If it would twist a 3/8ths x 12 inch extension, you need to go to 1/2 inch. If it would strain a six inch extension, you are way over the limit for 3/8.
1/2 inch is a quantum leap stronger than 3/8, and usually you will break a 1/2'' breaker bar before anything else will break. At that point you should already be using an impact gun. If you haven't got air, the electric jobs do fine on most things, and are highly reccomended.
Many years ago, I broke my 1/2 inch breaker bar standing on a four foot piece of pipe, trying to loosten a big nut. I put the engine into a truck and took it to a friends garage where he zipped it off in seconds with an air impact. In fact I had broken TWO 1/2 inch bars that day. Impact guns make many jobs pathetically easy.