So in principle its simple but what i think is hard is to calibrate it because you need to have very good reference values. From here to find the fat mass of the subject by subtracting y from the total mass.

E Health Sensor Platform V2 0 For Arduino And Raspberry Pi
Arduino body fat measurement. Introduction for our final project we have decided to use the microcontroller provided to make a device which would measure body fat percentage of ones body. The basic principle behind this project is known as bioelectrical impedance analysis. We sent an electrical current that is used to measure a difference in impedance between people with different fat compositions. The body fat calculator works measuring the conductivity of the body so it applies a signal an ac voltage and measures the very small for safety current. For our final project we have decided to use the microcontroller provided to make a device which would measure body fat percentage of ones body. The basic principle behind this project is known as bioelectrical impedance analysis.
We were assigned to build a body fat composition circuit using arduino. This project was created by ameen farwana and mikail siddiki for our biomedical instrumentation class at vanderbilt university. This technique uses a small alternating current flowing between two electrodes attached to skin surface to determine impedance. Explore 13 projects tagged with measurement. This technique uses a small alternating current flowing between two electrodes attached to skin surface to determine. Find these and other hardware projects on arduino project hub.
Percent body fat can be found by dividing the fat mass by the total mass and multiplying by 100. The above relationship was found by lukaski et al in their paper assessment of fat free mass using bioelectrical impedance measurements of the human body.