
<PAGE>
 
                                                                    EXHIBIT 12.1
 
                              HALLIBURTON COMPANY
 
               COMPUTATION OF RATIO OF EARNINGS TO FIXED CHARGES
 
<TABLE>
<CAPTION>
                                       -----------------------------------------
                          SIX MONTHS
                             ENDED
                         JUNE 30, 1998
                           UNAUDITED    1997     1996     1995    1994    1993
                         ------------- -------  -------  ------  ------  -------
                                (MILLIONS OF DOLLARS, EXCEPT RATIOS)
<S>                      <C>           <C>      <C>      <C>     <C>     <C>
Earnings:
  Income (loss) from
   continuing operations
   before provision for
   income taxes,
   minority interest,
   and cumulative effect
   of changes in
   accounting methods...    $427.1     $ 766.3  $ 404.2  $387.8  $297.8  $(132.4)
Add (deduct):
  Interest expense......      23.8        42.4     24.0    46.5    47.4     49.9
  Amortization of debt
   discount and issue
   costs................       0.2         0.3      0.1     0.6     0.7      0.8
  One-third of long-term
   fixed rent...........      17.5        35.0     30.7    30.5    46.6     58.3
  Equity in income of
   joint venture
   operations...........     (61.2)     (124.4)  (105.5)  (88.4)  (93.0)   (76.3)
  Dividends received
   from joint venture
   operations...........       3.7        43.6      7.2     7.3    12.0      9.3
                            ------     -------  -------  ------  ------  -------
    Total earnings......    $411.1     $ 763.2  $ 360.7  $384.3  $311.5  $ (90.4)
                            ======     =======  =======  ======  ======  =======
Fixed charges:
  Interest expense......    $ 23.8     $  42.4  $  24.0  $ 46.5  $ 47.4  $  49.9
  Amortization of debt
   discount and issue
   costs................       0.2         0.3      0.1     0.6     0.7      0.8
  One-third of long-term
   fixed rent...........      17.5        35.0     30.7    30.5    46.6     58.3
                            ------     -------  -------  ------  ------  -------
    Total fixed charges.    $ 41.5     $  77.7  $  54.8  $ 77.6  $ 94.7  $ 109.0
                            ======     =======  =======  ======  ======  =======
Ratio of earnings to
 fixed charges..........       9.9         9.8      6.6     5.0     3.3    (a)
                            ======     =======  =======  ======  ======  =======
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(a) Earnings were inadequate to cover fixed charges in 1993 by $199.4 million.
