp valued diamond. It is described as
a fist-sized diamond
So there is at least one canon-described diamond. However, it is only described in general.
There is a second example of a 5000 GP diamond available in 5th Edition officially published materials. In "Tales of the Yawning Portal" chapter "Tomb of Horrors" adventurers can find the following:
six pointed (marquis cut) diamonds set as teeth in the jaw (each diamond is worth 5,000 gp).
In this example, its given that the diamonds are in fact finished and cut, and have been fitted into the teeth of a human skull. This gives us a second reference for the potential size of a 5000 GP diamond as roughly the size of a human tooth.
The primary in game identifier for diamonds is their value, so this is a question for your DM. Since your DM is the one responsible for world-building, it is up to them how the people of the world relate to valuable gems and place value on their size. There is no such relationship described in general in any campaign setting or rulebook.
To illustrate this point, consider this rule about selling gems found in chapter 5 of the Player's Handbook:
These items retain their full value in the marketplace, and you can either trade them in for coin or use them as currency for other transactions. For exceptionally valuable treasures, the DM might require you to find a buyer in a large town or larger community first.
The important takeaway here is: their full value at the marketplace is the value referenced in the description of costly spell components. If a diamond would fetch less than 5000 gp at the marketplace, it is not suitable for casting a spell requiring a 5000 gp diamond.
So the question a DM must consider when valuing a diamond is:
Since the value of gems is always exchangeable for exactly their value in gold, how much does this diamond fetch at market?
This is the first concern when evaluating diamonds, and any further description is narrative.
Now, in Waterdeep: Dungeon of the Mad Mage on page 2301, a certain diamond is described:
Pedestal. In the middle of the room, two mind flayers grip the top of a 4-foot-tall, three-sided crystal pedestal with a fist-sized diamond floating 1 foot above it.
We are later told:
Treasure. The diamond is worth 5,000 gp.
So this particular diamond in this particular setting and context is worth 5000 gp and about fist sized, but your DM's setting may be different.
Additionally, in Storm King's Thunder, there is a magic item called a Blod Stone (pg. 233). In its description, we do get a single adjective to point us in the right direction:
This item is made from a large diamond worth at least 5,000 gp.
So a 5000 gp diamond may be described as large, at least in relation to other diamonds, whatever that means.
1Level 17, section 16, "Old Dwarven Halls".
The value of gemstones in real life is complicated and somewhat subjective. In general, a small stone with good clarity, color, and other attributes (such as cut and "fire", depending on the kind of stone) will be much more valuable than a far larger stone with inferior characteristics. For example, a diamond that's somewhat milky or cloudy and full of inclusions (that is, dark specks of rock trapped inside the gem) is often considered a trash stone and can be had for less than a tenth the price of a decently clear gem of the same size. In many cases, an unusual tint can elevate the value of a diamond, such as the famous deep blue Hope diamond, which could almost be confused for sapphire. And that's to say nothing of accusations that diamond companies artificially inflate the value of their product by withholding the majority of the supply they produce.
While the game is not necessarily reflective of real life, it seems reasonable that in-game gems will vary in quality in the same ways, and that such variations will affect their value similarly.
So, in game terms, a 5000 gp diamond might be relatively small but absolutely perfect, or might be a huge softball-sized rock that's inferior in every way save its sheer size. It's really up to the DM to decide how big the stone should be (when it even matters), and it doesn't need to be consistent from one diamond to the next.
How big is 1 gp?
There's a rule of thumb that 50 gp is 1 lb gold. That means 5000 gp is equivalent to 100 lbs or roughly 1460 troy ounces. The current price of gold is about $1950 per troy ounce, so we arrive at $2.85M as the expected price of such a diamond in our world.
The Allnatt is supposedly worth about $3M and is ~100 carats. However next on that list is a 5 carat diamond valued at $7M so clearly there are factors beside size. But if we consider primarily the size, Wikipedia gives us a formula correlating price and size, so based on this we would expect about a 50 carat diamond for $2.8M.
Obviously the price of gold, the value and purity of gold currency, the average price per carat of small and unremarkable diamonds, the color and cut of the diamond, the history and notoriety of the particular article in question are all very important unknowns and could vary widely depending on your particular setting. But without any further knowledge about your setting, it's probably fair to say that you are looking at a diamond in the 10-100 carat range. 50 ct is therefore a decent estimate.
A 50 ct diamond is 10 g, and if diamond has a density of 3.5 g/cm3 we get a volume of 2.86 cm3. If this was a perfect sphere, it would be about 1.8 cm across (other shapes will be larger along the longest axis). So not quite fist sized as others have proposed, but perhaps the size of a plum.
One thing I always wondered is whether the spell draws power from the value of the diamond or its quantity. In the latter case, presumably the quality and cut of the diamond is not terribly important. You would imagine mages buying up large, low quality rough diamonds to cut costs. Perhaps they could even create a magical version of the process we use to manufacture synthetic diamonds. I personally feel it's more plausible, and more exciting, if the spell doesn't care how big the diamond is, but rather the value attached to it by intelligent creatures. In that case, the physical size of the diamond is minor detail, and the real question is how much the magician believes himself to be sacrificing. It is then an open question whether the spell would still work when unwittingly attempted with a counterfeit diamond, or whether the object must have had a sufficiently long history of being valued by different people in order to serve as a suitable spell component.
This is an adjunct of @Chris' excellent calculations, with a different set of assumptions, but a final answer in the same order-of-magnitude. In summary: I'm estimating a much lower overall value, but roughly the same physical size as his estimate.
I wouldn't start by just translating the current value of gold, but rather with a broader look at the whole D&D economic system. Working from original D&D sources in the past, my best estimate is that what's listed as 1 gp value in the books roughly correlates to about a half-shilling of real-world medieval purchasing power. (In 1E PHB Gygax defended standard prices as reflecting a hyper-inflated adventuring area, and those assumptions were baked into the system ever after.) See my blog here.
Using this site reports that 1 shilling in 1270 had the purchasing power of 36 pounds sterling in 2017. This site reports that on this date in 2017, a British pound was worth 1.20 U.S. dollars. So we would estimate that a 5000 gp gem is worth 5000 gp × 0.5 s/gp × 36 £/s × 1.20 $/£ = $108,000 in modern terms.
Looking at this site for current wholesale diamond prices currently shows 1 carat, with color H and mid-range clarity VVS2, at a price of $5,327. (For more information see here.) If we use Tavernier's law that @Chris linked to in reverse, then we get a weight of √(108,000 / 5,327) = 4.5 carats.
Finally, this site states that the most popular 3 carat round diamond has a face-up area (by which I assume it means width) of about 9 mm. If the overall dimensions vary by the cube-root of the volume, then we'd get a face width of (4.5)^(1/3) × 9 mm = 1.65 × 9 = 15 mm = 1.5 cm. That's about a half-inch, or around the size of a grape.
As established here, we can use a general formula for Carat to gold value for normal sized diamonds. the weight in carat is somewhere between \$ 0.0454 \times \text{price in gp}\$ and \$0.0119\times\text{price in gp}\$. So a 5000 gp diamond would, under that formula, be between 59.5 and 227 carat. However, both weights are far beyond what is traded under normal pricing. The formula doesn't work for those. These are exceptional large stones. No, we need to look up a different pricing and sizing area. We know, as established on the other answer, that 5000 gp would be equivalent to somewhere between 1 (modern coins) and 5-million (1st edition coins) in USD. From the same source quoted there:
- $200,000 – $999,999 Diamonds in this price range tend to be greater than 3-carats (though not always) and will require a customized setting (standard settings generally accommodate up to three carats).
We are talking perfect diamonds of above 3 carats. We are talking exceptional stones. Really exceptional stones. Large stones. Such as this 10-carat blue diamond worth approx 10k gp in old coin, and 50k in new ones. And if you look for a diamond worth pretty much exactly 1-million USD, there had been a VVS2, color E, triple excellent, no fluorescence, 10 carat stone for sale in 2018.
