<PAGE>   1

                        STERLING CHEMICALS HOLDINGS, INC.
                                  EXHIBIT 11.1
                         EARNINGS PER SHARE COMPUTATION
                  (Amounts in thousands, except per share data)


<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED MARCH 31,   SIX MONTHS ENDED MARCH 31,
                                                              ----------------------------   --------------------------
                                                                  1999           1998           1999           1998
                                                               ----------     ----------     ----------     ----------
<S>                                                            <C>            <C>            <C>            <C>        
     BASIC EARNINGS PER SHARE

Weighted average of common stock outstanding ..............        12,466         11,984         12,446         11,918

Net Loss ..................................................    $  (24,820)    $  (16,288)    $  (37,920)    $  (26,433)
Less: Preferred dividend requirements and accretion .......          (658)          (591)        (1,303)        (1,219)
Plus: Depreciation of value of Released Shares ............         1,048            505          1,048            505
                                                               ----------     ----------     ----------     ----------

Net loss used in basic loss per share .....................    $  (24,430)    $  (16,374)    $  (38,175)    $  (27,147)
                                                               ==========     ==========     ==========     ==========

     BASIC LOSS PER SHARE .................................    $    (1.96)    $    (1.37)    $    (3.07)    $    (2.28)
                                                               ==========     ==========     ==========     ==========

     DILUTED EARNINGS PER SHARE

Weighted average of common stock outstanding ..............        12,466         11,984         12,446         11,918

Total weighted average shares outstanding used in
     diluted loss per share computation (1) ...............        12,466         11,984         12,446         11,918

Net loss ..................................................    $  (24,820)    $  (16,288)    $  (37,920)    $  (26,433)
Less: Preferred dividend requirements and accretion .......          (658)          (591)        (1,303)        (1,219)
Plus: Depreciation of value of Released Shares ............         1,048            505          1,048            505
                                                               ----------     ----------     ----------     ----------

Net loss used in diluted earning per share ................    $  (24,430)    $  (16,374)    $  (38,175)    $  (27,147)
                                                               ==========     ==========     ==========     ==========

         DILUTED LOSS PER SHARE (1) .......................    $    (1.96)    $    (1.37)    $    (3.07)    $    (2.28)
                                                               ==========     ==========     ==========     ==========
</TABLE>

(1)  Due to losses resulting in anti-dilution, same as amount used in basic
     computation.



                                       26