Trees have different growth rates, depending on their species. A shagbark hickory with a 10 inch diameter and competing with other forest-grown trees can easily be 75 years old while a neighboring red oak with the same diameter would only be approximately 40 years old. Trees, by species, are genetically coded to grow at about the same rate under similar conditions.
A formula was previously developed and used by the International Society of Arboriculture to predict and determine a tree's age. Running the calculations and comparing them to a species growth factor is regionally and species specific. ISA says "Tree growth rates are affected tremendously by conditions such as water availability, climate, soil conditions, root stress, competition for light, and overall plant vigor. Further, growth rates of species within genera can vary significantly." Only use this data as a very rough estimate.
The Tree Aging Formula
Begin by determining the tree species and taking a diameter measurement (or circumference measurement) using a tape measure at Diameter Breast Height or 4.5 feet above stump level. If you are using circumference, you will need to make this calculation to determine the tree diameter: Diameter = Circumference divided by 3.14 (pi)
Then calculate the age of the tree by multiplying the tree's diameter by its growth factor (see below): Diameter X Growth Factor = Approximate Tree Age. Let's use the hickory above to calculate age. A shagbark hickory's growth factor has been determined to be 7.5 and its diameter is 10 inches: 10 inch diameter X 7.5 growth factor = 75 years. Remember that the growth factors I provide are more accurate when taken for forest grown trees.
Growth Factors by Tree Species
Red Maple Species - 4.5 Growth Factor X diameter
Silver Maple Species - 3.0 Growth Factor X diameter
Sugar Maple Species - 5.0 Growth Factor X diameter
River Birch Species - 3.5 Growth Factor X diameter
White Birch Species - 5.0 Growth Factor X diameter
Shagbark Hickory Species - 7.5 Growth Factor X diameter
Green Ash Species - 4.0 Growth Factor X diameter
Black Walnut Species - 4.5 Growth Factor X diameter
Black Cherry Species - 5.0 Growth Factor X diameter
Red Oak Species - 4.0 Growth Factor X diameter
White Oak Species - 5.0 Growth Factor X diameter
Pin Oak Species - 3.0 Growth Factor X diameter
Basswood Species - 3.0 Growth Factor X diameter
American Elm Species - 4.0 Growth Factor X diameter
Ironwood Species - 7.0 Growth Factor X diameter
Cottonwood Species - 2.0 Growth Factor X diameter
Redbud Species - 7.0 Growth Factor
Dogwood Species - 7.0 Growth Factor X diameter
Aspen Species - 2.0 Growth Factor X diameter
Using a Rule of Thumb When Aging Street and Landscape Trees
Because trees in a landscape or park are often pampered, protected and sometimes older than forest grown trees, it is more of an art to aging these trees without significant error. There are foresters and arborists with enough tree core and stump evaluations under their belts who can age a tree with significant accuracy.
It is still impossible to do anything but estimate a tree age under these conditions. I would suggest in younger trees in the landscape, you pick a genus or species from above and slightly reduce the Growth Rate Factor. For old to ancient trees I would significantly increase the Growth Rate Factor.