Exhibit 5.1

December 7, 2015

Roper Technologies, Inc.

6901 Professional Parkway East

Suite 200

Sarasota, Florida 34240

Ladies and Gentlemen:

Roper Technologies, Inc., a Delaware corporation (the “Company”), has filed with the Securities and Exchange Commission a Registration Statement on Form S-3 (File No. 333-208200) (the “Registration Statement”) for the purpose of registering under the Securities Act of 1933, as amended (the “Securities Act”), certain securities, including $600,000,000 aggregate principal amount of the Company’s 3.000% senior notes due 2020 (the “2020 Notes”) and $300,000,000 aggregate principal amount of the Company’s 3.850% senior notes due 2025 (the “2025 Notes”, together with the 2020 notes, the “Notes”). The Securities are to be issued pursuant to the provisions of the Indenture dated as of August 4, 2008 (the “Indenture”) between the Company and Wells Fargo Bank, National Association, as trustee (the “Trustee”). The Notes are to be sold pursuant to the Underwriting Agreement dated November 30, 2015 (the “Underwriting Agreement”) among the Company and the several underwriters named therein (the “Underwriters”).

We, as your counsel, have examined originals or copies of such documents, corporate records, certificates of public officials and other instruments as we have deemed necessary or advisable for the purpose of rendering this opinion.

In rendering the opinion expressed herein, we have, without independent inquiry or investigation, assumed that (i) all documents submitted to us as originals are authentic and complete, (ii) all documents submitted to us as copies conform to authentic, complete originals, (iii) all signatures on all documents that we reviewed are genuine, (iv) all natural persons executing documents had and have the legal capacity to do so, (v) all statements in certificates of public officials and officers of the Company that we reviewed were and are accurate and (vi) all representations made by the Company as to matters of fact in the documents that we reviewed were and are accurate.

Based on the foregoing, and subject to the additional assumptions and qualifications set forth below, we advise you that, in our opinion, when the Notes have been duly executed and authenticated in accordance with the provisions of the Indenture and delivered to and paid for by the Underwriters in accordance with the Underwriting Agreement, the Notes will constitute valid and binding obligations of the Company, enforceable in accordance with their terms, subject to applicable bankruptcy, insolvency and similar laws affecting creditors’ rights generally, concepts of reasonableness and equitable principles of general applicability, provided that we express no opinion as to the validity, legally binding effect or enforceability of any provision that permits holders to collect any portion of stated principal amount upon acceleration of the Notes to the extent determined to constitute unearned interest.

In connection with the opinion expressed above, we have assumed that the Company is validly existing as a corporation in good standing under the laws of Delaware. In addition, we have assumed that the Indenture and the Notes (collectively, the “Documents”) are valid, binding and enforceable agreements of each party thereto (other than as expressly covered above in respect of the Company). We have also assumed that the execution, delivery and performance by each party to each Document to which it is a party (a) are within its corporate powers, (b) do not contravene, or constitute a default under, the certificate of incorporation or bylaws or other constitutive documents of such party, (c) require no action by or in respect of, or filing with, any governmental body, agency or official and (d) do not contravene, or constitute a default under, any provision of applicable law or regulation or any judgment, injunction, order or decree or any agreement or other instrument binding upon such party.

We are members of the Bars of the States of New York and California and the foregoing opinion is limited to the laws of the State of New York and the General Corporation Law of the State of Delaware, except that we express no opinion as to any law, rule or regulation that is applicable to the Company, the Documents or such transactions solely because such law, rule or regulation is part of a regulatory regime applicable to any party to any of the Documents or any of its affiliates due to the specific assets or business of such party or such affiliate.

We hereby consent to the filing of this opinion as an exhibit to a report on Form 8-K to be filed by the Company on the date hereof and its incorporation by reference into the Registration Statement and further consent to the reference to our name under the caption “Legal Matters” in the prospectus supplement which is a part of the Registration Statement. In giving this consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Davis Polk & Wardwell LLP