diff --git a/src/cmd/compile/internal/noder/noder.go b/src/cmd/compile/internal/noder/noder.go
index 1c38f1a934..d692bf97aa 100644
--- a/src/cmd/compile/internal/noder/noder.go
+++ b/src/cmd/compile/internal/noder/noder.go
@@ -1455,6 +1455,20 @@ func (p *noder) basicLit(lit *syntax.BasicLit) constant.Value {
 	switch lit.Kind {
 	case syntax.IntLit, syntax.FloatLit, syntax.ImagLit:
 		checkLangCompat(lit)
+		// The max. mantissa precision for untyped numeric values
+		// is 512 bits, or 4048 bits for each of the two integer
+		// parts of a fraction for floating-point numbers that are
+		// represented accurately in the go/constant package.
+		// Constant literals that are longer than this many bits
+		// are not meaningful; and excessively long constants may
+		// consume a lot of space and time for a useless conversion.
+		// Cap constant length with a generous upper limit that also
+		// allows for separators between all digits.
+		const limit = 10000
+		if len(lit.Value) > limit {
+			p.errorAt(lit.Pos(), "excessively long constant: %s... (%d chars)", lit.Value[:10], len(lit.Value))
+			return constant.MakeUnknown()
+		}
 	}
 
 	v := constant.MakeFromLiteral(lit.Value, tokenForLitKind[lit.Kind], 0)
diff --git a/src/cmd/compile/internal/types2/expr.go b/src/cmd/compile/internal/types2/expr.go
index c66e115c1f..a1a626fb33 100644
--- a/src/cmd/compile/internal/types2/expr.go
+++ b/src/cmd/compile/internal/types2/expr.go
@@ -1154,6 +1154,23 @@ func (check *Checker) exprInternal(x *operand, e syntax.Expr, hint Type) exprKin
 		if e.Bad {
 			goto Error // error reported during parsing
 		}
+		switch e.Kind {
+		case syntax.IntLit, syntax.FloatLit, syntax.ImagLit:
+			// The max. mantissa precision for untyped numeric values
+			// is 512 bits, or 4048 bits for each of the two integer
+			// parts of a fraction for floating-point numbers that are
+			// represented accurately in the go/constant package.
+			// Constant literals that are longer than this many bits
+			// are not meaningful; and excessively long constants may
+			// consume a lot of space and time for a useless conversion.
+			// Cap constant length with a generous upper limit that also
+			// allows for separators between all digits.
+			const limit = 10000
+			if len(e.Value) > limit {
+				check.errorf(e, "excessively long constant: %s... (%d chars)", e.Value[:10], len(e.Value))
+				goto Error
+			}
+		}
 		x.setConst(e.Kind, e.Value)
 		if x.mode == invalid {
 			// The parser already establishes syntactic correctness.
diff --git a/test/const7.go b/test/const7.go
new file mode 100644
index 0000000000..9ffd678fc5
--- /dev/null
+++ b/test/const7.go
@@ -0,0 +1,77 @@
+// run
+
+// Copyright 2021 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Check that the compiler refuses excessively long constants.
+
+package main
+
+import (
+	"bytes"
+	"fmt"
+	"io/ioutil"
+	"log"
+	"os"
+	"os/exec"
+	"path/filepath"
+	"runtime"
+	"strings"
+)
+
+// testProg creates a package called name, with path dir/name.go,
+// which declares an untyped constant of the given length.
+// testProg compiles this package and checks for the absence or
+// presence of a constant literal error.
+func testProg(dir, name string, G_option, length int, ok bool) {
+	var buf bytes.Buffer
+
+	fmt.Fprintf(&buf,
+		"package %s; const _ = %s // %d digits",
+		name, strings.Repeat("9", length), length,
+	)
+
+	filename := filepath.Join(dir, fmt.Sprintf("%s.go", name))
+	if err := os.WriteFile(filename, buf.Bytes(), 0666); err != nil {
+		log.Fatal(err)
+	}
+
+	cmd := exec.Command("go", "tool", "compile", fmt.Sprintf("-G=%d", G_option), filename)
+	cmd.Dir = dir
+	output, err := cmd.CombinedOutput()
+
+	if ok {
+		// no error expected
+		if err != nil {
+			log.Fatalf("%s: compile failed unexpectedly: %v", name, err)
+		}
+		return
+	}
+
+	// error expected
+	if err == nil {
+		log.Fatalf("%s: compile succeeded unexpectedly", name)
+	}
+	if !bytes.Contains(output, []byte("excessively long constant")) {
+		log.Fatalf("%s: wrong compiler error message:\n%s\n", name, output)
+	}
+}
+
+func main() {
+	if runtime.GOOS == "js" || runtime.Compiler != "gc" {
+		return
+	}
+
+	dir, err := ioutil.TempDir("", "const7_")
+	if err != nil {
+		log.Fatalf("creating temp dir: %v\n", err)
+	}
+	defer os.RemoveAll(dir)
+
+	const limit = 10000 // compiler-internal constant length limit
+	testProg(dir, "x1", 0, limit, true)    // -G=0
+	testProg(dir, "x2", 0, limit+1, false) // -G=0
+	testProg(dir, "x1", 1, limit, true)    // -G=1 (new type checker)
+	testProg(dir, "x2", 1, limit+1, false) // -G=1 (new type checker)
+}