1 cr is around 0,00022$, if not mistaken

One of the three main flaws to that equation is that not everyone will purchase Crystal Energy in bundles of 45k, which will ultimately cloud the actual value of both CE and their Crown prices in-game.

The second flaw is common knowledge to everyone in that the ratio between CE and Crowns is purely decided by players without any apparent or obvious use of a formulaic process, making the actual value of Crowns even more intangible to decipher as a whole (at least, as far as Energy is involved in the equation).

The third flaw is far more influencial. Every player has a largely variable Crowns-per-minute output during their active playtime. The Crowns in question here have to come from being generated by normal means such as defeating enemies and selling items to vendors, not gained from trades with players or via the market. As such, the value of Crowns changes every passing second and more fluidly than CE possibly could in a consistant manner, even as we speak.

Nailing the true value of Crowns would only last for so long until its next fluctuation. Players with strong ties to the market would do well to learn how to properly estimate going-rates on the go.

Somebody drop a shivermist cause Makugan just got burned!

The real world $ for in came currency is going to fluctuate based on the demand in game for crowns or crystal energy through the Supply Depot energy market window.

Let me stumble through math.

As a baseline:

CE purchased through Spiral Knights

$100 (US) = 45000 Crystal energy
45000CE / $100 US = 45 Crystal Energy per $1 spent

Now look at the Supply Depot CE market window for what the current trades for selling Crystal Energy for Crowns (right hand box). Take an average of the group or estimate an arbitrary but reasonable amount of crowns per 100 C.E.

(Selling C.E. price in Crowns) / 100 units of Crystal Energy = Crowns per 1 unit of Crystal Energy
example:

Today August 30th at about the time I'm typing this the bids for crowns is around 9300.
9300 crowns / 100 CE = 93 crowns per 1 CE

Now take the first value we calculated, 45 CE per $1, and the second value we calculated, 93 crowns per 1 CE, and use them to find a crowns per $.
45 CE is equal to $1 and vice versa.
(93 crowns / 1 CE) * (45 CE / $1) = 4185 Crowns per $1

Last assumption, that you only convert your CE to Crowns through the Supply Depot with means the amount of crowns that you would receive would be reduced by the 2% auction fee that the seller (you) would pay.

4185 Crowns * (1 - .02) = 4101.3 Crowns per $1

This assumes that you'd be able to sell all 45000 CE from a $100 purchase at the assumed price of 9300 crowns per 100 CE (which will practically never happen unless you are super patient and leave your sell bids up in the Supply Depot Market at the assumed price for as long as it takes to sell all 45000 CE.

Most of the numbers in the equations are pretty constant. The only variable that fluctuates wildly is the assumed value in Crowns of 100CE. If you sell directly to a player and do not incur the 2% seller fee you will make a bit more. You could change the 100CE amount to whatever CE amounts you happen to sell directly to players.

tl;dr we're all angry and bad at math