diff --git a/api/next/76821.txt b/api/next/76821.txt
new file mode 100644
index 00000000000000..481fbb44b714b5
--- /dev/null
+++ b/api/next/76821.txt
@@ -0,0 +1,2 @@
+pkg math/big, method (*Rat) Floor() *Int #76821
+pkg math/big, method (*Rat) Ceil() *Int #76821
diff --git a/doc/next/6-stdlib/99-minor/math/big/76821.md b/doc/next/6-stdlib/99-minor/math/big/76821.md
new file mode 100644
index 00000000000000..91e11ab1a94e28
--- /dev/null
+++ b/doc/next/6-stdlib/99-minor/math/big/76821.md
@@ -0,0 +1,2 @@
+<!-- go.dev/issue/76821 -->
+[Rat] now has [Rat.Floor] and [Rat.Ceil] methods.
diff --git a/src/math/big/rat.go b/src/math/big/rat.go
index c7f79a56661b12..1a8e2a6f591d11 100644
--- a/src/math/big/rat.go
+++ b/src/math/big/rat.go
@@ -559,3 +559,18 @@ func (z *Rat) Quo(x, y *Rat) *Rat {
 	z.a.neg = a.neg != b.neg
 	return z.norm()
 }
+
+// Floor returns the largest [Int] <= z.
+func (z *Rat) Floor() *Int {
+	// z.b is positive, so Euclidean division == floor division
+	return new(Int).Div(&z.a, &z.b)
+}
+
+// Ceil returns the smallest [Int] >= z.
+func (z *Rat) Ceil() *Int {
+	if z.IsInt() {
+		return new(Int).Set(&z.a)
+	}
+	f := z.Floor()
+	return f.Add(f, intOne)
+}
diff --git a/src/math/big/rat_test.go b/src/math/big/rat_test.go
index d98c89b3578a7a..3883bd3bd6cf57 100644
--- a/src/math/big/rat_test.go
+++ b/src/math/big/rat_test.go
@@ -744,3 +744,51 @@ func TestDenomRace(t *testing.T) {
 		<-c
 	}
 }
+
+func TestRatFloor(t *testing.T) {
+	var tests = []struct {
+		rat string
+		out int64
+	}{
+		{"123456.78", 123456},
+		{"100.5", 100},
+		{"5645.0222", 5645},
+		{"89898989", 89898989},
+		{"0", 0},
+		{"-123456.78", -123457},
+		{"-100.5", -101},
+		{"-5645.0222", -5646},
+		{"-89898989", -89898989},
+	}
+	for i, test := range tests {
+		x, _ := new(Rat).SetString(test.rat)
+		out := x.Floor()
+		if out.Cmp(NewInt(test.out)) != 0 {
+			t.Errorf("#%d got out = %v; want %v", i, out, test.out)
+		}
+	}
+}
+
+func TestRatCeil(t *testing.T) {
+	var tests = []struct {
+		rat string
+		out int64
+	}{
+		{"123456.78", 123457},
+		{"100.5", 101},
+		{"5645.0222", 5646},
+		{"89898989", 89898989},
+		{"0", 0},
+		{"-123456.78", -123456},
+		{"-100.5", -100},
+		{"-5645.0222", -5645},
+		{"-89898989", -89898989},
+	}
+	for i, test := range tests {
+		x, _ := new(Rat).SetString(test.rat)
+		out := x.Ceil()
+		if out.Cmp(NewInt(test.out)) != 0 {
+			t.Errorf("#%d got out = %v; want %v", i, out, test.out)
+		}
+	}
+}