EXHIBIT 5.1

Nicole C. Brookshire

T: 617 237-9357

nbrookshire@cooley.com

August 22, 2018

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”), with respect to certain matters in connection with the offering of up to 2,300,000 shares of its Class A common stock, par value $0.0001 (the “Shares”), including up to 300,000 Shares that may be sold pursuant to the exercise of an option to purchase additional Shares, pursuant to a Registration Statement on Form S-3 (Registration Statement No. 333-226941) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), the prospectus included within the Registration Statement (the “Base Prospectus”), and the prospectus supplement, dated August 20, 2018, and filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations of the Act (together with the Base Prospectus, the “Prospectus”). Of the Shares, up to 1,975,000 of the Shares are to be sold by the Company (the “Company Shares”) and up to 325,000 of the Shares are to be sold by certain selling stockholders (the “Selling Stockholder Shares”) as described in the Registration Statement and the Prospectus.

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and the Prospectus, (b) the Company’s Amended and Restated Certificate of Incorporation and the Company’s Amended and Restated Bylaws, each as currently in effect, and (c) 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 undertaken no independent verification with respect to such matters. We have assumed the genuineness and authenticity of all documents submitted to us as originals, and the conformity to originals of all documents submitted to us as copies and the due execution and delivery of all documents where due execution and delivery are a prerequisite to the effectiveness thereof. 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 to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that:

1. The Company Shares have been duly authorized and, when sold and issued in accordance with the Registration Statement and the related Prospectus, will be validly issued, fully paid and non-assessable.

2. The Selling Stockholder Shares have been validly issued and are fully paid and non-assessable.

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus included in the Registration Statement and to the filing of this opinion as an exhibit to the Registration Statement.

Sincerely,