I'm interested in knowing how long it would take to travel by ship from Vivec to Tear - I don't know how to calculate the distance or the length of time one of the standard Dunmer ships would take to make the voyage - any seafarers able to provide some thoughts?

Between 5 to 12 days would be my estimate depending on how many transfers you would have to make. IMO.

Given the amount of distance covered, I'd put it at a month- a month and a half, by ship. That's going around. If you went down the Thir river and then took a carriage from Silnim Vale to Tear, I'd highball it to around a month and lowball it to 2.5 weeks.

So what sort of distance are we talking about here? Am assuming travelling around Azura's coast then around the cape down past Necrom, etc to get to Tear.

I had wondered about going down the Thir but am unsure if that would have been a preferred trade route or whether going around the coast would have been?

I would say that the searoute is atleast 3 (maybe 4-5) times longer than the land route, if you are taking the Azura′s coast way.
Lets say a caravan moves at like 5 km/h and you walk around 8 hours/day. 40 km/day.
I would say that in the best of circumstances a fast ship could move at 12 km/h for 24h/day. But the circumstances are only in a few cases the best and most merchant ships are not very fast. So make that more like 5 km/h for 16h/day. 80-288 km/day.

That means the journey COULD go faster via land than via sea. It could also go a whole lot slower. Depends much on type of ship, cargo of the ship, wind and luck, the captain and the sailors if you go the searoute.

For example if the route by land is 120 km long and by sea its 360 km long. Then the fast ship with good luck would get there in 1.3 days while the land caravan would get there in 3 days. But the slow ship would get there in 4.5 days while the land caravan still would get there in 3 days.

EDIT: Just rechecked... Seems the searoute is more like 6-8 times longer than the landroute...

So 120 km landroute=700-1000 km searoute. 300 km/day... I would say that the landroute is faster, unless ofcourse you hire one of the fastest ships on Nirn, throw out any cargo and hire the best sailors on Tamriel....

EDIT2: Note that this is all just pure speculation on my part...

I assume you're going to use this in story? How long do you need it to take?

It's for a mod - where there is no fast travel from Vvardenfell to Tear - so I want a sea voyage - this can be scripted without an issue for days passing by - however I wanted to get an idea of how many days need to pass by. I can go in game and time how long the boat trips take from Vivec to Dagon Fel - however if I can get an idea of the correct distance between Vivec and tear then I can calculate how long a ship trip should take

Eyeballing it on a map, the Thir looks to be a little smaller than the Nibenay, which can support Imperial Warships. So a dinky little merchant vessel would go down the Thir (unless they had to smuggle something and not go through customs and inspections at every port they pass through).

By the way, we don't really have a good estimate of distance to travel, we just know how long it takes, thanks to Daggerfall; Which I checked Daggerfall quickly and it takes 32 days leisurely travelling on foot from Daggerfall to Sentinel. However, the intro describes going by ship down two rivers to Daggerfall as taking weeks (at least 2). The time calculations may not be the greatest, but given that the distance (down the Thir) is a little shorter than what the Intro describes, I'd put it at 2 weeks down the Thir, then half a week from Silnim Vale to Tear. Again, going around is going to take a lot more time, and I stand by my initial estimate.