Accurately predicting the intake of dairy cows is essential for evaluating their efficiency. However, measuring individual intake can be challenging and costly, especially in constrained environments. While mathematical models can help predict intake, they are typically designed for normal farm conditions. To overcome this limitation, this article presents a framework for predicting the dry matter intake of dairy cows allowed by constrained environmental conditions, i.e. the environmentally attainable intake (EAI, g DM/d). The framework represents EAI as the product of two main components: maximum sustainable Eating Rate (ER, g DM/min) and Eating Time (ET, min/d). The ER is determined by the physical NDF content of the food and the animal’s age, which is a proxy for oral capacity. The daily time available for feeding is divided into four activities: seeking for food, ET, rumination, and additional processing time, influenced by environmental factors such as temperature, photoperiod, farm activities, and food availability. The framework includes assumptions such as a mandatory minimum amount of time for animals to sleep soundly, farm activities that prevent access to food, and the effect of heat stress. To define the most influential parameters, Bayesian inference and a database of 79 treatments from 24 published papers covering grazing and housed cows from several countries, was used for Sensitivity Analysis. The framework is sensitive to six of the 18 inferred parameters. The mean absolute errors for EAI prediction were 2.4 and 4.2 kg DM/d for grazing and housed cows, respectively. The framework separates the animal side of intake from the environmental side, enabling the study of complex phenotypes such as feed efficiency, and genotype by environment interactions. It is simple, suitable for use with resource acquisition-allocation models, and can be readily adapted for use in other livestock species. The framework is extensible to add constraints such as predation pressure, reproductive costs, competition, parasitism, or diseases. We believe this framework could provide a useful tool for designing management strategies to optimize productivity and animal welfare in dairy farms under challenging environmental conditions.