Two major muscles power every movement of your lower leg: The gastrocnemius, which points your feet and flexes your knee, and the soleus, which points your foot, especially when your knee is bent. Although standing is the most convenient way to stretch both muscles, you can also sneak a few convenient seated calf stretches into your daily routine.
Dorsiflexing your ankle -- that is, flexing the top of your foot up toward your shin -- is an easy movement to perform while seated. It's also the most effective way to stretch both your gastrocnemius and soleus. Dorsiflexion with a straight knee focuses on the gastrocnemius; bend the knee and you'll focus the stretch on your soleus.
If you stretch your calves while standing, all you have to do is relax into the stretch -- your body weight does the rest. If you want to stretch your calves while seated, however, you'll need to apply some gentle traction to get your foot into the right position.
One of the easiest ways to do this is by looping a belt or yoga strap around the ball of your foot. Hold both ends of the strap and gently pull back, dorsiflexing your foot until you feel a stretch in your calf. Remember: Keep your leg straight to focus the stretch on your gastrocnemius, or bend your knee to shift the stretch to your soleus.
Because your knee must be straight to stretch the gastrocnemius, using a belt or strap is by far the most convenient way to ease your foot into the right position. You do have another option for stretching your soleus, however. Place a wooden block or a few thick books on the floor just in front of your chair, or scoot the chair up against a wall. Prop the toes of one foot against the block, books or wall and gently lean forward -- think of pressing your knee forward -- until you feel the stretch in your calf.
If you happen to lean forward while doing a seated calf stretch, you may feel quite a bit of tension behind the knee and in the back of your thigh. This usually means that you're stretching the hamstring, which flexes the knee more powerfully than your gastrocnemius does, in addition to your calf muscles.
This is why using a belt or yoga strap to get your ankle into the proper calf-stretching position is so helpful. A strap or belt is long enough that you can sit up straight while you stretch your calves, thus easing the pressure off your hamstrings and focusing the stretch on your calves. You can always stretch your hamstrings later.