How many acres does a center pivot irrigate?
A center pivot waters a circle, so its irrigated area follows the same formula as any circle: area equals pi times the radius squared. Here the radius is the pivot's wetted radius — the system length plus any end gun throw — and the only real-world complication is converting that circle into acres or hectares and, on a square field, working out how much of the field the circle actually reaches.
A standard quarter-mile pivot, radius about 1,320 feet, irrigates roughly 126 acres of a 160-acre quarter section, or about 79% of the field. Water Well Journal cites this exact figure as the most common center pivot configuration in the US. Shorter or longer systems scale with the square of the radius, so doubling the system length roughly quadruples the acreage.
| System length | Irrigated area (full circle) |
|---|---|
| 800 ft (244 m) | about 46.2 acres (18.9 ha) |
| 1,000 ft (305 m) | about 72.1 acres (29.5 ha) |
| 1,200 ft (366 m) | about 103.9 acres (42.6 ha) |
| 1,320 ft (400 m) — quarter mile | about 125.7 acres (50.3 ha) |
| 1,600 ft (488 m) | about 184.6 acres (75.4 ha) |
| 2,000 ft (610 m) | about 288.5 acres (117.4 ha) |
| 2,600 ft (792 m) | about 487.5 acres (198.6 ha) |
These figures assume a full 360° circle with no end gun. Add an end gun or a partial arc, or compare against your own field size, in the calculator above. If you also need the system's flow rate or design capacity rather than just its footprint, the center pivot calculator covers GPM, application depth and runtime for a system you've already sized.
How this center pivot acreage calculator works
The calculator finds the wetted radius, applies the circle-area formula (scaled down for a partial arc), then compares that figure with a square field — either the one you enter or the smallest square that contains a full circle.
1. Wetted radius
Total radius
Radius = System length + End gun throw (if fitted)
Leave the end gun off if your system doesn't have one; the radius then equals the system length alone.
2. Irrigated area
US units
Acres = (Arc ÷ 360) × π × Radius² (ft) ÷ 43,560
Metric units
Hectares = (Arc ÷ 360) × π × Radius² (m) ÷ 10,000
For a full circle, Arc ÷ 360 = 1 and drops out of the equation.
3. Comparing with a square field
Default square (full circle only)
Square side = 2 × Radius
This is the smallest square a full circle fits inside, matching the classic quarter-section layout.
Corner area
Corner area = Square field size − Irrigated area
Whether you enter your own field size or use the default square, this is the acreage the circle doesn't reach.
A circle inscribed in a square always covers exactly π ÷ 4, or about 78.5%, of the square's area — that ratio is fixed by geometry and doesn't depend on the radius. The other 21.5% is what a corner arm or end gun tries to reclaim.
4. Corner arm estimate
Added acreage, capped
Added = min(typical range, corner area)
The typical range — about 17 to 25 acres (7 to 10 hectares) — comes from USDA ARS. This calculator never shows more added acreage than your corners actually have available.
Rounding used on this page
Acres are shown to one decimal place and hectares to two, matching the precision used in the formulas above. Percentages are shown to one decimal place. Nothing here is rounded before the underlying calculation runs, only in what's displayed.
When this calculator isn't the right tool
It only works out the footprint of a circular or arc-shaped pivot. Use a different tool for:
- Flow rate, application depth or runtime for a system you've already sized. See the center pivot calculator.
- Well or pump capacity for the acreage you find here. See the irrigation well capacity calculator.
- Linear-move, furrow or flood systems, which don't irrigate a circle. See the agriculture calculators.
- Irregular or non-square fields, where the square-field comparison here is only a rough guide.
Center pivot acreage calculation example
A quarter-mile pivot has a system length of 1,320 feet, runs a full circle, has no end gun, and its owner wants to know how a corner arm would help. No field size is entered, so the calculator uses the default square.
- Radius: 1,320 ft (no end gun added).
- Irrigated area: π × 1,320² ÷ 43,560 = about 125.7 acres.
- Default square field: side = 2 × 1,320 = 2,640 ft; area = 2,640² ÷ 43,560 = 160.0 acres.
- Corner area: 160.0 − 125.7 = about 34.3 acres outside the circle.
- With a corner arm: USDA ARS's typical 17–25 acre range fits inside the 34.3 available acres, so it applies unchanged: about 142.7–150.7 acres total.
The same calculation in metric
A 400 m pivot, full circle, no end gun, corner arm installed, no field size entered:
- Irrigated area: π × 400² ÷ 10,000 = about 50.27 ha.
- Default square field: side = 800 m; area = 800² ÷ 10,000 = 64.00 ha.
- Corner area: 64.00 − 50.27 = about 13.73 ha.
- With a corner arm: the 7–10 ha typical range fits inside 13.73 ha, so it applies unchanged: about 57.27–60.27 ha total.
Both examples land close to the 126-acre, 34-acre-corner figures widely cited for a standard quarter-mile pivot on a quarter section, which is a useful sanity check on the geometry.
Measuring your system and using the result
The two numbers this calculator needs most — system length and end gun throw — are usually easiest to find on the pivot's original design printout or an as-built drawing from the dealer. Failing that, a tape measure or GPS reading from the pivot point to the last tower gives the system length directly; the end gun throw is on the nozzle chart or manufacturer spec sheet for that model of gun.
Once you have an acreage figure, it feeds directly into sizing decisions elsewhere. The GPM per acre calculator and irrigation well capacity calculator both take an acreage as their starting input, and the crop water requirement calculator turns it into a seasonal water volume. If you're weighing whether the extra acreage from a corner arm justifies its cost, run the added acres through the irrigation energy cost per acre-inch calculator against the crop revenue you'd expect from those corners.
Common mistakes
- Measuring to the outer wheel track instead of the pivot point. System length is always measured from the center, not between towers.
- Counting the end gun twice. If the "system length" you have already includes the gun's throw, leave the end gun field blank so it isn't added again.
- Assuming a full circle when the system stops and reverses. A pivot that only sweeps three-quarters of a circle needs the partial-arc option, not the full-circle default.
- Treating the corner arm figure as exact. It's a typical range from USDA ARS capped at your available corner area, not a calculation from your specific machine's swing geometry.
What changes a center pivot's irrigated acreage
| Factor | Effect on acreage | What to adjust |
|---|---|---|
| System length | Acreage grows with the square of the radius, so small length changes near the outer end matter most. | Confirm the radius, not the pivot's full diameter. |
| Full vs. partial arc | A partial arc reduces acreage in direct proportion to the degrees covered. | Select "Partial circle" and enter your degrees. |
| End gun | Adds acreage fastest of any single change, since it extends the radius at its widest point. | Enter the gun's throw distance if one is fitted. |
| Corner arm | Reclaims some of the corner acreage a plain circle leaves dry. | Toggle it on to see the typical added range. |
| Field shape | The square-field comparison assumes a square field around the pivot. | For rectangular or irregular fields, treat the comparison as approximate. |
| Wind and pressure | Real wetted radius can run a little short of the nameplate length in windy or low-pressure conditions. | Use a slightly shorter length for a conservative estimate. |
Frequently asked questions
How many acres does a center pivot irrigate?
A center pivot's irrigated area comes from the circle formula: area equals pi times the wetted radius squared, divided by 43,560 for acres or 10,000 for hectares. A common quarter-mile system, with a radius of about 1,320 feet, covers roughly 126 acres. Longer or shorter systems, a partial arc, or an end gun all change the number, which is exactly what this calculator works out from your own inputs.
How do I find my system's length for this calculator?
System length is the distance from the pivot point to the last regular tower or sprinkler, not counting the end gun. It's usually on the manufacturer's design printout or as-built drawing, or you can measure it directly outward from the pivot point. If you only know the total distance to the outer wetted edge, subtract the end gun's throw first so you don't count it twice.
How much land is lost in the corners of a square field?
A circle inscribed in a square always covers pi divided by 4, or about 78.5%, of the square's area, leaving roughly 21.5% in the corners. On a standard 160-acre quarter section this works out to about 34 acres left dry, a figure commonly cited in irrigation engineering references. This calculator shows your own corner area once you enter a field size, or uses that same quarter-section-style default automatically for a full circle.
How many more acres does a corner arm add?
The USDA Agricultural Research Service reports that corner systems typically add about 17 to 25 acres (7 to 10 hectares) of corner coverage without requiring more land, though the real gain depends on the field and machine. This calculator applies that range to your own corner area and caps it if your corners are smaller than the typical range.
How much extra acreage does an end gun add?
It depends on the throw distance and how much of the rotation the gun runs during, since acreage grows with the square of the radius. Water Well Journal cites roughly 10 to 14 additional acres as a typical gain from an end gun on a standard-length pivot. This calculator's own figure can run higher than that because it assumes the gun fires across the whole arc you select, which is the maximum-case estimate, not a measurement of intermittent corner-only firing.
Does a partial-circle pivot use the same formula?
Yes. A partial arc uses the same circle formula and multiplies it by the fraction of 360 degrees the system actually covers, so a half-circle pivot on the same radius irrigates exactly half the full-circle acreage. Select "Partial circle" above and enter the arc in degrees to use this.
What's a typical quarter-section center pivot size?
A quarter section is 160 acres, a half-mile by half-mile square, or 2,640 feet on a side. A full-circle pivot with a radius close to 1,320 feet fits inside it and irrigates roughly 126 acres, leaving about 34 acres in the corners unless an end gun or corner arm is added.
Can this calculator size my pump or well for the acreage it finds?
No, it only works out the irrigated area, not flow, pressure or well capacity. Once you have the acreage, the irrigation well capacity calculator and GPM per acre calculator turn that number into a required flow rate.
See the irrigation well capacity calculator or the GPM per acre 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
- Circle and arc formulas, the square-field comparison, and both worked examples verified by hand.
- Corner arm and end gun figures checked against the USDA ARS and Water Well Journal ranges cited below.
- Geometry follows standard circular-sector math; the quarter-section example matches figures independently published by Water Well Journal.
Sources
- USDA Agricultural Research Service. Center Pivot Irrigation (design reference on end guns and corner systems). [VERIFY URL]
- Water Well Journal. Irrigation Fundamentals (center pivot sizing and quarter-section coverage).
- PASSEL (Plant and Soil Sciences eLibrary), University of Nebraska–Lincoln. Sprinkler Irrigation Basics.
- USDA NRCS. National Engineering Handbook, Part 652 — Irrigation Guide, Center-Pivot Irrigation Systems (Alabama supplement). [VERIFY URL]