diff --git a/util/almost/almost.go b/util/almost/almost.go
index a40462658..5f866b89b 100644
--- a/util/almost/almost.go
+++ b/util/almost/almost.go
@@ -22,10 +22,10 @@ import (
 var minNormal = math.Float64frombits(0x0010000000000000) // The smallest positive normal value of type float64.
 
 // Equal returns true if a and b differ by less than their sum
-// multiplied by epsilon.
+// multiplied by epsilon, or if both are StaleNaN, or if both are any other NaN.
 func Equal(a, b, epsilon float64) bool {
-	// StaleNaN is a special value that is used as staleness maker, so
-	// the two values are equal when both are exactly equals to stale NaN.
+	// StaleNaN is a special value that is used as staleness maker, and
+	// we don't want it to compare equal to any other NaN.
 	if value.IsStaleNaN(a) || value.IsStaleNaN(b) {
 		return value.IsStaleNaN(a) && value.IsStaleNaN(b)
 	}
diff --git a/util/almost/almost_test.go b/util/almost/almost_test.go
new file mode 100644
index 000000000..fba37f13f
--- /dev/null
+++ b/util/almost/almost_test.go
@@ -0,0 +1,50 @@
+// Copyright 2024 The Prometheus Authors
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package almost
+
+import (
+	"fmt"
+	"math"
+	"testing"
+
+	"github.com/prometheus/prometheus/model/value"
+)
+
+func TestEqual(t *testing.T) {
+	staleNaN := math.Float64frombits(value.StaleNaN)
+	tests := []struct {
+		a       float64
+		b       float64
+		epsilon float64
+		want    bool
+	}{
+		{0.0, 0.0, 0.0, true},
+		{0.0, 0.1, 0.0, false},
+		{1.0, 1.1, 0.1, true},
+		{-1.0, -1.1, 0.1, true},
+		{math.MaxFloat64, math.MaxFloat64 / 10, 0.1, false},
+		{1.0, math.NaN(), 0.1, false},
+		{math.NaN(), math.NaN(), 0.1, true},
+		{math.NaN(), staleNaN, 0.1, false},
+		{staleNaN, math.NaN(), 0.1, false},
+		{staleNaN, staleNaN, 0.1, true},
+	}
+	for _, tt := range tests {
+		t.Run(fmt.Sprintf("%v,%v,%v", tt.a, tt.b, tt.epsilon), func(t *testing.T) {
+			if got := Equal(tt.a, tt.b, tt.epsilon); got != tt.want {
+				t.Errorf("Equal(%v,%v,%v) = %v, want %v", tt.a, tt.b, tt.epsilon, got, tt.want)
+			}
+		})
+	}
+}