If you're altogether certain, you know it for a fact. Since you're altogether sure that your calculations are correct, go ahead with the experiment. Please wear your goggles just in case.
Never use “all together” (meaning “all in one place”) when you mean altogether (which can also mean "all things considered"). It was risky to bring us all together again after so many years, but you have to admit that altogether we had a good time. Altogether, it could have been worse. It wasn't altogether bad. I suppose we won't do it again next year.