diff --git a/compiler/rustc_typeck/src/impl_wf_check.rs b/compiler/rustc_typeck/src/impl_wf_check.rs
index 891e482b43133..4901d6041d6f0 100644
--- a/compiler/rustc_typeck/src/impl_wf_check.rs
+++ b/compiler/rustc_typeck/src/impl_wf_check.rs
@@ -187,7 +187,7 @@ fn enforce_impl_params_are_constrained(
     }
 
     // (*) This is a horrible concession to reality. I think it'd be
-    // better to just ban unconstrianed lifetimes outright, but in
+    // better to just ban unconstrained lifetimes outright, but in
     // practice people do non-hygenic macros like:
     //
     // ```
@@ -207,7 +207,7 @@ fn enforce_impl_params_are_constrained(
 }
 
 fn report_unused_parameter(tcx: TyCtxt<'_>, span: Span, kind: &str, name: &str) {
-    struct_span_err!(
+    let mut err = struct_span_err!(
         tcx.sess,
         span,
         E0207,
@@ -215,9 +215,17 @@ fn report_unused_parameter(tcx: TyCtxt<'_>, span: Span, kind: &str, name: &str)
         impl trait, self type, or predicates",
         kind,
         name
-    )
-    .span_label(span, format!("unconstrained {} parameter", kind))
-    .emit();
+    );
+    err.span_label(span, format!("unconstrained {} parameter", kind));
+    if kind == "const" {
+        err.note(
+            "expressions using a const parameter must map each value to a distinct output value",
+        );
+        err.note(
+            "proving the result of expressions other than the parameter are unique is not supported",
+        );
+    }
+    err.emit();
 }
 
 /// Enforce that we do not have two items in an impl with the same name.
diff --git a/src/test/ui/const-generics/issues/issue-68366.rs b/src/test/ui/const-generics/issues/issue-68366.rs
new file mode 100644
index 0000000000000..a06b99d6645ec
--- /dev/null
+++ b/src/test/ui/const-generics/issues/issue-68366.rs
@@ -0,0 +1,18 @@
+// Checks that const expressions have a useful note explaining why they can't be evaluated.
+// The note should relate to the fact that it cannot be shown forall N that it maps 1-1 to a new
+// type.
+
+#![feature(const_generics)]
+#![allow(incomplete_features)]
+
+struct Collatz<const N: Option<usize>>;
+
+impl <const N: usize> Collatz<{Some(N)}> {}
+//~^ ERROR the const parameter
+
+struct Foo;
+
+impl<const N: usize> Foo {}
+//~^ ERROR the const parameter
+
+fn main() {}
diff --git a/src/test/ui/const-generics/issues/issue-68366.stderr b/src/test/ui/const-generics/issues/issue-68366.stderr
new file mode 100644
index 0000000000000..bba16f421535a
--- /dev/null
+++ b/src/test/ui/const-generics/issues/issue-68366.stderr
@@ -0,0 +1,21 @@
+error[E0207]: the const parameter `N` is not constrained by the impl trait, self type, or predicates
+  --> $DIR/issue-68366.rs:10:13
+   |
+LL | impl <const N: usize> Collatz<{Some(N)}> {}
+   |             ^ unconstrained const parameter
+   |
+   = note: expressions using a const parameter must map each value to a distinct output value
+   = note: proving the result of expressions other than the parameter are unique is not supported
+
+error[E0207]: the const parameter `N` is not constrained by the impl trait, self type, or predicates
+  --> $DIR/issue-68366.rs:15:12
+   |
+LL | impl<const N: usize> Foo {}
+   |            ^ unconstrained const parameter
+   |
+   = note: expressions using a const parameter must map each value to a distinct output value
+   = note: proving the result of expressions other than the parameter are unique is not supported
+
+error: aborting due to 2 previous errors
+
+For more information about this error, try `rustc --explain E0207`.