How to Convert Cubic Meters to Square Feet

A cubic meter is the unit of volume defined in the International System of Units (SI). A square foot is the unit of area used in United State and some other countries. Apparently the direct conversion between volume and area is not possible until you add the third dimension to the unit of area. Consider the following example. Calculate the area (in square feet) that can be covered with 15 cubic meters of soil if the soil layer should be 1 inch thick.

Difficulty: Moderately Challenging

Instructions

Things You'll Need:

• Calculator

1. Calculate the conversion coefficient between a foot and a meter using the definition by U.S. National Bureau of Standards (see reference).
   1 foot = 1200/3937 meter = 0.3048 meter.
   Feet= meters/ 0.3048.

2. Obtain the formula to convert cubic meters to cubic feet.
   Cubic feet=Cubic meters/ (0.3048x0.3048x0.3048)= Cubic meters/0.028316846592= 35.3147 x Cubic meters.

3. Obtain the relationship between cubic and square feet.
   cubic feet=square feet x height
   square feet= cubic feet/height.
   Height is the third dimension that allows the conversion between cubic and square units and needs to be measured in feet. In our example, height is the thickness of a soil layer.

4. Obtain the formula to convert cubic meters to square feet by combining equations in Steps 3 and 2:
   Square feet= (35.3147 x cubic meters)/height.
   
   In our example, height=1 inch =1/12 feet as 1 foot =12 inches.
   Area=(35.3147 x 15 cubic meters)/(1/12 feet)= 6356.646 Square feet.

References

• "Refinement of values for the yard and the pound," A.V. Astin & H.A. Karo, National Bureau of Standards, Washington DC, Jun. 30, 1959.