Reference
Grade systems
Five scales in common use, none of which measure quite the same thing. The converter below lines them up; the caveats underneath explain where it stops being reliable.
What each scale measures
Yosemite Decimal System (United States)
Classes 1 to 4 describe walking through scrambling. Class 5 is technical roped climbing and is subdivided decimally: 5.0 through 5.9, then 5.10 onward with letter suffixes a to d. The scale was designed as closed-ended at 5.9 in the 1950s and simply kept going when climbers got better, which is why it reads oddly. The number grades the hardest single move, not the sustained difficulty or the seriousness of the protection.
French sport grades
Numerals from 1 upward with letter and plus modifiers: 6a, 6a+, 6b and so on. Unlike YDS, French grades assess the overall difficulty of a pitch rather than its crux move, so a long sustained pitch grades harder than a short one containing the same hardest move. This is the default system across continental Europe and for sport climbing almost everywhere.
UIAA
Roman numerals with plus and minus modifiers, running I to XII. Still standard in Germany, Austria and much of Scandinavia, and the system you will see on Norwegian route descriptions. Like the French scale it grades the pitch as a whole.
British trad
Two components. An adjectival grade (Moderate, Difficult, Very Difficult, Severe, Hard Severe, Very Severe, Hard Very Severe, then E1 upward) describes the overall seriousness: how sustained it is, how good the protection is, how committing a retreat would be. A technical grade (4a, 5b, 6a…) describes the hardest move. The pair carries information neither number does alone. E1 5a is poorly protected and not very hard; E1 5c is well protected and physically harder.
Alpine adjectival (overall route grade)
F, PD, AD, D, TD, ED1 through ED4, from facile to extrêmement difficile. This is not a rock grade. It describes the whole undertaking: length, altitude, objective danger, commitment, quality of descent, and how far you are from help. A D route at 4,000 m in the Alps and a D route at 7,000 m in the Karakoram are not comparable in effort even though the label matches, which is why the register also records the route's rock grade where one exists.
Where conversion breaks down. Below about 5.9 the systems track each other closely enough to be useful. Above that they diverge, because they are weighting different things and because grading is consensus-based and drifts by region. A conversion table is a starting point for an unfamiliar guidebook, not an equivalence.
Ice and mixed
Water ice is graded WI1 to WI7 on steepness and sustained character; WI4 is roughly vertical for short sections, WI6 is vertical and strenuous with poor rests. Alpine ice uses AI with the same numbers but implies glacier ice, which is usually more consolidated. Mixed ground combining rock and ice with tools takes an M grade, M1 to M13 and upward, where the higher numbers describe overhanging dry-tooling rather than anything found on a mountain.
Faces in the register are often described by angle instead, which is unambiguous: Alpamayo's southwest face runs at about 70 degrees, and the rime formations on Cerro Torre's Ragni route reach vertical and beyond.