You don't actually need the circle
This is a little thing I like to call, "The circle of fifths without the circle."
You can get the keys with sharps just as easily by counting correctly without the circle, so how do you count?You start by counting from C Major, C Major has no sharps or flats, you then count 5 forward for the key and 4 from that same place for the sharp.
You then also have to remember that new keys keep old sharps, this means that each new key will keep all previous sharps. So let us count.
5 forward from C gives you C, D, E, F, G (Remember inclusive counting).
4 forward from that same place (C) gives you C, D, E, F.
G Major the key with one sharp has an F#
Now onward from G this time.
5 forward from G gives you G, A, B, C, D.
Remember new keys keep old sharps. D Major, the new key, will keep its F#.
You then count 4 from G for the new sharp G, A, B, C.
D Major has both an F# and a C#
Now we count onward from D
5 forward from D gives you D, E, F, G, A
New keys keep old sharps, it will have an F# and C#.
4 Forward for the new sharp (From D) gives you D, E, F, G
A major has both a F, C and G sharp
You then count 5 from A. A, B, C, D, E
E Major is the new key, new keys keep old sharps, it will have an F,
C, and G sharp.
4 from A gives you. A, B, C, D
E major has four sharps, F, C, G and D
Now we count 5 forward from E. E, F, G, A, B
B Major is the new key and will keep all previous sharps, it will have an F, C, G, D sharp.
We count 4 from E for the new sharp, that means E, F, G, A
B Major has 5 sharps, an F#, C#, G#, D# and A#.
Now we count 5 forward from B, B, C, D, E, F
We remind ourselves that the key with six sharps is not F Major that has a Bb but F# Major
F# Major will have all the previous sharps, that is to say F#,
C#, G#, D#, and A#
We will then count 4 from B for the new (6th) sharp. B, C, D,
F# major has six sharps, F#, C#, G#, D#, A# and E#
And now for the last one, the one with all the sharps. We count 5 forward from F# for the new key. F, G, A, B, C. We remind ourselves that C Major has no sharps or flats the key with seven sharps is actually C# Major.
It keeps all previous sharps (F, C, G, D, A, E) and we count 4 forward from F for the seventh sharp F, G, A, B, The seventh sharp is the B Sharp.
C# Major has an F#, C#, G#, D#, A#, E#, and B#.
Congratulations you have now succsessfully gone from zero to seven sharps.