The article combines fractals and box-counting dimension to find the dimension of complex shapes. By using a specific formula, the dimension of a fractal made from multiple contractions or combining fractals can be calculated. When the scale factors are the same, this dimension matches the Hausdorff dimension. The study also provides a condition for when the box-counting dimension and Hausdorff dimension are equal. Additionally, it reveals that the dimension of a combined fractal is the average of the dimensions of the individual fractals.