Sir, a good variety of staircases needs no calculations - the great number of standard structures exist many years. More than possible you have one of the standard or similar solutions.
I used standard stairs structures many times in real practice of architecture, design and construction - in steel, wood and reinforced concrete. I am able to do this work for you with many relative tips from experienced architect.
I could specify the bid if you let me know more. Do not hesitate to request more info,