A novel ultra-simplified computational spectrometer based on one-to-broadband diffraction is introduced. This spectrometer uses a simple, arbitrarily shaped pinhole as a partial disperser, eliminating the need for complex encoding designs and full spectrum calibration. It employs a numerical regularized transform that depends only on the spectrum of diffracted radiation to reconstruct the incident spectrum. The spectrometer achieves a reconstructed spectral peak location accuracy of better than 1 nm over a 200 nm bandwidth and excellent resolution for peaks separated by 3 nm in a bimodal spectrum, all within a compact footprint of under half an inch. The design also enables broadband coherent diffractive imaging without requiring prior knowledge of the broadband illumination spectrum, assumptions of non-dispersive specimens, or correction for detector quantum efficiency. The spectrometer works by capturing a broadband diffraction pattern and using a single-shot monochromatic diffraction pattern as a reference. A multi-variable linear equation (MLE) is solved using coherent mode decomposition and adaptive Tikhonov regularization to determine the incident light's spectrum. The method allows for single-shot spectrum measurements across a wide wavelength range, from ultraviolet to infrared, with miniaturized lab-on-chip integration. This advancement is crucial for portable applications, offering high robustness, low cost, and long-term stability. The spectrometer's performance was validated using a supercontinuum light source and optical filters. Experimental results demonstrated a reconstructed spectral peak location accuracy better than 1 nm over a 200 nm bandwidth and excellent resolution for peaks separated by 3 nm in a bimodal spectrum. The design also showed high spectral resolution and the ability to distinguish a bimodal spectrum with peaks of 3 nm separation from a pre-captured narrowband diffraction with a FWHM of 1 nm. The spectrometer's performance was compared with a commercial grating-based spectrometer, showing good agreement and low error bars. The proposed method also reveals a significant breakthrough in broadband coherent diffractive imaging without requiring prior knowledge of the broadband illumination spectrum, assumptions of non-dispersive specimens, or correction for detector quantum efficiency. The spectrometer's design is ultra-compact, simple, and cost-effective, making it suitable for a wide range of applications in broadband spectrum metrology and computational imaging.A novel ultra-simplified computational spectrometer based on one-to-broadband diffraction is introduced. This spectrometer uses a simple, arbitrarily shaped pinhole as a partial disperser, eliminating the need for complex encoding designs and full spectrum calibration. It employs a numerical regularized transform that depends only on the spectrum of diffracted radiation to reconstruct the incident spectrum. The spectrometer achieves a reconstructed spectral peak location accuracy of better than 1 nm over a 200 nm bandwidth and excellent resolution for peaks separated by 3 nm in a bimodal spectrum, all within a compact footprint of under half an inch. The design also enables broadband coherent diffractive imaging without requiring prior knowledge of the broadband illumination spectrum, assumptions of non-dispersive specimens, or correction for detector quantum efficiency. The spectrometer works by capturing a broadband diffraction pattern and using a single-shot monochromatic diffraction pattern as a reference. A multi-variable linear equation (MLE) is solved using coherent mode decomposition and adaptive Tikhonov regularization to determine the incident light's spectrum. The method allows for single-shot spectrum measurements across a wide wavelength range, from ultraviolet to infrared, with miniaturized lab-on-chip integration. This advancement is crucial for portable applications, offering high robustness, low cost, and long-term stability. The spectrometer's performance was validated using a supercontinuum light source and optical filters. Experimental results demonstrated a reconstructed spectral peak location accuracy better than 1 nm over a 200 nm bandwidth and excellent resolution for peaks separated by 3 nm in a bimodal spectrum. The design also showed high spectral resolution and the ability to distinguish a bimodal spectrum with peaks of 3 nm separation from a pre-captured narrowband diffraction with a FWHM of 1 nm. The spectrometer's performance was compared with a commercial grating-based spectrometer, showing good agreement and low error bars. The proposed method also reveals a significant breakthrough in broadband coherent diffractive imaging without requiring prior knowledge of the broadband illumination spectrum, assumptions of non-dispersive specimens, or correction for detector quantum efficiency. The spectrometer's design is ultra-compact, simple, and cost-effective, making it suitable for a wide range of applications in broadband spectrum metrology and computational imaging.