No.Grand PrixCircuitPoleWinner
1Argentina Buenos Aires Stirling Moss • Cooper Bruce McLaren • Cooper
2Monaco Monaco Stirling Moss • Lotus Stirling Moss • Lotus
3Indianapolis Indianapolis Eddie Sachs • Ewing Jim Rathmann • Watson
4Netherlands Zandvoort Stirling Moss • Lotus Jack Brabham • Cooper
5Belgium Spa-Francorchamps Jack Brabham • Cooper Jack Brabham • Cooper
6France Reims Jack Brabham • Cooper Jack Brabham • Cooper
7Britain Silverstone Jack Brabham • Cooper Jack Brabham • Cooper
8Portugal Porto John Surtees • Lotus Jack Brabham • Cooper
9Italy Monza Phil Hill • Ferrari Phil Hill • Ferrari
10USA Riverside Stirling Moss • Lotus Stirling Moss • Lotus

Engines

2.5 L atmospheric or 0.75 L supercharged.
4.5 L atmospheric or 3.0 L supercharged engines were allowed at Indianapolis 500.

Points System

8-6-4-3-2-1 points for the top 6 places.
Best 6 results count toward championship.
Only the points of the highest-scoring driver for each constructor at each race (including privateer entries) are counted towards the Constructors' Championship.
The points in Indianapolis 500 race are only awarded to drivers, not constructors.

Read more

This season on Wikipedia.