[BroJoeK]

Apparently only 18,000 were actually engaged on each side.
All the rest never made it to the battle, most notably Union Gen. Patterson's 18,000 which could have turned the battle.

So...
If we count everybody within the battle's general vicinity, then:

• Union (including Patterson's 18,000): ~54,000
• Confederate: ~34,000

[Pikachu_Dad]

I was always curious as to why the Union forces did not include having Patterson attack.

His inaction allowed Johnston to slip his forces away without penalty.

But then the Union was ‘blessed’ with inactive General’s early on.