Every acre has the same land area, regardless of whether it is hilly, bowl-shaped, or flat like the Great Plains. This consistency comes from long-established land surveying conventions and methods for determining property boundaries. However, there’s a catch: not every measured acre has the same ground surface. For example, you would need a larger quilt to cover an acre in Vermont compared to one in Kansas.
An acre is defined as a two-dimensional measure of land area, not by the size of a quilt needed to cover it. Historically, an acre was the amount of land a team of oxen could plow in one day. It was specifically shaped as a rectangle, with the longer side defined by the distance the oxen could plow before needing a break. This distance, known as a furlong (equivalent to 40 rods or 660 feet), determined the length of the rectangle, while the shorter side was 4 rods (66 feet). Multiplying these dimensions gives an acre an area of 43,560 square feet.
Today, an acre remains fixed at 43,560 square feet. If a one-acre parcel were shaped like a perfect square, each side would measure 208.71 feet. However, an acre can take any shape, as long as the total area equals 43,560 square feet. For instance, if you wanted a rectangular acre with one side a mile long, the other side would need to be just 8.25 feet wide.
Regardless of the parcel’s shape or terrain, surveyors calculate acreage based on a common two-dimensional surface, using basic geometry. While it’s possible to account for the earth’s curvature in land surveying, most boundary surveys for smaller parcels use plane surveying, treating the measured area as a flat horizontal plane.
Thus, land area is measured based on this two-dimensional common surface projected onto the ground. In hilly areas, an acre is measured as if the hill were leveled off horizontally. This means that property boundaries are often measured as horizontal distances rather than the actual ground distance between two points, whether marked by iron rods, stone bounds, or rock piles. In wooded areas, surveyors can either keep the measuring tape horizontal or measure the slope and then apply a correction to convert the slope distance to horizontal.
Since the sloped line along steep terrain is longer than a horizontal line between the same two points, an acre of hilly land does indeed have a greater surface area than an acre of flat land. For instance, an acre with a uniform 15 percent slope would have about 1.12 percent more surface area, requiring a quilt of approximately 44,047.8 square feet. But does this mean that sloped land will support more trees or wood volume because of the increased surface area?
Possibly. If steeper slopes offer more surface area, it seems reasonable that an acre of good forest soil on a moderate slope could support more trees and yield greater production than a similar acre of flat forest. This assumption holds true if tree growth is primarily influenced by surface factors. However, other factors also play a role, as tree growth is often limited by sunlight and precipitation.
A crucial aspect of sloped land is its orientation or aspect, which affects sunlight exposure. This, in turn, impacts air and soil temperature, precipitation, and soil moisture—all important for plant growth. Therefore, while an acre on a hill has more surface area than a flat acre, surface area alone does not determine which acre will have more trees.