| Document and Entity Information | May 29, 2020 |
| Cover [Abstract] | |
| Document Type | 8-K |
| Amendment Flag | false |
| Document Period End Date | May 29, 2020 |
| Entity Registrant Name | KURA ONCOLOGY, INC. |
| Entity Central Index Key | 0001422143 |
| Entity Emerging Growth Company | false |
| Entity File Number | 001-37620 |
| Entity Tax Identification Number | 61-1547851 |
| Entity Incorporation State Country Code | DE |
| Entity Address, Address Line One | 3033 Science Park Road |
| Entity Address, Address Line Two | Suite 220 |
| Entity Address, City or Town | San Diego |
| Entity Address, State or Province | CA |
| Entity Address, Postal Zip Code | 92121 |
| City Area Code | (858) |
| Local Phone Number | 500-8800 |
| Written Communications | false |
| Soliciting Material | false |
| Pre-commencement Tender Offer | false |
| Pre-commencement Issuer Tender Offer | false |
| Security 12b Title | Common Stock, par value $0.0001 per share |
| Trading Symbol | KURA |
| Security Exchange Name | NASDAQ |
