My calves are super tight when I finish my ride, and my Achilles are sore for days after a 20 mile rolling hill ride. Could it be that my seat height is too low? If not, what could be the root cause?
Biking has actually alleviated my Achilles/heel pain. I have the arch of my foot more or less over the middle of the pedal. I am so grateful for it now.
A smaller frame allowed me to lessen my back pain, I was too far from the bars (dropped effective top tube length ~.6'' and that did the trick. The seat position is also important. Change this up and down until you find what works, remember you want near full leg extension when the pedal is at its lowest point, but not beyond that. If the seat is as low as it goes and you're still having to pedal with your toes to keep contact at the bottom of the rotation, the bike is too big.
The achilles pain and some tightness in the back of the calves comes from ankling too much, by pedaling high on the balls of your feet. I find that I do this when the seat is a bit too high. Lowering the seat slightly and making sure my cleats are positioned more toward the center of my foot as opposed to toward the toes helped me to alleviate this.
Try to notice whether you are pushing with your ankles while pedaling, this is the motion that causes the stress on the tendon. I lowered my seat such that it didn't feel like I was overextending my leg during a pedal stroke or trying to tip/toe at the greatest point of extension.
See sheldon for more info on pain in the tendon.
Related question on cleat postion: Why not place the cleats further back on the foot?