diff --git a/CHANGELOG.md b/CHANGELOG.md
index 7f1bf0164..ec736c8a2 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,7 @@
+## 2.8.1
+
+* Improve precision of polygon ring area calculations
+
 ## 2.8.0
 
 * Add the option to use a different simplification level at maxzoom
diff --git a/decode.cpp b/decode.cpp
index 04593e701..9a7869b22 100644
--- a/decode.cpp
+++ b/decode.cpp
@@ -207,9 +207,9 @@ void handle(std::string message, int z, unsigned x, unsigned y, std::set<std::st
 		}
 
 		double scale = 0;
-		if (coordinate_mode == 1) { // fraction
+		if (coordinate_mode == 1) {  // fraction
 			scale = layer.extent;
-		} else if (coordinate_mode == 2) { // integer
+		} else if (coordinate_mode == 2) {  // integer
 			scale = 1;
 		}
 		layer_to_geojson(layer, z, x, y, !pipeline, pipeline, pipeline, false, 0, 0, 0, !force, state, scale);
diff --git a/geometry.cpp b/geometry.cpp
index 91f765faf..595fd7ef0 100644
--- a/geometry.cpp
+++ b/geometry.cpp
@@ -160,13 +160,88 @@ drawvec remove_noop(drawvec geom, int type, int shift) {
 	return out;
 }
 
-double get_area(drawvec &geom, size_t i, size_t j) {
+double get_area_scaled(const drawvec &geom, size_t i, size_t j) {
+	const double max_exact_double = (double) ((1LL << 53) - 1);
+
+	// keep scaling the geometry down until we can calculate its area without overflow
+	for (long long scale = 2; scale < (1LL << 30); scale *= 2) {
+		long long bx = geom[i].x;
+		long long by = geom[i].y;
+		bool again = false;
+
+		// https://en.wikipedia.org/wiki/Shoelace_formula
+		double area = 0;
+		for (size_t k = i; k < j; k++) {
+			area += (double) ((geom[k].x - bx) / scale) * (double) ((geom[i + ((k - i + 1) % (j - i))].y - by) / scale);
+			if (std::fabs(area) >= max_exact_double) {
+				again = true;
+				break;
+			}
+			area -= (double) ((geom[k].y - by) / scale) * (double) ((geom[i + ((k - i + 1) % (j - i))].x - bx) / scale);
+			if (std::fabs(area) >= max_exact_double) {
+				again = true;
+				break;
+			}
+		}
+
+		if (again) {
+			continue;
+		} else {
+			area /= 2;
+			return area * scale * scale;
+		}
+	}
+
+	fprintf(stderr, "get_area_scaled: can't happen\n");
+	exit(EXIT_IMPOSSIBLE);
+}
+
+double get_area(const drawvec &geom, size_t i, size_t j) {
+	const double max_exact_double = (double) ((1LL << 53) - 1);
+
+	// Coordinates in `geom` are 40-bit integers, so there is no good way
+	// to multiply them without possible precision loss. Since they probably
+	// do not use the full precision, shift them nearer to the origin so
+	// their product is more likely to be exactly representable as a double.
+	//
+	// (In practice they are actually 34-bit integers: 32 bits for the
+	// Mercator world plane, plus another two bits so features can stick
+	// off either the left or right side. But that is still too many bits
+	// for the product to fit either in a 64-bit long long or in a
+	// double where the largest exact integer is 2^53.)
+	//
+	// If the intermediate calculation still exceeds 2^53, start trying to
+	// recalculate the area by scaling down the geometry. This will not
+	// produce as precise an area, but it will still be close, and the
+	// sign will be correct, which is more important, since the sign
+	// determines the winding order of the rings. We can then use that
+	// sign with this generally more precise area calculation.
+
+	long long bx = geom[i].x;
+	long long by = geom[i].y;
+
+	// https://en.wikipedia.org/wiki/Shoelace_formula
 	double area = 0;
+	bool overflow = false;
 	for (size_t k = i; k < j; k++) {
-		area += (long double) geom[k].x * (long double) geom[i + ((k - i + 1) % (j - i))].y;
-		area -= (long double) geom[k].y * (long double) geom[i + ((k - i + 1) % (j - i))].x;
+		area += (double) (geom[k].x - bx) * (double) (geom[i + ((k - i + 1) % (j - i))].y - by);
+		if (std::fabs(area) >= max_exact_double) {
+			overflow = true;
+		}
+		area -= (double) (geom[k].y - by) * (double) (geom[i + ((k - i + 1) % (j - i))].x - bx);
+		if (std::fabs(area) >= max_exact_double) {
+			overflow = true;
+		}
 	}
 	area /= 2;
+
+	if (overflow) {
+		double scaled_area = get_area_scaled(geom, i, j);
+		if ((area < 0 && scaled_area > 0) || (area > 0 && scaled_area < 0)) {
+			area = -area;
+		}
+	}
+
 	return area;
 }
 
@@ -518,7 +593,7 @@ drawvec simple_clip_poly(drawvec &geom, int z, int buffer) {
 
 drawvec reduce_tiny_poly(drawvec &geom, int z, int detail, bool *reduced, double *accum_area) {
 	drawvec out;
-	const long long pixel = (1 << (32 - detail - z)) * tiny_polygon_size;
+	const double pixel = (1LL << (32 - detail - z)) * (double) tiny_polygon_size;
 
 	*reduced = true;
 	bool included_last_outer = false;
diff --git a/geometry.hpp b/geometry.hpp
index 8a388cca0..cfcb29594 100644
--- a/geometry.hpp
+++ b/geometry.hpp
@@ -74,7 +74,7 @@ drawvec reorder_lines(drawvec &geom);
 drawvec fix_polygon(drawvec &geom);
 std::vector<drawvec> chop_polygon(std::vector<drawvec> &geoms);
 void check_polygon(drawvec &geom);
-double get_area(drawvec &geom, size_t i, size_t j);
+double get_area(const drawvec &geom, size_t i, size_t j);
 double get_mp_area(drawvec &geom);
 
 drawvec simple_clip_poly(drawvec &geom, long long x1, long long y1, long long x2, long long y2);
diff --git a/main.cpp b/main.cpp
index e20eaf7a9..6c87639a9 100644
--- a/main.cpp
+++ b/main.cpp
@@ -2289,7 +2289,7 @@ int read_input(std::vector<source> &sources, char *fname, int maxzoom, int minzo
 				if (maxzoom == 0) {
 					droprate = 2.5;
 				} else {
-					droprate = exp(log((long double) max[0].count / max[maxzoom].count) / (maxzoom));
+					droprate = exp(log((double) max[0].count / max[maxzoom].count) / (maxzoom));
 					if (!quiet) {
 						fprintf(stderr, "Choosing a drop rate of -r%f to get from %lld to %lld in %d zooms\n", droprate, max[maxzoom].count, max[0].count, maxzoom);
 					}
@@ -2298,7 +2298,7 @@ int read_input(std::vector<source> &sources, char *fname, int maxzoom, int minzo
 
 			basezoom = 0;
 			for (z = 0; z <= maxzoom; z++) {
-				double zoomdiff = log((long double) max[z].count / max_features) / log(droprate);
+				double zoomdiff = log((double) max[z].count / max_features) / log(droprate);
 				if (zoomdiff + z > basezoom) {
 					basezoom = ceil(zoomdiff + z);
 				}
@@ -2314,7 +2314,7 @@ int read_input(std::vector<source> &sources, char *fname, int maxzoom, int minzo
 				double interval = exp(log(droprate) * (basezoom - z));
 
 				if (max[z].count / interval >= max_features) {
-					interval = (long double) max[z].count / max_features;
+					interval = (double) max[z].count / max_features;
 					droprate = exp(log(interval) / (basezoom - z));
 					interval = exp(log(droprate) * (basezoom - z));
 
diff --git a/tests/single-polygons/in.json b/tests/single-polygons/in.json
new file mode 100644
index 000000000..685b259de
--- /dev/null
+++ b/tests/single-polygons/in.json
@@ -0,0 +1,30 @@
+{"type":"Feature","properties":{"seq":6},"geometry":{"type":"Polygon","coordinates":[[[174.72151704933612,-37.16620984485238],[174.721517058737,-37.16620953185807],[174.7215172151761,-37.16620953486748],[174.72151720953557,-37.16620972266407],[174.72151705121628,-37.166209782253527],[174.72151704933612,-37.16620984485238]]]}}
+{"type":"Feature","properties":{"seq":7},"geometry":{"type":"Polygon","coordinates":[[[174.7215178334118,-37.16620979730054],[174.72151760063333,-37.16620973018757],[174.72151760627387,-37.16620954239099],[174.72151784093254,-37.16620954690509],[174.72151791351156,-37.166209736206379],[174.7215178334118,-37.16620979730054]]]}}
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diff --git a/tests/single-polygons/out/-Z21_-zg_-D10_-d10.json b/tests/single-polygons/out/-Z21_-zg_-D10_-d10.json
new file mode 100644
index 000000000..941fddc14
--- /dev/null
+++ b/tests/single-polygons/out/-Z21_-zg_-D10_-d10.json
@@ -0,0 +1,116 @@
+{ "type": "FeatureCollection", "properties": {
+"bounds": "174.721517,-37.166211,174.721564,-37.166209",
+"center": "174.721541,-37.166211,22",
+"description": "tests/single-polygons/out/-Z21_-zg_-D10_-d10.json.check.mbtiles",
+"format": "pbf",
+"generator_options": "./tippecanoe -q -a@ -f -o tests/single-polygons/out/-Z21_-zg_-D10_-d10.json.check.mbtiles -Z21 -zg -D10 -d10 tests/single-polygons/in.json",
+"json": "{\"vector_layers\": [ { \"id\": \"in\", \"description\": \"\", \"minzoom\": 21, \"maxzoom\": 22, \"fields\": {\"seq\": \"Number\"} } ],\"tilestats\": {\"layerCount\": 1,\"layers\": [{\"layer\": \"in\",\"count\": 30,\"geometry\": \"Polygon\",\"attributeCount\": 1,\"attributes\": [{\"attribute\": \"seq\",\"count\": 30,\"type\": \"number\",\"values\": [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,6,7,8,9],\"min\": 6,\"max\": 35}]}]}}",
+"maxzoom": "22",
+"minzoom": "21",
+"name": "tests/single-polygons/out/-Z21_-zg_-D10_-d10.json.check.mbtiles",
+"strategies": "[ {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, {  }, { \"tiny_polygons\": 27 }, { \"tiny_polygons\": 1 } ]",
+"type": "overlay",
+"version": "2"
+}, "features": [
+{ "type": "FeatureCollection", "properties": { "zoom": 21, "x": 2066402, "y": 1282091 }, "features": [
+{ "type": "FeatureCollection", "properties": { "layer": "in", "version": 2, "extent": 1024 }, "features": [
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+,
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+,
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+,
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+,
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+,
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+] }
+] }
+] }
diff --git a/version.hpp b/version.hpp
index 7aedadb96..5709b4a09 100644
--- a/version.hpp
+++ b/version.hpp
@@ -1,6 +1,6 @@
 #ifndef VERSION_HPP
 #define VERSION_HPP
 
-#define VERSION "v2.8.0"
+#define VERSION "v2.8.1"
 
 #endif
diff --git a/write_json.cpp b/write_json.cpp
index 545e726b2..5a3e18705 100644
--- a/write_json.cpp
+++ b/write_json.cpp
@@ -505,11 +505,11 @@ void layer_to_geojson(mvt_layer const &layer, unsigned z, unsigned x, unsigned y
 			int outer = 0;
 
 			for (size_t i = 0; i < rings.size(); i++) {
-				long double area = 0;
+				double area = 0;
 				for (size_t k = 0; k < rings[i].size(); k++) {
 					if (rings[i][k].op != VT_CLOSEPATH) {
-						area += (long double) rings[i][k].x * (long double) rings[i][(k + 1) % rings[i].size()].y;
-						area -= (long double) rings[i][k].y * (long double) rings[i][(k + 1) % rings[i].size()].x;
+						area += (double) rings[i][k].x * (double) rings[i][(k + 1) % rings[i].size()].y;
+						area -= (double) rings[i][k].y * (double) rings[i][(k + 1) % rings[i].size()].x;
 					}
 				}
 				area /= 2;