I have been cutting numerous circles for my Zinnia Pillow and it is a time consuming process. I would trace the circle then cut it out. Two steps that led to black ink on my hands and on the edges of my fabric. Then a reader suggested I purchase an Olfa Circle Rotary Cutter.
I found it at Joann's and luckily it was 50% off since regular price is $27.99. It will cut circles 1 7/8" to 8 1/2". Made mostly of plastic but pretty sturdy with metal spike and blade. Claims it will cut thru cloth,leather,paper,vinyl,film,wallpaper and more. It took awhile for me to get use to how much pressure to apply to get a complete cut circle but once I got it the cutting went very fast.
Much like a compass it was easy to use and the only drawback was that the package came with very little instruction but referred you to olfa.com for project demonstrations. I watched the video and it explained a few things such as an easy way to set it for the circle size by lining it up on your cutting mat at 1/2 the size of the circle you want to cut. Also when cutting use only one hand. I was using two and pushing it along when in fact you press and turn the cutter for the best results.I would highly recommend if you cut a lot of circles or curves I have used it on felt and leather and it worked great, now just to find more project with circles!