Fat-Free Mass Index (FFMI) Calculator

What is the Fat-Free Mass Index (FFMI)?

The Fat-Free Mass Index (FFMI) is a measure of an individual's muscle mass relative to their height, with the impact of body fat removed from the equation. It's an extension of the Body Mass Index (BMI) that takes into account a person's body composition, making it a more accurate indicator of muscularity, especially for athletes and bodybuilders.

The Formula

The formula for calculating FFMI is:

\[FFMI = \frac{LBM}{height^2} \times \sqrt{\frac{height}{170}}\]

Where:

• LBM (Lean Body Mass) = Total body weight - (Total body weight × Body fat percentage)
• Height is in meters

An adjusted FFMI formula is also used to account for the tendency of taller individuals to have higher FFMI values:

\[Adjusted FFMI = FFMI + (6.1 \times (1.8 - height))\]

Where height is in meters.

Calculation Steps

1. Calculate Lean Body Mass (LBM) using total body weight and body fat percentage
2. Convert height to meters if necessary
3. Apply the FFMI formula
4. If desired, calculate the adjusted FFMI

Example Calculation

Let's calculate the FFMI for a person who weighs 80 kg, is 180 cm tall, and has 15% body fat:

1. Calculate LBM:
   \[LBM = 80 - (80 \times 0.15) = 68 kg\]
2. Convert height to meters:
   \[180 cm = 1.8 m\]
3. Calculate FFMI:
   \[FFMI = \frac{68}{1.8^2} \times \sqrt{\frac{1.8}{1.7}} = 21.01\]
4. Calculate Adjusted FFMI:
   \[Adjusted FFMI = 21.01 + (6.1 \times (1.8 - 1.8)) = 21.01\]

Visual Representation

This visual representation shows the calculated FFMI of 21.01 for the example person. The blue area represents the proportion of fat-free mass relative to the total body composition.