Total testosterone is the whole amount circulating in your blood. But most of that is bound to proteins - chiefly SHBG (sex hormone-binding globulin) and albumin - and while it's bound, your body can't use it. Free testosterone is the small unbound fraction that's actually available to do the work.
The analogy that helps: total is the money in your account; free is the cash you can spend right now. The rest is committed elsewhere.
That distinction is the whole reason two men with the same total can feel completely different.


