If you are looking for overnight accommodation on race weekend, then you may wish to consider the following:

Brussels International Airport, or Cologne Airport in Germany, are approximately the same distance from the circuit - 110km and 90km respectively. The closest airport is in Maastricht, but it can be more difficult to get a direct flight.
There are a number of smaller accommodation options close to the circuit in the beautiful town of Spa but these sell-out quickly. More likely you will need to look in Liege, Aachen, or Maastricht. These towns are a reasonable distance from the rural setting of the circuit and so make sure you plan your travel ahead.
Useful information and assistance on accommodation can be obtained from the Belgian Tourist Office at www.belgiumtheplaceto.be.

Camping is a popular choice over race weekend and temporary campsites are set-up by both the circuit and local landowners. Because of their temporary nature, these campsites usually have only very basic facilities and are not as secure as some permanent campsites.
The circuit hosts an official campsite near the Green and Yellow parking areas. Please see the Transport and Parking section of the shop which includes a combined camping/parking space at the circuit campsite.
The privately run Elephant campsite has received positive feedback from customers and can be found at www.francorchamps-camping.com.
IntentsGP provide a campsite with pre-erected tents so all you need to do is arrive and they will take care of everything else. The package includes: more information and booking
Prices range from £299 to £950 per pitch.

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