The direct answer: any builder who gives a firm number before seeing the yard is guessing. A custom timber pergola quote depends on size, roof layout, footings, site access, finish direction, and whether the design needs permit coordination. A free 3D design and written quote is the cleanest way to compare real options for your yard.
Open-roof pergolas usually differ from pavilions because they do not include the same solid roof assembly, but structure size, roof rhythm, span, and site work can still change the scope.
A useful quote starts with the structure type, property ZIP, rough dimensions, and a short note about how you want to use the space.