Does an Acre of Hilly Land Contain More Land Than an Acre of Flat Land?

Does an Acre of Hilly Land Contain More Land Than an Acre of Flat Land?

Every acre contains the same measure of land regardless of whether it is steep, bowl-shaped, or the Great Plains. This is due to long-standing conventions of land surveying and accepted procedures for determining ownership boundaries. There is definitely a catch, however, in that not every measured acre contains the same amount of ground surface. In other words, you’d need a bigger quilt to cover an acre of Vermont than you’d need to cover an acre of Kansas.

But they don’t measure an acre by measuring the size of the quilt needed to cover it. An acre is a two-dimensional measure of land area. Originally, it was the amount of land that could be plowed by a team of oxen in a day. In fact, the acre had specific dimensions because of this. It was a rectangle, whose length was determined by the distance the oxen could plow before needing a rest. This furrow-long distance became the furlong, which was equal to 40 King’s rods (660 feet to commoners like us). That determined the long side of the rectangle, and the short side of this one-acre rectangle was 4 rods (66 feet). Multiply these to get 43,560 square feet of area.

Still today, an acre is fixed at 43,560 square feet. If a particular one-acre parcel happens to be in the shape of a perfect square, its sides would be 208.71 feet each. But an acre need not be square. It is fixed at 43,560 square feet but has no specific length, width, or shape. The number and length of its sides can be anything, just so long as the total area they bound equals 43,560 square feet. If you wanted to create a one-acre rectangular parcel of land with one side a mile long, then it would be 8.25 feet wide.

Whatever the shape of a parcel – or the topography of the land it contains – surveyors calculate its acreage based on a common surface, using basic geometry (whose Greek root words mean earth measure). And while it is possible to account for the curvature of the earth in land surveying, most boundary surveys for parcels less than a few hundred square miles use plane surveying. That is, the portion of the earth being measured is considered a horizontal plane.

By convention, then, land area is measured on a two-dimensional common surface plane projected onto the ground. So even in hilly terrain, the acre is measured as if the hill were cut off at the horizontal, parallel to the horizon. In practice, this means that property boundary lines are not measured as the true ground distance between two points on the ground, be they iron rods, stone bounds, or rock piles. Instead, boundary lines are typically measured as the horizontal distance between those two points. In the woods, if you measure distance along the sloped surface, you can either hold the tape horizontal at all times when recording distances or measure the slope distance and angle and then later apply a correction to reduce this slope distance to the horizontal distance.

Because the sloped line that runs along steep ground is longer than a horizontal line above the ground between the same two points, an acre of hilly land does have greater surface area than would an acre of flat land. For instance, a hypothetical acre that had a uniform 15 percent slope would have approximately 1.12 percent more surface area and would require a quilt that measured 44,047.8 square feet. Does this mean that the sloped land will have more trees or wood volume per acre, because it has more surface, and trees grow on the surface?

Maybe. If greater slopes have greater surface area per acre, it stands to reason that an acre of decent forest soil on a moderate slope would contain more trees and produce greater yields per acre than a similar acre of flat forest. This would make even more sense if tree establishment and growth were driven only by surface-related factors. But other factors are also at work, and tree growth is driven – and often limited – by sunlight and precipitation. 

Perhaps the more important feature of sloping land is the direction it faces – its aspect or orientation – because that influences the amount of sunlight the acre receives. This, in turn, indirectly governs other related factors such as air and soil temperature, precipitation, and soil moisture – all of which are important for the establishment and growth of plants. So as land is measured, an acre on a hill would be the same size as, but would have more surface area than, a flat acre. But surface area alone does not determine which acre would have more trees.

Michael Snyder is the Chittenden (Vermont) County Forester.

 
Discussion
  1. roman → in austin
    Apr 24, 2011

    so if your given 50 acres alongside a montain side you would take the measurement from the arial view, not the actual walked off square footage alongside the slope?

  2. Herb Helbig → in Damariscotta, ME
    May 27, 2011

    Thank you for that clear explanation.  What raised this question in my mind was discovering Pick’s theorem which, since acreage is measured as the projection on a plane, should allow a simple way to make excellent approximations of the acreage of parcels with irregular boundaries.

  3. Jac Knust
    Jan 19, 2012

    So if I have a survey plat showing courses and distances that depict a measurement of a sloped hill and I want to locate the courses and distances on the earth’s surface of the the sloped hill, I would run my surveyor’s tape from the top of the hill to the bottom of the hill and reduce the actual distance measured as required by the angle of the hill. Right?

  4. Phonia → in Jamaica
    Jan 07, 2013

    This was very helpful to me as I am buying a land that is sloped and I was wondering if, when I level it down, I would end up with less surface area, because I did not understand how land was measured. This now clarifies that it is not measures by the distant surface.

  5. Seymour Blackman → in Antigua and Barbuda
    Apr 11, 2013

    This article confirmed my thoughts on the matter but I just needed some confirmation of the issue.

    Regarding the amount of trees you could plant on a sloped area, just a thought, trees grow vertically and the spacing of the trees would be adjusted to maintain the same horizontal spacing as they would need on flat land.

  6. Mark Hari → in New Jersey
    Apr 22, 2013

    Thank you for the excellent explanation.  So just to confirm what I have thought, if you have a 5 acre plot with a slope that starts at sea level on one side and rises 200 foot at the other side your property line would not be based on a tape measure following the slope.  It would measured as if you projected the sea level end up 200 feet and measured between a 200 foot elevated starting point and the 200 foot back property actual height, correct?

    Thank you.

  7. Carolyn Pruitt → in Knoxville Tn
    Jul 31, 2013

    If you have livestock on a grassy hilly acre of land you will have more grassy area for them to feed on then you would on a flat acre of land, simply because they can feed up and down the hills that are on the property event though by sight line it is only an acre.

  8. Warren Oldham → in Atlanta, GA
    Sep 09, 2013

    This is an interesting topic. If you wanted to cover this hill and know the degree of slope, is there a conversion formula to convert from footprint (2 dimensional) to the actual surface area to be covered?

  9. John Cargile → in Mevada City, CA
    Feb 02, 2014

    Thank you for this article. I measured my property by my slope before I found your article. Then I started looking for an article like yours where I discovered the answer I was seeking matched my long time thinking. For years I have commented to others that they had more square feet of land that the acres described on their deed because their land was also sloped. I went from 5.09 acres to 5.83 acres using the land mass. Actually the county register says I have only 4.79 but that does not compute with the measurements on the map?

  10. Rolfe Jaremus → in IL
    Aug 22, 2016

    So I wonder how countries or states compare when we consider surface area?  For example, Colorado is ranked 8th in size.  But with all of it’s mountains, maybe in surface area it’s ranked 3rd?

  11. Ryan B → in WA
    Jan 23, 2017

    Great article. It make’s complete sense. Can’t believe I didn’t piece it together. My measurements kept being way off from what our township map showed which made it difficult finding my property corners on a steep sloped forest.
    By using Pythagorean A*2+B*2=C*2 the measurements came out correct. And Rise/Run for slope. The distance on the map squared + the rise in elevation squared = the actual measured distance by hand squared. Just need distance numbers and elevation which most phones nowadays can give you a decent estimate. I tried it on my own property and it worked within a couple feet.

  12. Ed Circusitch → in Souderton, Pa
    Sep 03, 2017

    Informative and amusing. I shall now seek out a cliff that would have a surface area of 1/4 of an acre but have an acreage footprint of maybe 1/20 of an acre. It would a great place to grow my lichen and moss crops.

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