What is the formula for converting milligrams per kilograms to parts per million?

The number of milligrams per kilogram is exactly the same as the number of parts per million. In other words, 1 mg/kg = 1 ppm.

According to Engineering Toolbox, parts per million, or ppm, is a term used to measure a small number of particles in air, water or bodily fluids. For example, a value of 10,000 parts per million refers to 1 percent of the solution, as 10,000 is 1 percent of 1 million. Similarly, 10,000 mg/kg x 1 g/1000 mg x 1 kg/1000 g = .01, showing that 10,000 mg/kg also represents 1 percent of the total solution. There is a one-to-one ratio between the number of parts per million and mg/kg.