| Cover | Aug. 12, 2024 |
| Cover [Abstract] | |
| Document Type | 8-K |
| Amendment Flag | false |
| Document Period End Date | Aug. 12, 2024 |
| Entity File Number | 001-39696 |
| Entity Registrant Name | Compass Therapeutics, Inc. |
| Entity Central Index Key | 0001738021 |
| Entity Tax Identification Number | 82-4876496 |
| Entity Incorporation, State or Country Code | DE |
| Entity Address, Address Line One | 80 Guest Street, Suite 601 |
| Entity Address, City or Town | Boston |
| Entity Address, State or Province | MA |
| Entity Address, Postal Zip Code | 02135 |
| City Area Code | 617 |
| Local Phone Number | 500-8099 |
| Written Communications | false |
| Soliciting Material | false |
| Pre-commencement Tender Offer | false |
| Pre-commencement Issuer Tender Offer | false |
| Title of 12(b) Security | Common Stock, $0.0001 par value per share |
| Trading Symbol | CMPX |
| Security Exchange Name | NASDAQ |
| Entity Emerging Growth Company | true |
| Elected Not To Use the Extended Transition Period | false |
