Exhibit 5.1

Brian F. Leaf

T: +1 703 456 8053

bleaf@cooley.com

May 30, 2017

Appian Corporation

11955 Democracy Drive, Suite 1700

Reston, VA 20190

Ladies and Gentlemen:

You have requested our opinion, as counsel to Appian Corporation, a Delaware corporation (the “Company”), in connection with the filing by the Company of a Registration Statement on Form S-8 (the “Registration Statement”) with the Securities and Exchange Commission covering the offering of up to (i) 7,776,168 shares (the “2007 Plan Shares”) of the Company’s Class B Common Stock, par value $0.0001 per share (the “Class B Common Stock”), pursuant to the Company’s 2007 Stock Option Plan, as amended (the “2007 Plan”), (ii) 14,197,610 shares (the “2017 Plan Shares,” together with 2007 Plan Shares, the “Shares”) of the Company’s Class A Common Stock, par value $0.0001 per shares (the “Class A Common Stock”) pursuant to the Company’s 2017 Equity Incentive Plan (the “2017 Plan,” together with the 2007 Plan, the “Plans”).

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and the related prospectuses, (b) the Company’s Third Amended and Restated Certificate of Incorporation and the Company’s Bylaws, each as currently in effect, (c) the Plans, and (d) the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. We have assumed the genuineness and authenticity of all documents submitted to us as originals, the conformity to originals of all documents submitted to us as copies, the accuracy, completeness and authenticity of certificates of public officials; and the due authorization, execution and delivery of all documents by all persons other than the Company where authorization, execution and delivery are prerequisites to the effectiveness of such documents. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not sought independently to verify such matters.

Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware. We express no opinion as to whether the laws of any particular jurisdiction other than those identified above are applicable to the subject matter of this opinion. We are not rendering any opinion as to compliance with any federal or state law, rule or regulation relating to securities, or to the sale or issuance thereof.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when sold and issued in accordance with the Plans, the Registration Statement and the related prospectuses, will be validly issued, fully paid and nonassessable (except as to shares issued pursuant to certain deferred payment arrangements, which will be fully paid and nonassessable when such deferred payments are made in full).

We consent to the filing of this opinion as an exhibit to the Registration Statement.

Sincerely,

COOLEY LLP
By:	/s/ Brian F. Leaf
	Brian F. Leaf