The volume of water sitting in a well is one of those figures that seems like it should be printed on the well log and almost never is. You need it to work out how long to purge before taking a sample, how much water a shock chlorination will have to reach, and how long a pump will run before the standing column is gone. This well volume calculator derives it from two measurements that are easy to take: the inside diameter of the casing and the depth from the top of the casing to the water surface.
Arb Digital kept the scope narrow on purpose. The page computes volume, purge volumes and pumping time and stops there. It publishes no chemical doses, no yield estimates and no water quality guidance, because those are decisions with real consequences that depend on a specific well, a specific aquifer and a specific test result. The arithmetic is the part a web page can do properly.
What This Calculator Does
It treats the water in the casing as a vertical cylinder. From the inside diameter it works out the volume held per foot or per metre of depth, and from the total depth minus the depth to water it works out how long that water column is. Multiplying the two gives the standing volume. It then multiplies by the number of casing volumes you specify and divides by your pump rate to give a pumping time.
It also lets you enter an expected drawdown, which is how far the water level falls while the pump is running. That reduces the standing column, and the tool reports the smaller volume at the pumping level alongside the static one, because purging plans made from the static figure alone can be optimistic.
This is a different job from the other volume tools on the site. The cylinder volume calculator handles the pure geometry, the pipe volume calculator works along a horizontal run, and the tank volume calculator handles capsule and cone-bottomed shapes. What is specific here is the depth-to-water measurement and the purge-volume convention that goes with it.
How to Use It
- Get the inside diameter, not the nominal size. Volume scales with the square of the bore, so a half-inch error on a 6-inch casing shifts the answer by about 17 per cent.
- Take the depth to water with the pump off and rested long enough for the level to recover, measuring from the top of the casing with a tape or a water level meter.
- Use the total drilled depth from the well log where you have one. If the log gives a cased depth and an open-hole depth below it, be clear which you are entering.
- Set the number of casing volumes to whatever your sampling protocol or contractor specified. Three is a figure that appears in many protocols, but it is theirs to set, not this page’s.
- Enter a realistic pump rate, measured with a bucket and a stopwatch if you have not got a meter, and read the pumping time as an order of magnitude rather than a schedule.
The Formula
The water column is a cylinder, so its volume is the cross-sectional area multiplied by the length: V = π ÷ 4 × d² × L. What makes it convenient is that the per-unit-depth figure can be precomputed for a given casing size.
In US customary units, a casing of inside diameter d inches holds πd²/4 square inches of area, and one foot of depth is 12 inches, so a foot of casing holds 12πd²/4 cubic inches. A US gallon is exactly 231 cubic inches, so gallons per foot = 3πd² ÷ 231 = 0.04080 × d². For a 6-inch casing that gives 0.04080 × 36 = 1.469 gallons per foot, which is the figure that appears rounded to 1.47 in well-owner literature.
In metric, a casing of inside diameter d metres holds πd²/4 cubic metres per metre of depth, and one cubic metre is 1,000 litres, so litres per metre = 250π × d² with d in metres. A 150 mm casing gives 250π × 0.15² = 17.67 litres per metre.
Worked example on the defaults. A 6-inch casing, 200 feet deep, with water standing 60 feet down, has a water column of 200 − 60 = 140 feet. At 1.4688 gallons per foot that is 140 × 1.4688 = 205.6 US gallons. Three casing volumes is 3 × 205.6 = 616.9 gallons, and at 8 gallons per minute that takes 616.9 ÷ 8 = 77.1 minutes, or a little over an hour and a quarter of continuous pumping.
Why the Casing Volume Is Not the Water in the Ground
This is the most common misreading of the number, and it matters. The volume computed here is the water standing inside the casing at the moment you measured. It is not the well’s capacity, it is not a reserve, and it is not how much water you can take before running dry.
A well in a productive aquifer refills as you pump, so you can draw many times the standing volume in an afternoon. A well in a poor formation may not refill fast enough to sustain the pump, and the standing volume is then the only buffer you have before the pump breaks suction. Which of those you have is a question of yield and recovery rate, established by a proper pumping test, and nothing about the geometry of the casing predicts it. The NGWA-supported well owner guidance on well construction is the place to start if you want to understand how the parts of a well relate to what the aquifer will do.
Nor does the casing volume account for water in the open borehole below the casing, or in a gravel pack around it, or in a screened section. Where a well is cased only through the upper formation and open below, the actual standing water is larger than this calculation, and where the bore is packed with gravel the void fraction of that pack holds water too. If your purge volume has to reflect all of that, the well log and the contractor who drilled it are the source, not a general formula.
What Purging Is Actually For
Water that has sat in a casing between the top of the water column and the screen is not representative of the aquifer. It has been in contact with the casing material, it may have exchanged gases with the air above it, and its chemistry drifts. Sampling protocols therefore require a fixed number of casing volumes to be removed first, so that what reaches the bottle has come from the formation rather than from the pipe.
The specific number varies with the protocol. Some methods purge a set number of volumes; others purge until field parameters such as temperature, pH and conductivity stabilise, which can be more or less than a fixed multiple. Low-flow sampling deliberately purges very little, on the argument that a slow draw at the screen never mobilises the stagnant column at all. The tool takes the multiple as your input because the choice is made by the method you are following, not by arithmetic.
Whatever the volume, where the purge water goes is a separate question with its own rules, particularly if the well is being investigated for contamination. In the United States, private wells fall outside the federal drinking water regulations and the owner carries responsibility for their own supply; the EPA guidance for private drinking water wells sets out what that responsibility involves and points to testing resources.
Arb Digital builds free tools that show the formula, name the convention and refuse the parts that need a professional. Browse the library, or tell us what your audience keeps getting wrong.
Browse Free Tools Talk To Arb DigitalCommon Mistakes to Avoid
- Using the nominal casing size as the bore. Volume goes with the square of the diameter, so a small error in the diameter becomes a large error in the volume.
- Measuring depth to water with the pump running. The level is drawn down while pumping and recovers afterwards. A static measurement needs the pump off and time for the level to settle.
- Treating standing volume as available water. It is the water in the pipe at one instant, not the well’s yield. A good well refills as you draw; a poor one does not, and only a pumping test tells you which you have.
- Forgetting the open hole below the casing. Where a well is cased only to a certain depth, the water below that is not in this calculation at all.
- Assuming a pump rate instead of measuring it. Pump output falls as head increases and as the pump ages, so a nameplate figure and the real flow at your tap can be a long way apart.
Related Free Tools From Arb Digital
For the pure geometry, the cylinder volume calculator handles any cylinder and the tank volume calculator covers capsule and cone-bottomed shapes with a partial fill. Horizontal runs belong in the pipe volume calculator, and swimming pools in the pool volume calculator. Convert between gallons, litres and cubic metres in the volume converter. On the household side, the water usage calculator estimates daily demand and the water hardness calculator works with a test result you already have. The full set is in the free online tools hub.
Frequently Asked Questions
It depends entirely on the casing bore and how long the water column is. For a casing of inside diameter d inches the figure is 0.0408 times d squared gallons per foot, so a 6-inch casing holds about 1.47 gallons per foot and a 4-inch casing about 0.65. Multiply by the depth of water standing in the casing.
With the pump off and the level rested, lower a water level meter or a weighted tape from the top of the casing until it reaches the water surface, and read the depth there. Measuring while the pump runs gives the pumping level rather than the static level, and the two can differ by many feet.
No, and confusing the two is the most common error with this number. Standing volume is the water in the pipe at one moment. What a well can supply depends on the aquifer’s yield and the recovery rate, which are established by a pumping test and have nothing to do with the geometry of the casing.
Because water standing in a casing is not representative of the aquifer: it has been in contact with the casing and with the air above it and its chemistry drifts. Removing several casing volumes replaces it with formation water. The exact multiple is set by the protocol being followed, and some methods purge to stable field parameters instead of a fixed count.
No. It measures the cylinder of water inside the casing only. Where a well is cased through the upper formation and left as open hole below, or where a gravel pack surrounds a screen, there is additional water the formula does not see, and the well log is the source for that.
The inside diameter, always. Nominal sizes are naming conventions rather than measurements, and the real bore depends on the casing material and wall thickness. Because volume goes with the square of the diameter, the error from using a nominal figure roughly doubles.
The volume figure is an input to that calculation, but this page deliberately publishes no doses. Disinfection quantities, contact times and the steps for handling a well afterwards are set by a health authority, a laboratory or a licensed well contractor, and getting them wrong has real consequences for both the water and the equipment.
Drawdown is the fall in water level once the pump runs, and it shortens the water column, so the volume standing in the casing while pumping is smaller than the static figure. Enter your expected drawdown and the tool reports both, which matters when a purge plan was built from the static number alone.
This page performs a geometric calculation only. It is not a hydrogeological assessment, a water quality assessment or a disinfection instruction, and no output from it says anything about whether a well is safe, productive or fit to drink. Well yield, water testing, disinfection and any work on the well itself belong with a licensed water well contractor, an accredited laboratory and your local health or environmental authority.
