Quadratic Mean Diameter

Quadratic Mean Diameter ($D_q$) is the diameter of the tree of average per tree basal area. This becomes a convenient in that we often have basal are per acre and trees per acre but not the diameters of all the trees.

In imperial units:

$$D_q = \sqrt{ \frac{\frac{ba}{tpa}}{0.005454154}}$$

where: $D_q$ is the Quadratic Mean Diameter in inches, $ba$ is the basal area in square feet per acre, $tpa$ is the trees per acre, and 0.005454154 is a constant.

In metric units:

$$D_q = \sqrt{ \frac{\frac{ba}{tpha}}{0.00007854}}$$

where: $D_q$ is the Quadratic Mean Diameter in centimeters, $ba$ is the basal area square meters per hectare, $tpha$ is the trees per hectare, and 0.00007854 is a constant.

Example

Imperial units
ba = 80 ft2/ac
tpa = 200
unittype = "imperial"
Answer = 8.56 in

Metric units
ba = 18.3 m2/ha
tpha = 494.1
unittype = "metric"
Answer = 21.7 cm

Code

Visual Basic

 
Function qmd(ba As Single, tpa As Single, Optional unittype As String = "imperial") As Double
' Function to calculate quadratic mean diameter from basal area per acre and trees per acre
' by David R. Larsen, Copyright October 9, 2012
' Creative Commons http://creativecommons.org/licenses/by-nc/3.0/us/

If (unittype = "imperial") Then
    qmd = Math.Sqr((ba / tpa) / 0.005454154)
ElseIf (unittype = "metric") Then
    qmd = Math.Sqr((ba / tpa) / 0.00007854)
Else
    qmd = 0#
    MsgBox ("Unknown unit type, options are: imperial or metic")
End If

End Function

Excel® Visual Basic Code

R Statistical Package Code

 
qmd = function( ba, tpa, unittype="imperial" )
{
# Function to calculate the quadratic mean diameter from basal area and tree per acre
# by David R. Larsen, Copyright October 9, 2012
# Creative Commons http://creativecommons.org/licenses/by-nc/3.0/us/

   if (unittype == "imperial"){
       qmd = sqrt((ba / tpa) / 0.005454154)
   }else if (unitype == "metric"){
       qmd = sqrt((ba / tpa) / 0.00007854)
   }else{
       qmd = 0
   }
   qmd
}
R Statistical Package Code

Python Code

 
#!/usr/local/bin/python
# Function to calculate the quadratic mean diameter 
# from basal area and tree per acre
# by David R. Larsen, October 11, 2012
# Creative Commons,  http://creativecommons.org/licenses/by-nc/3.0/us/

import math

def qmd( ba, tpa, unittype="imperial"):
    if( unittype == "imperial" ):
       value = math.sqrt( (ba/tpa)/0.005454154 )	
       return value
    elif( unittype == "metric"):
       value = math.sqrt( (ba/tpa)/0.00007854 )
       return value
    else:
       print "Unknown unittype, options are imperial or metric"
       return 

print "qmd =", qmd(80.0, 200.0)
print "qmd =", qmd(80.0, 200.0, "imperial")
print "qmd =", qmd(18.3, 494.1, "metric")
print "qmd =", qmd(1.0, 1.0, "cunits")
Python Code

Note the python file has a extra "txt" at the end to allow the files to be viewed in a web browser.

Go Code

 
// Function to calculate the quadratic mean diameter 
// from basal area and tree per acre
// by David R. Larsen, August 15, 2013
// Creative Commons,  http://creativecommons.org/licenses/by-nc/3.0/us/
package main

import (
	"fmt"
	"math"
)

// Function to calculate a quadratic mean 
func Qmd( ba float64, tpa float64, unittype string) float64 {
	if unittype == "imperial" {
		return math.Sqrt( (ba/tpa)/0.005454154 )
	}else if unittype == "metric" {
		return math.Sqrt( (ba/tpa)/0.00007854 )
	}
	return 0.0
}

func main() {
	fmt.Println("qmd =", Qmd(80.0, 200.0, "imperial") )
	fmt.Println("qmd =", Qmd(18.3, 494.1, "metric") )
	fmt.Println("qmd =", Qmd(80.0, 200.0, "cunits") )
}	
Run code in the Go Playground
Go Code

Note the go file has a extra "txt" at the end to allow the files to be viewed in a web browser.


Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

Author: Dr. David R. Larsen, Copyright 2012
Created: October 9, 2012
Last Updated: June 23, 2015