Most charge 1/3 of gross but a lot depends on how the insurance pays for medical. My friend Joe is dealing with it in NH. In NH the vehicle that he was in, that insurance pays all of his medical bills. Then after everything is settled, the at fault insurance company pays the lawyer. The lawyer takes a third of what his insurance paid out for med, then pays the insurance co 2/3 of what they paid out. Then his lawyer takes 1/3 for Joe's share and gives Joe what is left.
Most also charge for expenses and profesional witnesses. The lawyer that joe is dealing with agreed to pay those out of the gross, so The lawyer is actually paying 1/3 of those expenses, and is on the hook for getting Joe's in co to agree to only recovering 2/3 of their out of pocket $. If he negotiates them down to 50% then he keeps 50%. That's his job.
For instance:
10K in med paid by Joe's insurance. Settles for 10K from at fault insurance
Lawyer pays Joe's insurance only $6,666 and keeps $3,333 for collecting it.
15K for my loss wage and P&S. Lawyer Keeps $5K and pays Joe $10K.
So, out of a 25K settlement w/ 10K in med bills, Joe takes home $10K - Lawyer makes $8,333.
Now, Joe only had to pay the lawyer 1/3 of his take, but the lawyer made 83.3% of what Joe got. It's a good deal for everybody except Joe's ins co.
The deal that you made with your lawyer at 40% actually meant that he took 50% after the Med expenses. Now if he has more than doubled (or more) what you would have been able to settle for after med expenses without him, Then he did a good job for you.
Remember, it's the well prepared suits that the at fault ins co will settle out for reasonable amounts.
NOW, depending on how your med bills were paid, you may be able to get those bills reduced or negotiate with who paid them. Ask your lawyer how to go about this.
Good luck