Exhibit 5.1

February 11, 2021

KalVista Pharmaceuticals, Inc.

55 Cambridge Parkway

Suite 901E

Cambridge, MA 02142

Gentlemen/Ladies:

We deliver this opinion with respect to certain matters in connection with the offering by KalVista Pharmaceuticals, Inc., a Delaware corporation (the “Company”), of up to 6,181,250 shares (the “Shares”) of the Company’s common stock, par value $0.001 per share (the “Common Stock”), including 806,250 shares of Common Stock subject to an underwriters’ option to purchase additional shares, to be issued pursuant to that certain Underwriting Agreement (the “Underwriting Agreement”), dated as of February 10, 2021 between the Company, Jefferies LLC, Stifel, Nicolaus & Company, Incorporated, and Cantor Fitzgerald & Co., as the representatives of the several underwriters named in Schedule A thereto (the “Underwriters”). The Shares were registered pursuant to a universal shelf Registration Statement on Form S-3 (File No. 333-228831) filed by the Company with the Securities and Exchange Commission (the “Commission”) on December 14, 2018 and declared effective on December 21, 2018 (the “Shelf Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”), and the registration statement on Form S-3MEF (File No. 333-252972) filed by the Company with the Commission pursuant to Rule 462(b) under the Securities Act on February 10, 2021 (the “462(b) Registration Statement” and together with the Shelf Registration Statement, the “Registration Statements”), the base prospectus dated December 21, 2018 included therein (the “Base Prospectus”), the preliminary prospectus supplement dated February 9, 2021 and the final prospectus supplement dated February 10, 2021, both of which were filed with the Commission pursuant to Rule 424(b) under the Securities Act (together, the “Prospectus Supplements” and collectively with the Base Prospectus, the “Prospectus”). The offering of the Shares by the Company pursuant to the Registration Statements, the Prospectus and the Underwriting Agreement is referred to herein as the “Offering.”

In connection with our opinion expressed below we have examined originals or copies of the Underwriting Agreement, the Registration Statements, the Company’s Amended and Restated Certificate of Incorporation, as amended (the “Restated Certificate”) and the Company’s Amended and Restated Bylaws, as amended (the “Bylaws” and, together with the Restated Certificate, as each may be amended, modified or restated, the “Charter Documents”), certain minutes and consents of the Company’s board of directors (the “Board”) or a committee or committees thereof and the Company’s stockholders relating to the Registration Statements, the Charter Documents, and such other agreements, documents, certificates and statements of the Company, its transfer agent and public or government officials, as we have deemed advisable, and have examined such questions of law as we have considered necessary. In giving our opinion, we have also relied upon a good standing certificate regarding the Company issued by the Delaware Secretary of State dated February 9, 2021, a good standing certificate regarding the Company issued by the Massachusetts Secretary of the Commonwealth dated February 5, 2021, a good standing certificate regarding the Company issued by the Utah Secretary of State dated February 9, 2021 and a management certificate addressed to us and dated of even date herewith executed by the Company containing certain factual representations (the “Management Certificate”).

In our examination of documents for purposes of this opinion, we have assumed, and express no opinion as to, the genuineness of all signatures on original documents, the authenticity and completeness of all documents submitted to us as originals, the conformity to originals and completeness of all documents submitted to us as copies, the legal capacity of all persons or entities executing the same (other than the

Company), the lack of any undisclosed termination, modification, waiver or amendment to any document reviewed by us, the absence of any other extrinsic agreements or documents that might change or affect the interpretation or terms of documents we have reviewed, and the due authorization, execution and delivery of all such documents where due authorization, execution and delivery are prerequisites to the effectiveness thereof.

We render this opinion only with respect to, and express no opinion herein concerning the application or effect of any laws other than the existing laws of the Delaware General Corporation Law.

In connection with our opinions expressed below, we have assumed that, (i) at or prior to the time of the issuance and delivery of any of the Shares, there will not have occurred any change in the law or the facts affecting the validity of the Shares, any change in actions of the Board or the Company’s stockholders, or any amendments to the Charter Documents, and (ii) at the time of the offer, issuance and sale of any Shares, no stop order suspending the Registration Statements’ effectiveness will have been issued and remain in effect, and that the Registration Statements will not have been modified or rescinded. We also have assumed that the issuance and delivery of the Shares subsequent to the date hereof and the compliance by the Company with the terms of such Shares will not result in a violation of any provision of any of the Charter Documents or of any instrument or agreement then binding upon the Company or any restriction imposed by any court or governmental body then having jurisdiction over the Company.

Based upon the foregoing, we are of the opinion that when the Shares are issued, sold and delivered in the manner and for the consideration stated in the Registration Statements, the Prospectus and the Underwriting Agreement and in accordance with the resolutions adopted by the Board or a committee thereof, such Shares will be validly issued, fully paid and nonassessable.

We consent to the use of this opinion as an exhibit to the Current Report on Form 8-K to be filed by the Company with the Commission in connection with the Offering, and further consent to all references to us, if any, in the Registration Statements, the Prospectus and any amendments or supplements thereto. We do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

[Concluding Paragraph Follows on Next Page]

2

This opinion is intended solely for use in connection with the issuance and sale of the Shares subject to the Registration Statements and is not to be relied upon for any other purpose. In providing this opinion, we are opining only as to the specific legal issues expressly set forth above, and no opinion shall be inferred as to any other matter or matters. This opinion is rendered on, and speaks only as of, the date of this letter first written above, is based solely on our understanding of facts in existence as of such date after the aforementioned examination and does not address any potential changes in facts, circumstance or law that may occur after the date of this opinion letter. We assume no obligation to advise you of any fact, circumstance, event or change in the law or the facts that may hereafter be brought to our attention whether or not such occurrence would affect or modify the opinion expressed herein.

3