   SEARCH HOME Math Central Quandaries & Queries  Question from Debbie: Please tell me how to calculate the amount of dirt stripped 5 feet deep over a 50 acre site. How do you calculate the amount of dirt in an acre and then excavating it a certain depth. How does one calculate the amount of dirt excavated and moved and how to price to charge for the service? We have two responses for you

Hi Debbie.

We need to know the volume of dirt. Volume is depth times area, but we have to be using compatible units. Since your area measurement is in acres and your depth is in feet, let's convert the area measurement to square feet first:

1 acre is equal to 43560 square feet. So 50 acres is 50 times this. That makes 2178000 square feet.

When we multiply this out and find the volume, we get 5 feet deep x 2178000 square feet in area = 10890000 cubic feet.

Most of the time, dirt quantities are measured in cubic yards.

Since 1 cubic yard = (1 yard)3 and 1 yard = 3 feet, that means 1 cubic yard = (3 feet)3 = 33 feet3 = 27 cubic feet.

So divide this into the amount of dirt:
10 890 000 cubic feet / (27 cubic feet per cubic yard) = 40 333 cubic yards.

That's how much dirt you would be excavating and moving. You will have to determine how much effort goes into the job in order to determine an appropriate price.

For comparison, I took a look at photos and descriptions of the Louisiana State Legislature Capitol Building and estimated that the main tower is 450 feet high and 100 feet wide and deep, with the top 12 floors roughly in the shape of a pyramid. This makes an estimated 3.4 million cubic feet.

So your dirt is approximately the same volume as 3 Capitol towers.

Cheers,
Stephen La Rocque

Hi Debbie,

According to Wikipedia, acre is 43,560 square feet. So, if you dig 1 foot deep over an acre, you get 43,560 cubic feet of dirt. If you dig 5 feet deep, then you have 5 times this amount of dirt. If you dig 5 feet of dirt out of 50 acres, then you have 50 times as much dirt as if you did that over 1 acre.

To price the service, it depends if you paying someone else or if you are charging (or just calculating how much it will cost to do it yourself). In the first case, you can ask for a quote based on the volume of dirt in cubic feet (or cubic yards or cubic metres) that needs to be moved. If you are moving he dirt, it depends on how much dirt will fit in the truck / trailer, how much in gas it costs to operate the truck for as long as necessary, whether you have to pay the driver, plus an amount for wear and tear on the vehicles. And there are probably other costs that you can think of that I don't know about. For example, there might be a tipping fee for dropping the dirt off at its destination.

Hope this helps.

Victoria     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.