diff --git a/docs/reference/aggregations/metrics/cardinality-aggregation.asciidoc b/docs/reference/aggregations/metrics/cardinality-aggregation.asciidoc
index fcb866cff26..b8ee0508618 100644
--- a/docs/reference/aggregations/metrics/cardinality-aggregation.asciidoc
+++ b/docs/reference/aggregations/metrics/cardinality-aggregation.asciidoc
@@ -69,11 +69,70 @@ about `c * 8` bytes.
 
 The following chart shows how the error varies before and after the threshold:
 
+////
+To generate this chart use this gnuplot script:
+-------
+#!/usr/bin/gnuplot
+reset
+set terminal png size 1000,400
+
+set xlabel "Actual cardinality"
+set logscale x
+
+set ylabel "Relative error (%)"
+set yrange [0:8]
+
+set title "Cardinality error"
+set grid
+
+set style data lines
+
+plot "test.dat" using 1:2 title "threshold=100", \
+"" using 1:3 title "threshold=1000", \
+"" using 1:4 title "threshold=10000"
+#
+-------
+
+and generate data in a 'test.dat' file using the below Java code:
+
+-------
+private static double error(HyperLogLogPlusPlus h, long expected) {
+    double actual = h.cardinality(0);
+    return Math.abs(expected - actual) / expected;
+}
+
+public static void main(String[] args) {
+    HyperLogLogPlusPlus h100 = new HyperLogLogPlusPlus(precisionFromThreshold(100), BigArrays.NON_RECYCLING_INSTANCE, 1);
+    HyperLogLogPlusPlus h1000 = new HyperLogLogPlusPlus(precisionFromThreshold(1000), BigArrays.NON_RECYCLING_INSTANCE, 1);
+    HyperLogLogPlusPlus h10000 = new HyperLogLogPlusPlus(precisionFromThreshold(10000), BigArrays.NON_RECYCLING_INSTANCE, 1);
+
+    int next = 100;
+    int step = 10;
+
+    for (int i = 1; i <= 10000000; ++i) {
+        long h = BitMixer.mix64(i);
+        h100.collect(0, h);
+        h1000.collect(0, h);
+        h10000.collect(0, h);
+
+        if (i == next) {
+            System.out.println(i + " " + error(h100, i)*100 + " " + error(h1000, i)*100 + " " + error(h10000, i)*100);
+            next += step;
+            if (next >= 100 * step) {
+                step *= 10;
+            }
+        }
+    }
+}
+-------
+
+////
+
 image:images/cardinality_error.png[]
 
 For all 3 thresholds, counts have been accurate up to the configured threshold
 (although not guaranteed, this is likely to be the case). Please also note that
-even with a threshold as low as 100, the error remains under 5%, even when
+even with a threshold as low as 100, the error remains very low, even when
 counting millions of items.
 
 ==== Pre-computed hashes
diff --git a/docs/reference/images/cardinality_error.png b/docs/reference/images/cardinality_error.png
index 1f871c2c674..cf405be69ab 100644
Binary files a/docs/reference/images/cardinality_error.png and b/docs/reference/images/cardinality_error.png differ