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• Nitrogen use efficiency [NUE] is best understood in terms of its constituent parts. • Interpreting N utilization efficiency depends on both N nutrition index and biomass. • A critical N utilization efficiency curve can be defined based on previous theory. • Increasing N uptake efficiency [NUpE] will reduce N losses to the environment. • Maximizing NUE does not necessarily improve agronomic or environmental outcomes. Maximizing nitrogen (N) use efficiency [NUE] is commonly identified as a key strategy to improve both agronomic and environmental outcomes; however, interpretation of NUE requires explicit consideration of crop N status. In this study, we derived a set of novel theoretical relationships between the nitrogen nutrition index [NNI] and NUE used to better interpret values for nitrogen uptake efficiency [NUpE] and nitrogen utilization efficiency [NUtE]. A small-plot trial for potato [ Solanum tuberosum (L.) 'Russet Burbank'] was conducted in 2016 and 2017 in Central Minnesota, USA, on a Hubbard loamy sand with six N rate, source, and timing treatments and two irrigation rate treatments. Impacts of treatments on NNI, NUpE, NUtE, NUE, biomass, harvest index, and potential N losses were interpreted within the context of a theoretical quantitative relationship between NUE and NNI. We found that for a constant NNI value, NUtE values increased non-linearly as biomass increased; at an NNI value of 1.0, this relationship defines the critical N utilization efficiency curve. As N rate increased from 40 to 270 kg N ha−1, NUtE significantly decreased from 109.8–69.7 g g−1 N, corresponding with a significant increase in both biomass (from 12.0–17.8 Mg ha−1) and in NNI (from 0.520 to 0.973), respectively. Additionally, we found that potential N losses (e.g., leaching) decreased as NUpE increased, or as total N inputs decreased. Potential N loss was lower in 2016 than 2017 (135 and 187 kg N ha−1, respectively) due to both greater NUpE and lower total N input from all sources in 2016 (0.602 g N g-1 N and 339 kg N ha-1, respectively) than in 2017 (0.526 g N g-1 N and 395 kg N ha-1, respectively). Interpreting NUE to evaluate agronomic and environmental outcomes requires separate consideration of its constituent factors (e.g., NUpE, NUtE, and HI) and explicit consideration of both NNI and biomass. [ABSTRACT FROM AUTHOR]