A gear ratio is a numerical representation of the relationship between two gears in a mechanical system. It is calculated by dividing the number of teeth on one gear by the number of teeth on another gear. This ratio determines how many times one gear will turn in relation to the other, affecting speed and torque in machines like bicycles and cars. For example, if a bicycle has a gear ratio of 2:1, the front gear turns twice for every single turn of the rear gear. Higher gear ratios provide more speed but less torque, while lower ratios offer more torque but less speed, allowing for better control in various situations.