Exhibit 32

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of W.W. Grainger, Inc. (“Grainger”) for the quarterly period ended September 30, 2018, (the “Report”), D.G. Macpherson, as Chairman and Chief Executive Officer of Grainger, and Thomas B. Okray, as Senior Vice President and Chief Financial Officer of Grainger, each hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of Grainger.

/s/ D.G. Macpherson

D.G. Macpherson

Chairman and Chief Executive Officer

November 1, 2018

/s/ Thomas B. Okray

Thomas B. Okray

Senior Vice President and Chief Financial Officer

November 1, 2018