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In magnetic resonance imaging, precise measurements of longitudinal relaxation time (T1) is crucial to acquire useful information that is applicable to numerous clinical and neuroscience applications. In this work, we investigated the precision of T1 relaxation time as measured using the variable flip angle method with emphasis on the noise propagated from radiofrequency transmit field (B+1) measurements. The analytical solution for T1 precision was derived by standard error propagation methods incorporating the noise from the three input sources: two spoiled gradient echo (SPGR) images and a B+1 map. Repeated in vivo experiments were performed to estimate the total variance in T1 maps and we compared these experimentally obtained values with the theoretical predictions to validate the established theoretical framework. Both the analytical and experimental results showed that variance in the B+1 map propagated comparable noise levels into the T1 maps as either of the two SPGR images. Improving precision of the B+1 measurements significantly reduced the variance in the estimated T1 map. The variance estimated from the repeatedly measured in vivo T1 maps agreed well with the theoretically-calculated variance in T1 estimates, thus validating the analytical framework for realistic in vivo experiments. We concluded that for T1 mapping experiments, the error propagated from the B+1 map must be considered. Optimizing the SPGR signals while neglecting to improve the precision of the B+1 map may result in grossly overestimating the precision of the estimated T1 values.