UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER

Pursuant to Rule 13a-16 or 15d-16

under the Securities Exchange Act of 1934

For the month of December 2025

COMMISSION FILE NUMBER: 001-33373

CAPITAL CLEAN ENERGY CARRIERS CORP.

(Translation of registrant’s name into English)

3 Iassonos Street

Piraeus, 18537 Greece

(Address of principal executive offices)

Indicate by check mark whether the Registrant files or will file annual reports under cover of Form 20-F or Form 40-F.

Form 20-F ☒ Form 40-F ☐

Attached as Exhibit I ~~are~~hereto is a copy of the ~~financial~~press ~~results~~release of Capital Clean Energy Carriers Corp. ~~(“CCEC”)~~announcing ~~for~~further ~~the~~expansion ~~nine-month~~with ~~period~~an ~~ended~~order ~~September 30,~~for ~~2025~~three ~~and~~latest ~~the~~specification ~~related~~LNG ~~Operating~~carriers ~~and~~delivering ~~Financial~~in ~~Review~~2028 and ~~Prospects discussion~~2029.

Attached as Exhibit II are the following Unaudited Interim Condensed Consolidated Financial Statements of CCEC:

(i) Unaudited Condensed Consolidated Balance Sheets as of September 30, 2025 and December 31, 2024

(ii) Unaudited Condensed Consolidated Statements of Comprehensive Income for the nine-month periods ended September 30, 2025 and 2024

(iii) Unaudited Condensed Consolidated Statements of Changes in Shareholders’ Equity and Partners’ Capital for the nine-month periods ended September 30, 2025 and 2024

(iv) Unaudited Condensed Consolidated Statements of Cash Flows for the nine-month periods ended September 30, 2025 and 2024

(v) Notes to the Unaudited Interim Condensed Consolidated Financial Statements

The financial results of CCEC and related Operating and Financial Review and Prospects discussion and the Unaudited Interim Condensed Consolidated Financial Statements of CCEC attached as Exhibit I and Exhibit II, respectively, are being filed to include the review report of CCEC’s Independent Registered Public Accounting Firm (PCAOB ID No. 1163). There are no other changes to the financial results of CCEC and related Operating and Financial Review and Prospects discussion and the Unaudited Interim Condensed Consolidated Financial Statements of CCEC attached as Exhibit I and Exhibit II, respectively, which were originally filed with the Securities and Exchange Commission (“SEC”) pursuant to CCEC’s Report on Form 6-K filed with the SEC on November 6, 2025.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Dated: December 12, 2025

CAPITAL CLEAN ENERGY CARRIERS CORP.

Dated: January 8, 2026

CAPITAL CLEAN ENERGY CARRIERS CORP.

/s/ Gerasimos (Jerry) Kalogiratos

Name: Gerasimos (Jerry) Kalogiratos

Title: Chief Executive Officer

Filing Compare · Capital Clean Energy Carriers Corp.