The Normalized Difference Vegetation Index (NDVI) is widely used for vegetation monitoring; however, its accuracy is affected by noise factors such as signal-to-noise ratio (SNR) and the spectral characteristics of sensor bands. In this study, a numerical sensitivity analysis of NDVI was conducted using both real and simulated data from Sentinel-2 and Landsat series sensors. The NDVI response under various noise scenarios (5%, 25%, 75%, and 100% noise) was evaluated as a function of SNR variations and spectral parameters including band center position and bandwidth in both real and simulated datasets. Relative Percentage Error (RPE) and numerical derivatives of NDVI with respect to noise and spectral changes were used to assess the stability of the index. Results showed that NDVI is more sensitive to SNR at lower noise levels (at 5%), with sensitivity values ranging from 0.0003 to 0.0005 nanometers per band. It was also found that NDVI stability varies by sensor and noise condition, with newer sensors yielding more stable results- indicating a lower vegetation equivalent noise (VEN ≈ -0.00045). Furthermore, the simulated data revealed potential sensitivities (e.g., saturation at high noise levels) that appeared only sporadically in real data. at noise levels above 50%, simulations estimated changes up to 20% greater than those observed in real data. These findings may assist in sensor selection and the interpretation of vegetation data across diverse environments.