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Radiation in the form of solar energetic particles (SEPs) presents a severe risk to the short-term health of astronauts and the success of human exploration missions beyond Earth’s protective shielding. Modeling how shielding mitigates the dose accumulated by astronauts is an essential step toward reducing these risks. PREDICCS (Predictions of radiation from REleASE, EMMREM, and Data Incorporating the CRaTER, COSTEP, and other SEP measurements) is an online tool for the near real-time prediction of radiation exposure at Earth, the Moon, and Mars behind various levels of shielding. We compare shielded dose rates from PREDICCS with dose rates from the Cosmic Ray Telescope for the Effects of Radiation (CRaTER) onboard the Lunar Reconnaissance Orbiter (LRO) at the Moon and from the Radiation Assessment Detector (RAD) on the Mars Science Laboratory (MSL) during its cruise phase to Mars for five solar events in 2012 when Earth, MSL, and Mars were magnetically well connected. Calculations of the accumulated dose demonstrate a reasonable agreement between PREDICCS and RAD ranging from as little as 2% difference to 54%. We determine mathematical relationships between shielding levels and accumulated dose. Lastly, the gradient of accumulated dose between Earth and Mars shows that for the largest of the five solar events, lunar missions require aluminum shielding between 1.0 g cm−2 and 5.0 g cm−2 to prevent radiation exposure from exceeding the 30-day limits for lens and skin. The limits were not exceeded near Mars.