Often the most challenging part of a painting for me is getting it from an idea onto the drawingboard. There are tools an artist can use to develop a composition, deal with color issues, and refine sizes and space. I once had a talented artist with skill staying with me, but I watched their frustration when the painting they were working on did not match their sketch. It was a problem that was not going to be solved because the proportions were different. I wondered if she didn't know how to scale up a sketch or had just decided to wing it to save time and suffered the consequences.
There are many ways to scale up a drawing or sketch, in fact deciding what size to make the painting is the first decision you usually make. Today you can use a digital projector, in the age of film it was a slide projector, and before that there was always a grid.
Start by placing a grid over the sketch
The grid can be expanded graphically along the angle of the diagonal or mathematically by a proportion
Start with the sides of the sketch, A&B
Once the length of the finished side is set and the unknown length found, a grid that is proportional to the sketch can be created for the desired size. Then it is a matter of copying individually each block of the grid.
It is a simple tool but it can be used to great effect. This is the artist Chuck Close with his acrylic painting Big Self Portrait done in 1968, 107.5" x 83.5"