Polygon Area Calculator

Area and perimeter from drawing or raw vertices

This tool measures any polygon two ways: draw it by clicking the map, or paste a list of 'lat, lng' vertices copied from a dataset, GPS log or GIS export. Either path produces the same rigorous result — spherical-excess area on the WGS84 sphere plus perimeter length — presented in every common unit and exportable as GeoJSON or KML. Pasting makes it a verification instrument: check what a shapefile claims, audit a colleague's boundary, or sanity-check a geofence before it ships.

The validator is honest about classic failure modes: fewer than three vertices, swapped coordinate order, or a ring that accidentally wraps the globe all produce clear messages instead of absurd numbers. Because the math integrates on the sphere, results hold for high-latitude shapes where projected-area tools drift. Holes are handled pragmatically — measure the outer ring, subtract the hole as a second measurement — and labelled as such. For pure circle geometry the circle-area tool is the one-click companion.

Worked examples

• 5-mile circle — encloses 50,265 acres (203 km²) with a circumference of 51 km — useful calibration for what a radius of that size really covers.
• 10-mile circle — encloses 201,061 acres (814 km²) with a circumference of 101 km — useful calibration for what a radius of that size really covers.
• 25-mile circle — encloses 1,256,629 acres (5,085 km²) with a circumference of 253 km — useful calibration for what a radius of that size really covers.

Circles, polygons and the honest measurement of area

A radius circle on a globe is a spherical cap: the set of points at a fixed surface distance from a centre. Drawn naively on a flat map it distorts badly toward the poles, so correct tools place each boundary vertex by destination-point trigonometry — stepping out the radius at 128 bearings — which keeps a 50 km circle genuinely 50 km wide at any latitude. The same care applies to area: the right method integrates around the boundary on the sphere (spherical excess), remaining accurate from garden plots to province-sized shapes, where flat shoelace formulas on raw lat/long silently produce nonsense.

Units carry culture as well as math. American land talks in acres, agriculture worldwide in hectares, plans in square metres, headlines in square miles. The conversions are exact by definition — a hectare is 10,000 m², an acre 4,046.86 m² — but intuition is not, which is why seeing the circle on a map matters: a five-kilometre radius feels modest in a spreadsheet and looks enormous over a city centre. The map is the unit your brain trusts.

Rings and multiple circles extend the single circle into analysis: concentric distance bands price deliveries and plan evacuations; stacked catchments compare stores, depots or services. And when reach is temporal rather than geometric — 'fifteen minutes by car' — the honest instrument is the isochrone, because roads make time anisotropic. Knowing which circle you need, geometric or temporal, is half the craft of spatial reasoning.

Tips & common mistakes

Decide geometric vs temporal reach before drawing anything: a 10 km circle and a 15-minute drive area answer different questions, and in car-dependent geography they barely overlap in shape. Circles for policy radii, isochrones for response promises.

Verify areas against a known object first — measure a football pitch or a city block you know — and you'll calibrate your eye for what a hectare or acre looks like at your zoom. The map preview is the unit your intuition trusts.

When exporting polygons for reports, store the radius and unit in the feature properties (the exports here do). Future-you, reopening the file in a GIS, will otherwise have to re-derive what the circle meant.

Thinking in circles without being fooled by them

Circles are the simplest spatial idea and the easiest to misuse. On a sphere they are honest caps; on flat screens they tempt distortion, so a good tool constructs them vertex by vertex and shows area computed on the same sphere. The deeper trap is semantic: a circle says 'distance as the crow flies', which is rarely how people, pizzas or plumbers travel. Before drawing, ask what moves along what network — if the answer involves roads, your circle is a sketch and an isochrone is the portrait.

Multiple circles and rings upgrade circles from illustration to analysis. Overlapping catchments compare service reach; concentric rings price distance bands; a circle minus a circle approximates a drive-time donut for marketing. The exports matter as much as the pixels: storing radius and unit inside each feature's properties turns a pretty map into a dataset a GIS can re-derive, audit and re-style. Measure twice, export once, and let the sphere do the arithmetic.

How professionals use this

• State the question first: geometric reach (circle) or temporal reach (isochrone) — then pick the instrument.
• Calibrate your eye with known areas (a hectare ≈ 1.4 football pitches) before judging unfamiliar polygons.
• Export radii with their parameters embedded; future audits should not require archaeology.
• For population claims inside circles, prefer transparent city sums with the list shown over black-box rasters.

Step-by-step masterclass

1. 1. Ask geometric or temporal — Before drawing anything, decide whether the question is 'within X km' (circle) or 'within X minutes' (isochrone); the wrong instrument answers the wrong question confidently.
2. 2. Calibrate with known areas — Measure a block or pitch you know; a hectare ≈ 1.4 FIFA pitches, and one calibration makes every later polygon legible at a glance.
3. 3. Drag to verify — Resize by the edge handle and watch area update live; the feedback loop between number and map is where intuition gets built.
4. 4. Store parameters with geometry — Exports here embed radius and unit in feature properties; an audited analysis should never require guessing what a circle meant.
5. 5. Compose for analysis — Rings for price bands, overlaps for catchment competition, circle-minus-circle for donuts — circles become analytical once they're combinable datasets.

Unit culture matters in radius work: US planning thinks in miles and acres, agriculture worldwide in hectares, marine contexts in nautical miles — converting exactly (1 ha = 2.471 acres) is trivial, but choosing the unit your audience trusts is the professional move.

Related questions people ask

Quick glossary

Spherical cap

The true shape of a radius circle on a globe.

Spherical excess

The method for exact polygon areas on a sphere.

Catchment

The area or population served from a centre, geometric or temporal.

Perimeter

The summed great-circle length of a drawn boundary.

Donut analysis

Subtracting an inner circle from an outer to study a distance band.

Anisotropy

Direction-dependent reach — the reason circles lie about travel time.

Honest limits & when to escalate

Circles and polygons are geometric truths with semantic limits. A radius says nothing about rivers, one-way systems or response times; an area says nothing about what is inside it. The most expensive misuse is treating a geometric catchment as a service promise — which is why the isochrone tools exist as the temporal counterpart, and why the pages cross-link the two insistently. A second limit is resolution: drawn vertices capture the boundary you click, so curved shores want more clicks, and the perimeter grows (correctly) as you add them — the coastline paradox, politely present in every honest measurement tool.

Within geometry, the numbers are exact on the sphere: areas by spherical excess, boundaries by destination math, exports with their parameters embedded. The escalation ladder is short: cadastral precision needs licensed surveys; population-inside-shapes needs census blocks; drive-time promises need the routing engine. Used as the fast, auditable, shareable geometric layer that feeds those heavier instruments, this is exactly the right tool — and it says so.

• Cadastral/legal area → licensed survey with local datum practice.
• Population inside shapes → census blocks, not city-point sums.
• Response-time promises → isochrones plus operational buffers.
• Ecological boundaries → field-verified polygons, not clicked ones.

Data & methodology note

Circle boundaries are placed vertex-by-vertex by spherical destination math; polygon areas use spherical excess on the WGS84 sphere — both remain correct at high latitudes where flat formulas fail.

Category context: Radius & Area — Draw radii, rings and polygons; measure areas in any unit. This page is one of the radius & area tools on MapForge; the related-tools links below and the header's Tools menu connect every sibling instrument.