I wanted to share my experience of calculating an arch made of square bricks to prevent others making the mistake that I did.
It seems obvious now that the circumference of the semi-circle is not going to be the sum of the widths of the bricks. One has to think of the arch as half of a regular polygon which has twice as many sides as the number of arch bricks, the former is then made from a semi-circle which would fit inside this straight-sided shape.
This image shows incircles for a number of shapes
There are few handy calculators online for easily calculating the radius of the incircle (a term I had never come across until my arch didn't meet in the middle!). Just remember to double the number of sides to complete the regular polygon. It's a shame that with the one in the link you cant put in your radius and have it work out how many bricks you need, but that version may be out there somewhere.
I found that putting in my brick width and then fiddling with the number of sides until I got a radius similar to what I wanted was effective. It's good to use an even number of sides because then the arch will have an odd number of bricks which is visually pleasing and structurally superior.