diff --git a/vlib/math/big/big_test.v b/vlib/math/big/big_test.v
index 17b7e6c169..32d681a7b3 100644
--- a/vlib/math/big/big_test.v
+++ b/vlib/math/big/big_test.v
@@ -432,3 +432,16 @@ fn test_set_bit() {
 	a.set_bit(100, false)
 	assert a == b
 }
+
+fn test_bit_len() {
+	assert big.zero_int.bit_len() == 0
+	assert big.one_int.bit_len() == 1
+
+	assert big.integer_from_u32(0xffffffff).bit_len() == 32
+
+	assert big.one_int.lshift(1239).bit_len() == 1240
+
+	assert big.integer_from_string('4338476092346017364013796407961305761039463198075691378460917856') or {
+		panic('Could not read from decimal')
+	}.bit_len() == 212
+}
diff --git a/vlib/math/big/integer.v b/vlib/math/big/integer.v
index 91f80a504f..c8c1b11106 100644
--- a/vlib/math/big/integer.v
+++ b/vlib/math/big/integer.v
@@ -634,8 +634,7 @@ pub fn (integer Integer) binary_str() string {
 	}
 	// Add the sign if present
 	sign_needed := integer.signum == -1
-	mut result_builder := strings.new_builder(integer.digits.len * 32 +
-		if sign_needed { 1 } else { 0 })
+	mut result_builder := strings.new_builder(integer.bit_len() + if sign_needed { 1 } else { 0 })
 	if sign_needed {
 		result_builder.write_string('-')
 	}
@@ -901,3 +900,17 @@ pub fn (x Integer) gcd_binary(y Integer) Integer {
 	}
 	return b.lshift(shift)
 }
+
+[direct_array_access]
+pub fn (x Integer) bit_len() int {
+	if x.signum == 0 {
+		return 0
+	}
+
+	mut length := 0
+	for _ in 1 .. x.digits.len {
+		length += 32
+	}
+
+	return length + (32 - bits.leading_zeros_32(x.digits.last()))
+}