Wordpress - Count posts in custom taxonomy

function wp_get_productcat_postcount($id) {

    //return $count;
    $args = array(
      'post_type'     => 'product', //post type, I used 'product'
      'post_status'   => 'publish', // just tried to find all published post
      'posts_per_page' => -1,  //show all
      'tax_query' => array(
        'relation' => 'AND',
        array(
          'taxonomy' => 'product_cat',  //taxonomy name  here, I used 'product_cat'
          'field' => 'id',
          'terms' => array( $id )
        )
      )
    );

    $query = new WP_Query( $args);

    /*
    echo '<pre>';

    print_r($query->post_count);
    echo '</pre>';
    */

    return (int)$query->post_count;

}

Use an instance of WP_Query to query the database. http://codex.wordpress.org/Class_Reference/WP_Query

To query database for custom taxonomies use,

$query = new WP_Query( array( 'people' => 'bob' ) );

For more details on available options see: Taxonomy Parameters http://codex.wordpress.org/Class_Reference/WP_Query#Taxonomy_Parameters

Retrieve published posts using

'post_status' => 'publish'

Use found_posts to retrive the number of posts

$count = $query->found_posts;

Below code will get count of article from particular taxonomy

<?php 
  $terms = get_the_terms( $post->ID , 'your-taxonomy' );
  foreach ( $terms as $term ) {
    echo $term->count;
  } ?>