How a center pivot applies water
A center pivot puts down water as it rotates, so the depth at any point in the field depends on how long the machine dwells there. Slow the pivot down and each point spends longer under the sprinklers, so the depth per pass goes up; speed it up and the depth per pass goes down. USDA NRCS irrigation engineering guides and university extension publications tie flow rate, acreage, and time together with one design formula so you can move between them.
That formula, from the USDA NRCS Field Office Technical Guide's center-pivot chapter and repeated in university extension sprinkler-selection guides, is:
Center pivot system flow rate
Q = 453 × A × D ÷ (F × H)
Q is flow in gpm, A is acres, D is gross depth per irrigation in inches, F is days for one revolution and H is hours pumped per day. F × H together is simply the total hours for one revolution.
This calculator rearranges that same formula to solve for depth or flow rate, whichever you need, and adds the metric equivalent for liters per minute and hectares.
Gross, not net. The depth this formula produces is what leaves the sprinkler nozzles, before losses to evaporation, wind drift and uneven coverage. Add an application efficiency below if you want an estimate of what actually reaches the root zone.
How this calculator works
The calculator first resolves your revolution time to hours, then applies the flow-area-time-depth relationship in the direction you asked for.
1. Revolution time
From a percent timer setting
Hours per revolution = Hours at 100% ÷ (Timer setting ÷ 100)
A lower percent setting means a longer revolution, because 100% is the machine's fastest speed.
2. Gross depth per revolution (US units)
Depth from flow rate
Depth (in) = GPM × Hours per revolution ÷ (453 × Acres)
453 converts gallons per minute to acre-inches per hour: one acre-inch is about 27,154 gallons, and 27,154 ÷ 60 minutes ≈ 453.
Flow rate from a target depth
GPM = 453 × Acres × Target depth (in) ÷ Hours per revolution
3. Gross depth per revolution (metric units)
In metric units the conversion is exact: one millimeter of water over one square meter is exactly one liter, so no constant like 453 is needed.
Depth from flow rate
Depth (mm) = Flow (L/min) × Hours per revolution × 60 ÷ (Area (ha) × 10,000)
Flow rate from a target depth
Flow (L/min) = Target depth (mm) × Area (ha) × 10,000 ÷ (Hours per revolution × 60)
4. Inches (or millimeters) per day
Application rate
Depth per day = Depth per revolution ÷ (Hours per revolution ÷ 24)
Because the flow rate is constant, this simplifies to a figure that depends only on flow and acreage, not on how fast the pivot is rotating: for continuous operation, the same total volume is pumped over any 24-hour span regardless of revolution speed.
5. Net (usable) depth, if you add an efficiency
Net depth
Net depth = Gross depth × Application efficiency
Application efficiency is the fraction of pumped water that reaches the crop root zone; the rest is lost to evaporation, wind drift and uneven coverage.
Rounding policy
Depths and application rates are shown to 2 decimal places in US units (0.01 in) and 1 decimal place in metric units (0.1 mm), matching the precision the math is done at. Flow rate results are rounded to the nearest whole gallon per minute or liter per minute, since pump and pivot controls are set in whole units. Nothing here is an estimate built on a typical rate — every result comes directly from the numbers you enter, so none of it is shown with "about."
When this calculator isn't the right tool
It's built specifically for center pivots rotating around a fixed point. Use a different tool for:
- Lateral-move or hose-reel travelers, which move in a line rather than rotating. See the traveler irrigation calculator.
- Furrow or flood-irrigated fields. See the furrow irrigation calculator or flood irrigation calculator.
- Fixed sprinkler zones on lawns or landscapes, where run time rather than revolution time is the unit that matters. See the sprinkler run time calculator.
- Working out your pivot's irrigated acreage from its length and any end gun. See the center pivot acreage calculator.
For other agriculture-system math, such as well capacity or converting between acre-inches and acre-feet, see the agriculture calculators.
Center pivot calculation example
A 130-acre pivot is fed by a well delivering 650 gpm, and the operator sets the timer so one revolution takes 72 hours (3 days). They also want to see the net depth using the 85% efficiency figure for their high-pressure impact sprinklers.
- Gross depth per revolution: 650 × 72 ÷ (453 × 130) = 46,800 ÷ 58,890 ≈ 0.79 in.
- Gross depth per day: 24 × 650 ÷ (453 × 130) = 15,600 ÷ 58,890 ≈ 0.26 in/day.
- Net depth per revolution: 0.79 in × 0.85 ≈ 0.68 in.
- Net depth per day: 0.26 in/day × 0.85 ≈ 0.23 in/day.
The same calculation in metric
A 50-hectare pivot with a 2,000 L/min flow rate and a 30-hour revolution:
- Gross depth per revolution: 2,000 × 30 × 60 ÷ (50 × 10,000) = 3,600,000 ÷ 500,000 = 7.2 mm.
- Gross depth per day: 7.2 mm ÷ (30 ÷ 24) = 7.2 ÷ 1.25 = 5.8 mm/day.
Reverse mode: flow rate for a target depth
A 200-acre pivot needs to apply 1.5 in (gross) every 48 hours:
- Required flow rate: 453 × 200 × 1.5 ÷ 48 = 135,900 ÷ 48 = 2,831 gpm.
Measuring your inputs and applying the result
Finding your acreage
Use the acreage actually wetted by the system, not the acreage of a full circle at the pivot's outer tower radius, unless that's the same thing for your setup. An end gun or corner arm adds acreage beyond the base circle; a part-circle system waters less than a full circle. The center pivot acreage calculator handles both cases from your system length.
Finding your flow rate
A flow meter on the mainline or pump discharge is the most reliable source. Without one, use the pump manufacturer's performance curve at your measured discharge pressure, or a recent well or pump test report from your driller or pump installer.
Finding your revolution time
Newer control panels typically display total hours per revolution directly at the current timer setting. Older panels often show only a percent setting; check the pivot's owner's manual or the nameplate for the "100% speed" revolution time, then use the percent mode above to convert.
Common mistakes
- Using the full-circle acreage for a part-circle or end-gun system, which overstates the area and understates the true depth applied.
- Mixing up gross and net depth when comparing this result with a crop's water-use figure, which is usually expressed as a net, root-zone requirement.
- Assuming a fixed daily depth regardless of revolution time. Slowing the pivot down increases depth per pass but does not, on its own, change the daily application rate if the flow rate and acreage stay the same.
- Ignoring pressure drop along the pivot's length, which can lower the flow rate delivered at outer sprinklers relative to the pump's rated output.
Factors that change the result
| Factor | Effect on result | What to adjust |
|---|---|---|
| Timer / percent setting | Lower percent slows the machine, raising depth per revolution and total revolution time. | Enter the resulting hours, or use percent mode. |
| Pump flow rate | Higher flow raises both depth per revolution and inches per day, for the same acreage. | Use a measured or metered flow rate, not a nameplate rating. |
| Irrigated acreage | The same flow and time spread over more acres gives less depth per acre. | Use actual wetted acreage, including or excluding the end gun as it applies. |
| Application efficiency | Determines how much of the gross depth reaches the crop root zone. | Use a manufacturer or NRCS figure for your sprinkler package, or your own field measurement. |
| Operating pressure | Low pressure at the pivot point or outer end reduces actual delivered flow versus the pump's rated output. | Check pressure at the pivot point against the sprinkler package's design pressure. |
| Wind | Strong wind increases drift and evaporation losses, lowering real-world efficiency below the sprinkler package's design figure. | Avoid irrigating during the highest-wind hours where practical. |
| Daily shutoff | If the system doesn't run continuously, actual elapsed time per revolution is longer than the moving time this calculator assumes. | Enter the elapsed hours for one full revolution, not just the hours the system is actively moving. |
Frequently asked questions
How much water does a center pivot apply per revolution?
It depends on the system's flow rate, the acreage it covers and how long one revolution takes. USDA NRCS and university extension guides express this with the design formula Q = 453 × A × D ÷ (F × H), which rearranges to give the gross depth D directly from your pump's gallons per minute, your acreage and the hours for one revolution. This calculator does that math for you and also converts the result into inches applied per day.
How do I find my center pivot's revolution time?
Most pivot control panels show a percent timer setting, plus a time for one revolution at 100 percent, usually printed in the owner's manual or set during commissioning. Divide that full-speed time by the percent setting, as a decimal, to get the actual hours for one revolution. If your panel already reports total hours per revolution directly, enter that instead.
What does the percent timer setting on a center pivot control?
The percent setting scales how fast the machine moves relative to its fastest, 100 percent speed for a full circle. A lower percentage slows the towers down, which increases how long each point in the field dwells under the sprinklers and so increases the depth applied per pass, and it lengthens the total revolution time. It does not change the pump's flow rate.
What's the difference between gross and net application depth?
Gross depth is the water pumped and applied at the sprinkler nozzles, which is what this calculator's core formula produces. Net depth is the smaller amount that actually reaches and stays in the crop root zone after losses to evaporation, wind drift and uneven distribution. USDA NRCS design worksheets apply an application efficiency, commonly 85 percent for high-pressure impact sprinklers up to 95 percent for LEPA systems, to convert gross to net.
How do I measure my center pivot's actual flow rate?
A flow meter on the pump discharge or mainline gives the most direct reading in gallons per minute. Where no meter is installed, a manufacturer's pump curve matched to your measured operating pressure, or a recent well or pump test report, are the usual sources irrigation designers rely on instead.
Does this calculator account for end guns or part circles?
Not directly. Enter the acreage your system actually irrigates, including any end gun or corner arm, rather than the acreage of a full 360-degree circle at the pivot's length. The center pivot acreage calculator works out that figure from your system length and any end gun or corner attachment.
See the center pivot acreage calculator.
Can I use this for a lateral-move or hose-reel traveler instead of a center pivot?
No. Those systems move in a straight line or are towed across the field rather than rotating around a fixed point, so their application depth depends on travel speed and lane spacing instead of a revolution time. Use the traveler irrigation calculator for a hose-reel or hard-hose traveler.
See the traveler irrigation calculator.
Who built and checked this calculator
Licensed Professional Engineer and Irrigation Association Certified Irrigation Designer with more than 20 years in irrigation design, system auditing and landscape water management. Full profile
How this page was checked
- Formulas, unit conversions and all three worked examples verified by hand against the calculator's output.
- Depth-to-flow relationship checked against the USDA NRCS and university extension sources below.
- Efficiency presets taken directly from a USDA NRCS center-pivot design worksheet.
Sources
- USDA Natural Resources Conservation Service, Field Office Technical Guide. Chapter 6-C, Center-Pivot Irrigation System.
- USDA Natural Resources Conservation Service, Nebraska. Center Pivot Design Worksheet (442-NE-IR-59).
- University of Georgia Cooperative Extension, Bulletin 882. Factors to Consider in Selecting a Farm Irrigation System.
- University of Nebraska–Lincoln Extension, NebGuide G1851. Selecting a Center Pivot System Capacity.