The proposed harvest methods by the U.S. Forest Service (USFS) often mention basal area. For example, here is a sentence from the USFS description of clearcut:

At least 15 basal area per acre (BA) is retained in any scoured ephemeral stream zones.

The diameter of a tree at 4.5 feet above the ground is called *diameter at breast height *(DBH). The *basal area* of a tree is its cross-sectional area at 4.5 feet above the ground.

Imagine if you cut down a tree, leaving a flat top stump 4½ feet tall. DPH is the diameter of the stump top, and BA is the area of its flat top. In mathematical terms:

BA (square feet) = (π / (4 * 144)) * DBH

^{2}=0.005454 * DBH^{2}Where π = 3.14159, DBH = diameter breast height in inches

The number 0.005454 is called the

foresters constant, which converts the measured inches into square feet.

Here are some examples of basal area for trees of different diameters:

DBH (inches) | BA (square feet) |

1 | 0.005 |

6 | 0.196 |

10 | 0.545 |

12 | 0.785 |

14 | 1.069 |

16 | 1.396 |

20 | 2.182 |

24 | 3.142 |

30 | 4.909 |

*Trees per acre *(TPA) is a common measure to describe tree density in young forests. However, as trees mature into different sizes, TPA becomes less meaningful, especially when estimating timber volumes.

Basal area is a much better measure of overall timber density, volume, and growth, and thus is the preferred measure for evaluating forest management decisions. To calculate *basal area per acre* in a forest stand, add up the basal area for all the trees in that stand, and divide by the number of acres.

Here are some examples of the number of trees of different diameters (DPH) that would remain standing per acre for various BA values:

DPH | BA10 | BA15 | BA20 | BA40 | BA50 | BA70 |

1″ | 1,834 | 2,751 | 3,667 | 7,334 | 9,168 | 12,835 |

6″ | 51 | 77 | 102 | 204 | 255 | 357 |

10″ | 18 | 27 | 37 | 73 | 92 | 128 |

12″ | 13 | 20 | 25 | 51 | 64 | 89 |

14″ | 9 | 14 | 19 | 37 | 47 | 65 |

16″ | 7 | 11 | 14 | 29 | 36 | 50 |

20″ | 5 | 8 | 9 | 18 | 23 | 32 |

24″ | 3 | 5 | 6 | 13 | 16 | 22 |

30″ | 2 | 3 | 4 | 8 | 10 | 14 |

For example, in the USFS description of clearcut, BA15 will be retained near streams. Based on the table above, that’s 20 trees of 12″ DPH, or 5 trees of 24″ DPH left standing per acre.

Reference: A&M and Auburn Universities