Well the 'easy' way to age a tree is to count the tree rings after you cut it down, but you may want to know the age without losing the tree. Instead you can take a core sample of a tree, which is much like coring an apple. This lets you view the tree rings without cutting the whole tree down, but can still damage the tree and invite disease if not sealed properly.
Another way, age the tree by measuring the diameter of the tree and using a growth factor to estimate how long your tree has stood there. The International Society of Arboriculture developed growth factors for numerous trees provided below:
A few quick steps and some math will give you an answer. Measure the trees circumference with a flexible measuring tape, take the circumference and divide by 3.14159 (pi) to obtain the diameter. Subtract from your diameter if your tree has thick bark to get a final diameter, then multiply for the growth factor found in the table above and you have your estimated age!
In our case we measured a black walnut, and ended up with a circumference of 46 inches. 46 divided by 3.14159, equals 14.64. We took off 2 inches as our Walnut had thick and dense bark for a final diameter of 12.64. Multiple 12.64 times the 4.5 growth factor to get just under 57 years old! How cool is that?!
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