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FFMI worksheet

Grades 6–7 · CCSS 6.RP.A.3.c, 6.EE.A.2.c

Solve each problem and show your work. Round answers to 2 decimal places where needed.

  1. Problem 1.
    • Units: Metric (cm, kg)
    • Height: 180 cm
    • Weight: 85 kg
    • Body fat: 21%

    Find: Fat-free mass index (FFMI)

  2. Problem 2.
    • Units: US (ft, in, lb)
    • Height (feet): 4 ft
    • Height (inches): 10 in
    • Weight: 150 lb
    • Body fat: 16%

    Find: Fat-free mass index (FFMI)

  3. Problem 3.
    • Units: Metric (cm, kg)
    • Height: 180 cm
    • Weight: 100 kg
    • Body fat: 15%

    Find: Fat-free mass index (FFMI)

  4. Problem 4.
    • Units: Metric (cm, kg)
    • Height: 146 cm
    • Weight: 90 kg
    • Body fat: 18%

    Find: Fat-free mass index (FFMI)

  5. Problem 5.
    • Units: Metric (cm, kg)
    • Height: 250 cm
    • Weight: 70 kg
    • Body fat: 20%

    Find: Fat-free mass index (FFMI)

  6. Problem 6.
    • Units: Metric (cm, kg)
    • Height: 200 cm
    • Weight: 85 kg
    • Body fat: 18%

    Find: Fat-free mass index (FFMI)

  7. Problem 7.
    • Units: Metric (cm, kg)
    • Height: 190 cm
    • Weight: 78 kg
    • Body fat: 18%

    Find: Fat-free mass index (FFMI)

  8. Problem 8.
    • Units: US (ft, in, lb)
    • Height (feet): 3 ft
    • Height (inches): 9 in
    • Weight: 160 lb
    • Body fat: 20%

    Find: Fat-free mass index (FFMI)

  9. Problem 9.
    • Units: US (ft, in, lb)
    • Height (feet): 6 ft
    • Height (inches): 9 in
    • Weight: 155 lb
    • Body fat: 16%

    Find: Fat-free mass index (FFMI)

  10. Problem 10.
    • Units: US (ft, in, lb)
    • Height (feet): 7 ft
    • Height (inches): 8 in
    • Weight: 230 lb
    • Body fat: 12%

    Find: Fat-free mass index (FFMI)

Answer key: FFMI worksheet

  1. 1. Fat-free mass index (FFMI): 20.7 kg/m²

    1. Take the fat out of your weight to find your fat-free mass: muscle, bone, organs and water

      85 kg×(1−21%100)=67.15 kg
    2. Change your height to meters, the unit the index uses

      180 cm100=1.8 m
    3. Divide your fat-free mass by your height times itself, so people of different heights can be compared

      67.151.82=20.73 kg/m²
    4. Adjust to a set height of 1.8 m: add 6.1 for every meter you are shorter, or take it off if taller

      20.725+6.1×(1.8−1.8)=20.73 kg/m²
  2. 2. Fat-free mass index (FFMI): 26.3 kg/m²

    1. Change your height to centimeters, because the formula uses metric units (1 in is exactly 2.54 cm)

      (4×12+10)×2.54=147.32 cm
    2. Change your weight to kilograms (1 lb is exactly 0.45359237 kg)

      150 lb×0.453592=68.039 kg
    3. Take the fat out of your weight to find your fat-free mass: muscle, bone, organs and water

      68.039 kg×(1−16%100)=57.153 kg
    4. Change your height to meters, the unit the index uses

      147.32 cm100=1.4732 m
    5. Divide your fat-free mass by your height times itself, so people of different heights can be compared

      57.1531.47322=26.33 kg/m²
    6. Adjust to a set height of 1.8 m: add 6.1 for every meter you are shorter, or take it off if taller

      26.334+6.1×(1.8−1.4732)=28.33 kg/m²
  3. 3. Fat-free mass index (FFMI): 26.2 kg/m²

    1. Take the fat out of your weight to find your fat-free mass: muscle, bone, organs and water

      100 kg×(1−15%100)=85 kg
    2. Change your height to meters, the unit the index uses

      180 cm100=1.8 m
    3. Divide your fat-free mass by your height times itself, so people of different heights can be compared

      851.82=26.23 kg/m²
    4. Adjust to a set height of 1.8 m: add 6.1 for every meter you are shorter, or take it off if taller

      26.235+6.1×(1.8−1.8)=26.23 kg/m²
  4. 4. Fat-free mass index (FFMI): 34.6 kg/m²

    1. Take the fat out of your weight to find your fat-free mass: muscle, bone, organs and water

      90 kg×(1−18%100)=73.8 kg
    2. Change your height to meters, the unit the index uses

      146 cm100=1.46 m
    3. Divide your fat-free mass by your height times itself, so people of different heights can be compared

      73.81.462=34.62 kg/m²
    4. Adjust to a set height of 1.8 m: add 6.1 for every meter you are shorter, or take it off if taller

      34.622+6.1×(1.8−1.46)=36.7 kg/m²
  5. 5. Fat-free mass index (FFMI): 9 kg/m²

    1. Take the fat out of your weight to find your fat-free mass: muscle, bone, organs and water

      70 kg×(1−20%100)=56 kg
    2. Change your height to meters, the unit the index uses

      250 cm100=2.5 m
    3. Divide your fat-free mass by your height times itself, so people of different heights can be compared

      562.52=8.96 kg/m²
    4. Adjust to a set height of 1.8 m: add 6.1 for every meter you are shorter, or take it off if taller

      8.96+6.1×(1.8−2.5)=4.69 kg/m²
  6. 6. Fat-free mass index (FFMI): 17.4 kg/m²

    1. Take the fat out of your weight to find your fat-free mass: muscle, bone, organs and water

      85 kg×(1−18%100)=69.7 kg
    2. Change your height to meters, the unit the index uses

      200 cm100=2 m
    3. Divide your fat-free mass by your height times itself, so people of different heights can be compared

      69.722=17.43 kg/m²
    4. Adjust to a set height of 1.8 m: add 6.1 for every meter you are shorter, or take it off if taller

      17.425+6.1×(1.8−2)=16.21 kg/m²
  7. 7. Fat-free mass index (FFMI): 17.7 kg/m²

    1. Take the fat out of your weight to find your fat-free mass: muscle, bone, organs and water

      78 kg×(1−18%100)=63.96 kg
    2. Change your height to meters, the unit the index uses

      190 cm100=1.9 m
    3. Divide your fat-free mass by your height times itself, so people of different heights can be compared

      63.961.92=17.72 kg/m²
    4. Adjust to a set height of 1.8 m: add 6.1 for every meter you are shorter, or take it off if taller

      17.717+6.1×(1.8−1.9)=17.11 kg/m²
  8. 8. Fat-free mass index (FFMI): 44.4 kg/m²

    1. Change your height to centimeters, because the formula uses metric units (1 in is exactly 2.54 cm)

      (3×12+9)×2.54=114.3 cm
    2. Change your weight to kilograms (1 lb is exactly 0.45359237 kg)

      160 lb×0.453592=72.575 kg
    3. Take the fat out of your weight to find your fat-free mass: muscle, bone, organs and water

      72.575 kg×(1−20%100)=58.06 kg
    4. Change your height to meters, the unit the index uses

      114.3 cm100=1.143 m
    5. Divide your fat-free mass by your height times itself, so people of different heights can be compared

      58.061.1432=44.44 kg/m²
    6. Adjust to a set height of 1.8 m: add 6.1 for every meter you are shorter, or take it off if taller

      44.441+6.1×(1.8−1.143)=48.45 kg/m²
  9. 9. Fat-free mass index (FFMI): 14 kg/m²

    1. Change your height to centimeters, because the formula uses metric units (1 in is exactly 2.54 cm)

      (6×12+9)×2.54=205.74 cm
    2. Change your weight to kilograms (1 lb is exactly 0.45359237 kg)

      155 lb×0.453592=70.307 kg
    3. Take the fat out of your weight to find your fat-free mass: muscle, bone, organs and water

      70.307 kg×(1−16%100)=59.058 kg
    4. Change your height to meters, the unit the index uses

      205.74 cm100=2.0574 m
    5. Divide your fat-free mass by your height times itself, so people of different heights can be compared

      59.0582.05742=13.95 kg/m²
    6. Adjust to a set height of 1.8 m: add 6.1 for every meter you are shorter, or take it off if taller

      13.952+6.1×(1.8−2.0574)=12.38 kg/m²
  10. 10. Fat-free mass index (FFMI): 16.8 kg/m²

    1. Change your height to centimeters, because the formula uses metric units (1 in is exactly 2.54 cm)

      (7×12+8)×2.54=233.68 cm
    2. Change your weight to kilograms (1 lb is exactly 0.45359237 kg)

      230 lb×0.453592=104.326 kg
    3. Take the fat out of your weight to find your fat-free mass: muscle, bone, organs and water

      104.326 kg×(1−12%100)=91.807 kg
    4. Change your height to meters, the unit the index uses

      233.68 cm100=2.3368 m
    5. Divide your fat-free mass by your height times itself, so people of different heights can be compared

      91.8072.33682=16.81 kg/m²
    6. Adjust to a set height of 1.8 m: add 6.1 for every meter you are shorter, or take it off if taller

      16.813+6.1×(1.8−2.3368)=13.54 kg/m²