A count of the number results of a search query can be obtained by appending /_count to the search URL.
POST /v1/contacts/_search/_count HTTP/1.1
Authorization: ***** Hidden credentials *****
Content-Type: application/json; charset=utf-8
Host: api.marketcircle.net
User-Agent: MC API Documentation
Content-Length: 2
{
"category" : {
"equal": "Customer"
}
}{"count":23}