There are a variety of different systems used around the world to define rock climbs grades. Below you will find a table that compares the different climbing grades across the five most popular systems
French The French system is an internationally recognised system for grading sport climbs and is therefore used on bolted routes within the UK.
UIAA This system is used in Germany, in other areas of Eastern Europe and in Italy for the classic trad routes.
United States Yosemite Decimal System(YDS) is a grading system commonly found in the United States, starts with a 5.something. Grades 1 to 4 refer to walks of increasing difficulty, by the time you reach 5 you are assumed to be scrambling over rocks which equates to about 5.0. Sub-Grade (Yosemite Decimal System). The sub-grade ranges from 1 to a theoretically infinite number (today the highest number is 15). The number is increased when a ‘harder’ climb is developed.
Great Britain The UK system is made of two sub-grades, an adjective grade, and a technical grade. The adjective grade describes the overall difficulty of the climb taking into consideration how strenuous the route is, the amount of exposure, and the availability of protection. The adjective grades are as follows: Moderate (M), Very Difficult (VD), Hard Very Difficult HVD), Mild Severe (MS), Severe (S), Hard Severe (HS), Mild Very Severe (MVS), Very Severe (VS), Hard Very Severe (HVS) and Extremely Severe. The Extremely Severe grade is also broken down into 10 further sub-grades from E1 to E11. The numerical technical grading describes the hardest (crux) move on the climb. For a brief explanation of UK traditional climbing grades follow this link.
Australian The system used in Australia and New Zealand is perhaps the most logical of all. There are no letters in secondary grades, just a single number that gets bigger as the routes get harder.
In the sport of bouldering, problems are assigned technical grades according to several established systems, which are often distinct from those used in roped climbing. Bouldering grade systems in wide use include the Hueco “V” grades (known as the V-scale), Fontainebleau technical grades, and more. You can read a very detailed article about bouldering grades here: www.99boulders.com. There are also other systems used around the world to grade rock climbs.