Brim shape is the most visible decision in a running cap and the least explained. Shops list it as a spec and leave you to guess what it means in practice. Here is the short version, based on what each one is actually good at.
Flat
Sits level across the front. Packs down flat, which is the real argument for it — a flat brim folds into a vest pocket and comes out the shape it went in. Good coverage straight ahead, less at the sides. It is also the shape that reads least like running kit, which is why these end up worn far more often off the run than on it.
Curved
Wraps toward the face. Better in a crosswind, better at keeping low sun out of your peripheral vision, and generally more comfortable for people who find a flat brim sits oddly on a rounder head. Does not pack quite as small. If you run anywhere exposed or coastal, this is the one that stays on your head.
Short brim
Less shade, more airflow, and a noticeably lighter feel on the move. The choice for hot, still conditions and for anyone who dislikes the sensation of a brim in their field of view. Also the most wearable off the run. The trade is real though — on a long sunny day you will feel the lack of coverage across the nose and cheekbones.
Long brim
Maximum coverage for the face and nose. Comes into its own on exposed routes with sun at a low angle, and on long days where accumulated UV matters more than it feels like it does at the start. The downside is wind: a long brim catches more of it, and on a gusty day you will be holding it.
360
A full brim around the whole circumference. Covers the ears and the back of the neck, which nothing else here does. Unbeatable on a shadeless trail in July and slightly conspicuous anywhere else. If you burn easily or run long in open country, the self-consciousness is worth getting over.
If you only want one
A curved brim in a mid length handles the widest range of conditions and is the hardest to regret. Build from there, and add the specialists once you know which conditions you actually run in most.
Browse by shape across Everyday Caps, Low-Profile Caps and Baseball Caps.