diff --git a/utils.go b/utils.go
index 98b6a07..95b3310 100644
--- a/utils.go
+++ b/utils.go
@@ -5,6 +5,7 @@ import (
 	"errors"
 	"fmt"
 	"io"
+	"math"
 	"os"
 	"path/filepath"
 	"strconv"
@@ -413,16 +414,30 @@ func WriteCgroupProc(dir string, pid int) error {
 	return err
 }
 
-// Since the OCI spec is designed for cgroup v1, in some cases
-// there is need to convert from the cgroup v1 configuration to cgroup v2
-// the formula for cpuShares is y = (1 + ((x - 2) * 9999) / 262142)
-// convert from [2-262144] to [1-10000]
-// 262144 comes from Linux kernel definition "#define MAX_SHARES (1UL << 18)"
+// ConvertCPUSharesToCgroupV2Value converts CPU shares, used by cgroup v1,
+// to CPU weight, used by cgroup v2.
+//
+// Cgroup v1 CPU shares has a range of [2^1...2^18], i.e. [2...262144],
+// and the default value is 1024.
+//
+// Cgroup v2 CPU weight has a range of [10^0...10^4], i.e. [1...10000],
+// and the default value is 100.
 func ConvertCPUSharesToCgroupV2Value(cpuShares uint64) uint64 {
+	// The value of 0 means "unset".
 	if cpuShares == 0 {
 		return 0
 	}
-	return (1 + ((cpuShares-2)*9999)/262142)
+	if cpuShares <= 2 {
+		return 1
+	}
+	if cpuShares >= 262144 {
+		return 10000
+	}
+	l := math.Log2(float64(cpuShares))
+	// Quadratic function which fits min, max, and default.
+	exponent := (l*l+125*l)/612.0 - 7.0/34.0
+
+	return uint64(math.Ceil(math.Pow(10, exponent)))
 }
 
 // ConvertMemorySwapToCgroupV2Value converts MemorySwap value from OCI spec
diff --git a/utils_test.go b/utils_test.go
index 2d30373..79023b7 100644
--- a/utils_test.go
+++ b/utils_test.go
@@ -535,15 +535,30 @@ func TestGetHugePageSizeImpl(t *testing.T) {
 }
 
 func TestConvertCPUSharesToCgroupV2Value(t *testing.T) {
+	const (
+		sharesMin = 2
+		sharesMax = 262144
+		sharesDef = 1024
+		weightMin = 1
+		weightMax = 10000
+		weightDef = 100
+		unset     = 0
+	)
 	cases := map[uint64]uint64{
-		0:      0,
-		2:      1,
-		262144: 10000,
+		unset: unset,
+
+		sharesMin - 1: weightMin,     // Below the minimum (out of range).
+		sharesMin:     weightMin,     // Minimum.
+		sharesMin + 1: weightMin + 1, // Just above the minimum.
+		sharesDef:     weightDef,     // Default.
+		sharesMax - 1: weightMax,     // Just below the maximum.
+		sharesMax:     weightMax,     // Maximum.
+		sharesMax + 1: weightMax,     // Above the maximum (out of range).
 	}
-	for i, expected := range cases {
-		got := ConvertCPUSharesToCgroupV2Value(i)
-		if got != expected {
-			t.Errorf("expected ConvertCPUSharesToCgroupV2Value(%d) to be %d, got %d", i, expected, got)
+	for shares, want := range cases {
+		got := ConvertCPUSharesToCgroupV2Value(shares)
+		if got != want {
+			t.Errorf("ConvertCPUSharesToCgroupV2Value(%d): got %d, want %d", shares, got, want)
 		}
 	}
 }