Holy moly!
That was about 9 months ago, which probably means I got at least some of the data from a university module I was studying, and obviously got from elsewhere (wherever I got the chart) without coming up with anything to the contrary of what I was saying at the time.
From a cursory glance at google your number does seem right for 1800.
All that said the start of the industrial revolution was around 1750, where the population was around 700million.
Looking again at what I replied to it looks like what I was actually saying (perhaps not entirely clearly) was that rather than the worlds population being around 1 billion for most of its history, it was closer to around 200 million, increasing dramatically around the time and after the industrial revolution.
For example in 1400 the population was around 350million, so it took 350 years for the population to double to the 700m of 1750, then another 150 years to double again to 1.5 billion, 60-70 years to double again to 3 billion then another 30-40 years to double again to around 6 billion...* I guess I used he industrial revolution as a convenient starting point for the population to increase dramatically, and go above 1 billion, which is pretty much what the graph shows.
* so prior to the industrial revolution population increase was about 7-10x slower than after the industrial revolution - 350 years to double just prior to, then 260 years to go up 7x more.