How much do your hives compete for the same flowers? See pairwise overlap, average competition, and unique territory per hive.
m between adjacent hives
Visscher & Seeley 1982 mean; the field default.
Overlap diagram
Each circle is one hive's foraging zone (radius 3 km). Overlapping shaded regions = shared forage.
Average competition100%of each hive's forage zone is sharedPairwise overlap summed and normalised against per-hive area.
Adjacent-pair overlap89%shared between neighbouring hivesLens area divided by single-hive area for the closest pair.
Total foraging area0.0km² covered by the apiary (approx)Single-hive area: 28.3 km² · sum of 4 hives minus overlap.
Significant overlap pairs6of 6 pairs share ≥ 25% of foragePairs whose lens area exceeds a quarter of one hive's territory.
What this means
Average competition is 100% — extreme. The hives are effectively working a single shared forage zone. Per-hive yield will track total nectar availability divided by colony count rather than scaling with hive number. Consider widening spacing or moving some hives to a separate yard.
Note: with spacing (500 m) much smaller than the foraging radius (3 km), three or more hives share regions of the map. The "Total foraging area" figure slightly under-counts the true union — read it as a lower-bound estimate.
Pairwise overlap
Pair
Distance
Overlap area
% of one hive
k apart by 1
0.5 km
25.3 km²
89%
k apart by 2
1.0 km
22.3 km²
79%
k apart by 3
1.5 km
19.4 km²
69%
"k apart by k" means hives separated by k spacing-steps in the linear arrangement. There are 3 such gap-classes for 4 hives. Adjacent pairs (k = 1) share the most; far pairs may share zero.
Frequently Asked Questions
+How far do honey bees actually forage from the hive?
Mean foraging distance is roughly 1–2 km in floral-rich landscapes (Visscher & Seeley 1982), with a typical maximum useful range of 3–5 km. Recorded maxima reach 13.5 km in heathland (Beekman & Ratnieks 2000), but bees prefer closer forage when available — energy return per trip falls quickly with distance. The 3 km default in this tool is a sensible mean for mixed agricultural / suburban landscapes.
+Why does foraging-zone overlap matter for apiary planning?
Two hives sharing a forage zone are not splitting a fixed nectar pool 50/50 — they are competing for the same flowers, and the colony with more foragers usually wins. In flow-limited landscapes (urban backyards, small farms, late-season dearth) overlap can suppress per-hive yield substantially. In flow-rich landscapes (canola fields, abundant linden) overlap matters less because the resource is not the limiting factor. The calculator helps you see how much overlap a given spacing produces — the management decision (accept, increase spacing, supplement) is yours.
+What is the formula for the overlap area between two foraging circles?
For two identical circles of radius R whose centres are distance d apart (with d < 2R), the lens-shaped overlap area is A = 2R²·acos(d/(2R)) − (d/2)·√(4R² − d²). When d ≥ 2R the circles do not intersect and the overlap is zero. When d = 0 the circles coincide and the overlap equals the full circle area πR².
+Is this a planning tool or a yield prediction?
A planning tool. The geometry of overlap is exact, but the link from overlap to honey yield depends on local nectar density, weather, colony strength, and varietal preferences. Use the percentage figures as a *spacing diagnostic* — "my four hives at 50 m share 80% of their forage zone, so I should not expect four times the yield of one hive" — not as a yield calculator.
+How should I space hives for minimum competition?
For a 3 km foraging radius, two hives need to be roughly 6 km apart for zero overlap — impractical for most apiaries. A more realistic target is to keep the average overlap below 25–30% of single-hive territory, which for typical foraging radii means 2–4 km spacing for outyards and accepting heavy overlap for backyard apiaries. Many beekeepers run 4+ hives in one yard and accept the competition because the convenience outweighs the yield-per-hive cost.
+Why is the "total area covered" only an approximation?
The calculator subtracts pairwise lens overlaps from the simple sum of single-hive areas. When three or more hives share a region, the formula slightly *under*-counts the union (because it has subtracted the triple-overlap region twice). For the linear arrangements this tool models, three-way overlaps are common only when spacing d is much smaller than R; the calculator flags this when it occurs.
+What about urban beekeeping — does the radius shrink?
Yes. Couvillon et al. (2014) found urban honey bees forage shorter mean distances than rural — around 0.5–1.5 km in central London — because forage is denser and more reliable in mixed gardens. If you are planning an urban apiary, set the foraging radius to 1.5 km to reflect that reality; overlap rises sharply at that radius.
+Can I embed the Apiary Foraging Overlap Calculator on my blog?
Yes — paste the iframe snippet shown on this page. The widget is free, mobile-friendly, and available in light and dark themes via ?theme=dark.
Sources. Visscher PK & Seeley TD (1982) Foraging strategy of honeybee colonies in a temperate deciduous forest. Ecology 63:1790–1801. Beekman M & Ratnieks FLW (2000) Long-range foraging by the honey-bee, Apis mellifera L. Functional Ecology 14:490–496. Couvillon MJ, Schürch R, Ratnieks FLW (2014) Dancing bees communicate a foraging preference for rural lands in high-level agri-environment schemes. Curr. Biol. 24:1212–1215. Seeley TD (1995) The Wisdom of the Hive. Harvard University Press.
Embed on your site
Paste this snippet anywhere on your page. Append ?theme=dark for the dark variant.