One flat (B♭). The F barre chord has humbled plenty of beginners. Capo 3 with D shapes or capo 5 with C shapes is the polite way around it.
| Chord | Number | Roman |
|---|---|---|
| F | 1 | I |
| Gm | 2m | ii |
| Am | 3m | iii |
| B♭ | 4 | IV |
| C | 5 | V |
| Dm | 6m | vi |
| Edim | 7° | vii° |
The 1, 4 and 5 (F, B♭, C) are the backbone. Add the 6m (Dm) and you can play most of what's on the radio. The 7° (Edim) mostly shows up as a passing chord, so don't lose sleep over it.
Those numbers are the Nashville number system. Learn the progression as numbers once and it works in every key.
Capo 1, play E shapes; capo 3, play D shapes; capo 5, play C shapes.
The capo chart has every key, and the transpose chart moves a song somewhere else entirely.
Songs that leave F usually go to its 4 or 5: key of B♭ or key of C. Or see every key.
Chartless listens to whatever is playing and shows the key, the chords and the numbers live, so you can check a recording against this page while it plays. How to find the key by ear if you'd rather do it yourself.