The party has just rescued 100 slaves. How many of them can conceivably enter a teleportation circle before the spell ends? It seems absurd to think all 100 can make it.
The teleportation circle spell description states that:
A shimmering portal opens within the circle you drew and remains open until the end of your next turn. Any creature that enters the portal instantly appears within 5 feet of the destination circle or in the nearest unoccupied space if that space is occupied.
Let's assume Medium creatures with a speed of 30, such as humans or elves.
The circle lasts one round, so anyone within 60 feet of it (assuming they can Dash) would make it through. A 60-foot radius circle holds 452 5-foot squares (and in reality they can pack together closer than that).
If they don't Dash (because getting 100 people all to sprint at the circle without colliding is really hard) you get a 30-foot-radius circle which holds 113 5-foot squares.
There is going to be some chaos at the destination, because the crowd will get their relative positions and directions of motion rearranged to prevent them from intersecting. Worst case, it places them 5 feet apart and running toward each other, which gives them (assuming a Dash speed of 60) 1/4 second to react before they collide head-on. One solution is for everyone to do diving rolls into the circle to stop their motion, but that only works if you're rescuing a hundred Cirque du Soleil acrobats or something and I'm guessing those guys would have escaped already.
On the other hand, you don't need open space around the destination circle; Teleportation Circle will spread them out as much as needed, even outside the room containing the circle.
As you cast the spell, you draw a 10-foot-diameter circle on the ground
The spell opens in a *10 foot diameter cube. That's 100 square feet. Some preparation and planning is needed with the slaves. You will need to predefine where the square will be and pack all the slaves together in that square like sardines in a can. Then cast the Teleportation Circle on the location where all the slaves are packed together to send them all through. Then you just hop in after them! Congratulation, you just saved the slaves! (As long as the location you're traveling to doesn't insta-kill them)
According to this post on Quora, ~9 people fit into a 1m x 1m square. That's approximately the same as 3ft x 3ft square which translates to 1 person per square foot.
It's still a simple problem to solve. As pointed out by Mark Wells, an actual circle with a diameter of 10ft would roughly contain 78 square feet. Therefore only 78 slaves could crowd inside the circle as it is cast. That leaves 22 slaves outside of the circle.
The circumference of a circle with a diameter of 10 ft is a little more than 30 feet, so it is not unreasonable to assume that each slave could be standing on the outer edge of the circle. After the initial slaves who are already in the circle get teleported, the others can just hop in with little to no crowding. There would be time to spare for the caster to hop in after them as well.
Now there's a fun question! If you and your friends are in a hurry, don't want to get hurt and don't have any buildings nearby, 864 of you can teleport with one casting of Teleportation Circle.
Otherwise you can fit 338304 medium or small creatures with 30ft walking speed through a single cast of Teleportation Circle - Now there's some spell slot efficiency! Most of them will end up dead, but that's beside the point.
The key is to build a 117 story skyscraper above the Teleportation Circle with 1.5m high halfling style ceilings and a 10ft square hole in the middle of every floor above the Teleportation Circle. Why? Well, on the turn when a creature starts falling, it immediately falls a turn's worth of distance.
The creatures take falling damage (20d6 bludgeoning damage from 41st floor upwards) and then teleport to the nearest unoccupied space at the destination teleportation circle.
Here's the math: The portal closes at the end of its caster's next turn, so everyone has one turn to get in. First they all crowd around the hole on their floor in order of increasing initiative so they won't get in each other's way. Then everyone besides the caster readies their 30ft of movement when a condition is triggered. Let's say the condition is "Having a free direct path to the hole on my floor after Teleportation Circle is cast below it.". After everyone's ready, the caster (one with the lowest initiative on the 1st floor) casts the circle and walks into it (lucky bastard). Then floor by floor everyone moves for their floor's hole on the caster's turn. Those within 30ft make it on the caster's turn. Others use the readied move to fill all spaces within 60ft of the hole to move and then Dash again on their next turn. This way a total of 101088 creatures would enter the portal - 192 creatures per floor with the readied move and 672 per floor on the next round (192 + 672 creatures from 117 floors = 101088).
Why 192 and 672?
To take the sillyness even further we add another 353 floors to that skyscraper (those will have a height between 177 and 705 meters, as it takes 12 seconds to fall 706m) and fill it with creatures below the caster's initiative, have them move and Dash into a hole and start falling one turn before the portal is opened, then next turn the portal is opened on the caster's turn just before they splatter through it on their initiative order, adding another 237216 likely dead creatures (353 floors * 672 creatures per floor), just so you can get the most value out of your 5th level spell slot! The Universe will also present you with the "Most dead creatures teleported" achievement and will disconnect you from the overcrowded tabletop game instance =P
