How can I determine US County by zip-code?

you can use the Google Maps API to Get Locations from Zip Codes

Google offers many API’s, among them is the Maps API. In this example we’ll show all the code necessary to hit Google with a zip code to get the location in the form of City, State and Country.

First thing to do is to reference Google’s Map API:

<script language="javascript" src="https://maps.google.com/maps/api/js?sensor=false"></script>

Next is a little form used to enter your zip code:

<form>
zip: <input type="text" name="zip" value="46032"> <a href="#" onclick="getLocation()">Get Address</a>
</form>

You can see that I have a link which fires a function called “getLocation()” – below you’ll find that function and the related code:

...
<script language="javascript">
function getLocation(){
  getAddressInfoByZip(document.forms[0].zip.value);
}

function response(obj){
  console.log(obj);
}
function getAddressInfoByZip(zip){
  if(zip.length >= 5 && typeof google != 'undefined'){
    var addr = {};
    var geocoder = new google.maps.Geocoder();
    geocoder.geocode({ 'address': zip }, function(results, status){
      if (status == google.maps.GeocoderStatus.OK){
        if (results.length >= 1) {
      for (var ii = 0; ii < results[0].address_components.length; ii++){
        var street_number = route = street = city = state = zipcode = country = formatted_address = '';
        var types = results[0].address_components[ii].types.join(",");
        if (types == "street_number"){
          addr.street_number = results[0].address_components[ii].long_name;
        }
        if (types == "route" || types == "point_of_interest,establishment"){
          addr.route = results[0].address_components[ii].long_name;
        }
        if (types == "sublocality,political" || types == "locality,political" || types == "neighborhood,political" || types == "administrative_area_level_3,political"){
          addr.city = (city == '' || types == "locality,political") ? results[0].address_components[ii].long_name : city;
        }
        if (types == "administrative_area_level_1,political"){
          addr.state = results[0].address_components[ii].short_name;
        }
        if (types == "postal_code" || types == "postal_code_prefix,postal_code"){
          addr.zipcode = results[0].address_components[ii].long_name;
        }
        if (types == "country,political"){
          addr.country = results[0].address_components[ii].long_name;
        }
      }
      addr.success = true;
      for (name in addr){
          console.log('### google maps api ### ' + name + ': ' + addr[name] );
      }
      response(addr);
        } else {
          response({success:false});
        }
      } else {
        response({success:false});
      }
    });
  } else {
    response({success:false});
  }
}
</script>

...

Thats it – open up the console in Chrome and notice the output as you enter different zip codes.

get it from here: http://rickluna.com/wp/2012/09/using-the-google-maps-api-to-get-locations-from-zip-codes/

you need to know the mapping of zip_code and country,

I've found a github project for this:

https://github.com/jgoodall/us-maps

once you get json mapping by instruction, you can implement the function you want.