How much would this cost me?

I would like to create a social media site that can host videos like YouTube and have Twitter like features. I'm thinking that I would make it into an app for both iPhone and Android. How much would it cost to make and to host the database? I would like a ballpark figure for total cost.

$1,000,000,0000,000

A lot.
Video hosting would cost an arm and a leg.
Hosting a database and other webstuff wouldn't cost much, maybe $5 a month if you got a VPS from OVH or something.

But what ever you are planning isn't going to happen, sorry.

The design itself, compatible with PC and mobiles, will probably cost a minimum of $10,000.
The hosting essentially depends on the number of concurrent visitors:
- less than 50 concurrent visitors: a "basic" server will do, at $50/year
- Between 50 and 200 concurrent visitors, you will need a dedicated server, at up to $1000/year (cheapest)
- Over, depends, again, on the visits you have. Count on one dedicated server per 25,000 users.
(in 2010, FB had over 60,000 servers. In 2017, FB had 2.2 BILLIONS users! Do the maths!)