I’ve had an on-going problem for about a year with my right calf, feels like a strain but I’m not sure. I’ve rested it a fair bit but it seems to come back whilst running anything over 5k, just like a twinge then a tightening/swelling which makes me stop
I had exactly the same problem almost to the letter, except that for me it would go at exactly 1k. I saw a physio and basically it was related to tight Achilles and weak calves (as others have pointed out above).
I did a month of strengthening exercises. Single leg calf raises twice a day, single legged squats (really concentrating on form – knee tracking over middle of foot, forcing off on the front of the foot) again twice a day. Both of those exercises were a bit sore on the calf at first but subsided after a couple of weeks. I then made a very gradual return to running, I kept the distance to just under the previous failure point for a couple of weeks. Since then, I have also been doing eccentric calf raises which has really helped my achilles. So far so good.
I have done physio in the past with not particularly good results. I think what worked this time was doing a very limited number of exercises but twice a day. I could quickly feel/see results particularly with the squats.
Oh course everyone is different.