<PAGE>
 
                                                                      EXHIBIT 11

CONSOLIDATED NATURAL GAS COMPANY AND SUBSIDIARIES

COMPUTATION OF PER SHARE EARNINGS
(In Thousands, Except Per Share Data)

<TABLE>
<CAPTION>
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Years Ended December 31,                                            1996           1995          1994
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<S>                                                               <C>            <C>           <C>
Earnings Per Share of Common Stock,
 as Shown on the Consolidated Statement of Income
 
 Net income.....................................................  $298,273       $21,344       $183,171
                                                                  --------       -------       --------
                                                                                         
 Average common shares outstanding..............................    94,434        93,246         93,000
                                                                  --------       -------       --------
                                                                                         
   Earnings per share of common stock...........................     $3.16          $.23          $1.97
                                                                  ========       =======       ========
 
Primary Earnings Per Share (Note 1)
                                                                               
 Net income.....................................................  $298,273       $21,344       $183,171
                                                                  --------       -------       --------
                                                                                        
 Average common shares outstanding..............................    94,434        93,246         93,000
 Incremental shares resulting from                                                      
   assumed exercise of stock options............................       736            99             78
                                                                  --------       -------       --------
 Average common shares, as adjusted.............................    95,170        93,345         93,078
                                                                  --------       -------       --------
                                                                                        
   Primary earnings per share...................................     $3.13          $.23          $1.97
                                                                  ========       =======       ========
                                                                                 
Fully Diluted Earnings Per Share                                                 
                                                                                 
 Net income.....................................................  $298,273       $21,344       $183,171
 Interest on 7 1/4% Convertible Subordinated                                               
   Debentures, net of tax effect................................    11,823        11,913         12,465
                                                                  --------       -------       --------
 Net income, as adjusted........................................  $310,096       $33,257       $195,636
                                                                  --------       -------       --------
                                                                                           
 Average common shares outstanding..............................    94,434        93,246         93,000
 Incremental shares resulting from                                                         
   assumed exercise of stock options............................       862           154             96
 Shares issuable from assumed conversion of 7 1/4%                                                                    
   Convertible Subordinated Debentures..........................     4,559         4,559          4,577
                                                                  --------       -------       --------
 Average common shares, as adjusted.............................    99,855        97,959         97,673
                                                                  --------       -------       --------
                                                                                             
   Fully diluted earnings per share.............................     $3.11(1)       $.34(2)       $2.00(2)
                                                                  ========       =======       ========
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Notes:
(1) This calculation is submitted in accordance with Regulation S-K Item
    601(b)(11) although not required by footnote 2 to paragraph 14 of APB
    Opinion No. 15 because it results in dilution of less than 3%.
(2) This calculation is submitted in accordance with Regulation S-K Item
    601(b)(11) although it is contrary to paragraph 40 of APB Opinion No. 15
    because the assumed conversion of the 7 1/4% Convertible Subordinated
    Debentures produces an antidilutive result.