The condition of being or having a plane surface.(noun)
The Century Dictionary (Public Domain)
Use "planeness" in a sentence
"- Size of the permissible tolerances of workpiece surfaces, planeness, parallelism and dimensions as well as surface finish"
"- The grade of parallelism depends on the planeness of the surface worked first."
"- After the finished size has been achieved, the workpiece is unclamped, deburred at the cutting edges and checked for planeness, accuracy to size and surface finish."