Acreage calculator from a map
The four corners in the worked example below enclose 36.8 acres — 14.89 hectares, 148,933 square metres, with 1,556 metres around the boundary. Paste one corner per line as latitude and longitude and the page closes the ring and measures the spherical polygon itself, so the acreage still arrives when the map tiles do not.
Your answer
Acreage inside these corners31.31 ac
- Corners used
- 4
- In hectares
- 12.67 ha
Plot sheet
What this means for the field in front of you:
- This plot in every unit
- 126,724 m² · 1,267 a · 12.67 ha · 1,364,042 ft² · 31.31 ac
- As the register writes it (ha a ca)
- 12 ha 67 a 24 ca
- Distance around the plot
- 1,442 m
- Measured by
- points on a map
Three fields are kept; saving a fourth replaces the oldest.
How the answer is worked out
A field on a map is a closed ring of points. The area inside that ring is not a rectangle problem and it is not a flat-earth problem either: over a quarter section the ground is curved enough that the honest way to do it is a spherical polygon.
The method. The ring is closed (a repeated last point is dropped, so a ring given either way measures the same), each edge contributes the integral of sin φ dλ along it, and the sum is multiplied by R² with R the IUGG mean Earth radius, 6,371,008.8 m. Longitude differences are normalised into ±180°, so a boundary that happens to cross the antimeridian does not fold the planet into the answer. The result is converted once, at full precision, into acres, hectares, square feet, ares and square metres.
The distance around comes from the haversine formula over the same ring — useful for fencing, for a headland pass, or as a sanity check that a corner was not typed with a digit missing.
No tiles required. Most “measure on the map” tools are a thin wrapper around a mapping provider: when the key expires or the provider changes its terms, the tool stops answering. Here the provider is decoration. Corners can be pasted, typed or edited by hand, and the calculation runs entirely in your browser — nothing about your field leaves the page.
What it is not. This is a measurement of the ring you drew, not a legal boundary and not enrolled acreage. Field boundaries on file with an agency come from that agency’s own records; use this to check them, to plan, and to measure the parts of a field that are actually farmed, then save the result as a named field so the seeding and fertiliser pages work on the same number.
A worked example
Every figure below is computed by the calculator above from this case — nothing here is typed in by hand:
- Corners of the field
- 40.1130,-88.2450 · 40.1146,-88.2411 · 40.1112,-88.2396 · 40.1096,-88.2436
Acreage inside these corners:36.8 ac
- Corners used
- 4
- In hectares
- 14.89 ha
- This plot in every unit
- 148,933 m² · 1,489 a · 14.89 ha · 1,603,103 ft² · 36.8 ac
- As the register writes it (ha a ca)
- 14 ha 89 a 33 ca
Worked by Agrimetra with the same engine the calculator above runs.
What this means in the United States
Farm Service Agency field boundaries and common land units are what most growers picture when they measure a field on a map, and the number that matters is enrolled acreage. This page draws the boundary you trace and computes the spherical polygon itself, so it keeps answering when the tile layer does not.
Questions growers actually ask
- How many corners do I need?
- Three, to enclose anything at all. Four is the normal case for a field; more corners simply follow the boundary more closely. Up to 500 are accepted, which is well past a hand-drawn field and into pasted GPS-track territory.
- Where do the coordinates come from?
- Any GPS app, a handheld receiver, a spreadsheet export, a guidance monitor or the corner coordinates printed on a plat. Right-clicking a point in most web map viewers also copies a latitude and longitude pair you can paste straight in.
- How accurate is a spherical calculation?
- For a field, far more accurate than the corners you feed it. The area is the line-integral form for a spherical polygon on the IUGG mean Earth radius of 6,371,008.8 m; against an ellipsoid the difference on a quarter section is smaller than a single phone-tap of imprecision on a corner.
- Does it need a map provider or an API key?
- No. The measurement is our own code working on the vertices, and the tile layer is decoration over it. A provider outage, a blocked key or a page opened offline degrades the picture, never the number.
Last updated:
Sources
- Chamberlain & Duquette (NASA JPL) — Some algorithms for polygons on a sphere (checked September 22, 2026)
- Bureau of Land Management — the Public Land Survey System (checked September 22, 2026)