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Grade systems for free climbing

USA France Brasil
5.1   I
5.2 1 Isup
5.3 2 II
5.4 3 IIsup
5.5 4a III
5.6 4b IIIsup
5.7 4c IV
5.8 5a IVsup
5.9 5b V
5.10a 5c Vsup
5.10b 6a VI
5.10c 6a+ VIsup
5.10d 6b  
5.11a 6b+ VIIa
5.11b 6c VIIb
5.11c 6c+  
5.11d 7a VIIc
5.12a 7a+ VIIIa
5.12b 7b VIIIb
5.12c 7b+ VIIIc
5.12d 7c IXa
5.13a 7c+ IXb
5.13b 8a IXc
5.13c 8a+ Xa
5.13d 8b Xb
5.14a 8b+ Xc
5.14b 8c  
5.14c 8c+  
5.14d 9a


5.15a 9a+  

source: M.Benge and D.Raleigh (1995)

Grade system for aid climbing

A0 A free climb with an occasional aid move that does not require specialized aid gear ("aiders" or "etriers").
A1 Requires specialized gear but all placements are solid and easy.
A2 Good placements, but sometimes tricky.
A3 Many difficult aid moves. Some of the placements might only hold body-weight. The risk is still low.
A4 Many body-weight placements in a row. The risk is increasing.
A5 Enough body-weight placements in a row that a fall might result in a fall of at least 20 meters.

source: Wikipedia