A universal model for mobility and migration patterns is introduced, which addresses the limitations of the gravity law in predicting population movement, cargo shipping, phone calls, and trade. The gravity law, though widely used, has adjustable parameters and lacks a rigorous derivation, leading to inconsistencies. The new model, called the radiation model, is based on first principles and does not require adjustable parameters. It predicts commuting and mobility fluxes using only population distribution data, and is parameter-free, making it applicable in areas with limited mobility data. The radiation model is derived from a stochastic process that captures local mobility decisions. It assumes that individuals seek job opportunities in all counties, with the number of opportunities proportional to the population. The best job offer is chosen based on benefits, which include income, working hours, and conditions. The model predicts commuting fluxes using the formula: $$ \left\langle T_{i j}\right\rangle=T_{i}\frac{m_{i}n_{j}}{(m_{i}+s_{i j})(m_{i}+n_{j}+s_{i j})} $$ where $ T_{ij} $ is the average flux between locations i and j, $ m_i $ and $ n_j $ are the populations of the source and destination, and $ s_{ij} $ is the population in the region surrounding the source. The model is independent of the benefit distribution and job density, and has no free parameters. The radiation model outperforms the gravity law in predicting commuting patterns, as demonstrated by comparisons with empirical data. It correctly predicts the order of magnitude difference in commuting fluxes between counties in Utah and Alabama, and resolves the unphysical divergence in the gravity law's predictions. The model also accounts for fluctuations in commuting numbers, unlike the deterministic gravity law. The radiation model is tested on various socio-economic phenomena, including hourly travel patterns, migrations, communication patterns, and commodity flows. It provides accurate quantitative descriptions of mobility and transport across different time scales and regions. The model's parameter-free nature allows it to predict commuting and transport patterns even in areas where such data is not systematically collected. The radiation model also reveals a scale-invariant property in commuting patterns, which is supported by empirical evidence. The model can be further improved by incorporating factors such as home-field advantage in job searching. Overall, the radiation model offers a more accurate and general framework for understanding mobility and migration patterns compared to the gravity law.A universal model for mobility and migration patterns is introduced, which addresses the limitations of the gravity law in predicting population movement, cargo shipping, phone calls, and trade. The gravity law, though widely used, has adjustable parameters and lacks a rigorous derivation, leading to inconsistencies. The new model, called the radiation model, is based on first principles and does not require adjustable parameters. It predicts commuting and mobility fluxes using only population distribution data, and is parameter-free, making it applicable in areas with limited mobility data. The radiation model is derived from a stochastic process that captures local mobility decisions. It assumes that individuals seek job opportunities in all counties, with the number of opportunities proportional to the population. The best job offer is chosen based on benefits, which include income, working hours, and conditions. The model predicts commuting fluxes using the formula: $$ \left\langle T_{i j}\right\rangle=T_{i}\frac{m_{i}n_{j}}{(m_{i}+s_{i j})(m_{i}+n_{j}+s_{i j})} $$ where $ T_{ij} $ is the average flux between locations i and j, $ m_i $ and $ n_j $ are the populations of the source and destination, and $ s_{ij} $ is the population in the region surrounding the source. The model is independent of the benefit distribution and job density, and has no free parameters. The radiation model outperforms the gravity law in predicting commuting patterns, as demonstrated by comparisons with empirical data. It correctly predicts the order of magnitude difference in commuting fluxes between counties in Utah and Alabama, and resolves the unphysical divergence in the gravity law's predictions. The model also accounts for fluctuations in commuting numbers, unlike the deterministic gravity law. The radiation model is tested on various socio-economic phenomena, including hourly travel patterns, migrations, communication patterns, and commodity flows. It provides accurate quantitative descriptions of mobility and transport across different time scales and regions. The model's parameter-free nature allows it to predict commuting and transport patterns even in areas where such data is not systematically collected. The radiation model also reveals a scale-invariant property in commuting patterns, which is supported by empirical evidence. The model can be further improved by incorporating factors such as home-field advantage in job searching. Overall, the radiation model offers a more accurate and general framework for understanding mobility and migration patterns compared to the gravity law.