Developed as a quantitative measurement of fire intensity, fire radiative power (FRP) and the potential applications to smoke plume injection heights, are currently limited by the pixel resolution of a satellite sensor. As a result, this study, the first in a two-part series, develops a new sub-pixel-based calculation of fire radiative power (FRPf) for fire pixels detected at 1 km2 nominal spatial resolution by the MODerate Resolution Imaging Spectroradiometer (MODIS) fire detection algorithm (collection 5), which is subsequently applied to several large wildfire events in California. The methodology stems from the heritage of earlier bi-spectral retrievals of sub-pixel fire area and temperature. However, in the current investigation, a radiative transfer model is incorporated to remove solar effects and account for atmospheric effects as a function of Earth-satellite geometry at 3.96 and 11 μm (MODIS fire detection channels). The retrieved sub-pixel fire (flaming) area is assessed via the multispectral, high-resolution data (3–50 m) obtained from the Autonomous Modular Sensor (AMS), flown aboard the NASA Ikhana unmanned aircraft. With fire sizes ranging from 0.001 to 0.02 km2, pixel-level fire area comparisons between MODIS and AMS are highly variable, regardless of the viewing zenith angle, and show a low bias with a modest correlation (R = 0.59). However, when lower confidence fire pixels and point-spread-function effects (fire hot spots on the pixel edge) are removed, the correlation becomes much stronger (R = 0.84) and the variability between MODIS and AMS is reduced. To account for these random errors via averaging, two clustering techniques are employed and the resulting AMS and MODIS comparisons of fire area, after correcting for overlapping MODIS pixels, are even more encouraging (R = 0.91). Drawing from the retrieved fire area and temperature, the FRPf is calculated and compared to the current MODIS pixel area-based FRP. While the two methods are strongly correlated (R = 0.93), the FRPf, in combination with retrieved fire cluster area, allows a large fire burning at a low intensity to be separated from a small fire burning at a high intensity. Similarly, the flux of FRPf over the retrieved fire area can be calculated, allowing for improved estimates of smoke plume injection heights in modeling studies and creating potential applications for the future VIIRS and GOES-R fire detection algorithms.