diff --git a/cmd/derive/derive.go b/cmd/derive/derive.go
new file mode 100644
index 0000000..dc45bac
--- /dev/null
+++ b/cmd/derive/derive.go
@@ -0,0 +1,267 @@
+package derive
+
+import (
+	"crypto/rsa"
+	"crypto/x509"
+	"encoding/pem"
+	"errors"
+	"fmt"
+	"io"
+	"io/fs"
+	"os"
+
+	"github.com/spf13/cobra"
+	"src.lwithers.me.uk/go/rsa/pkg/pemfile"
+	"src.lwithers.me.uk/go/stdinprompt"
+	"src.lwithers.me.uk/go/writefile"
+)
+
+var (
+	public bool
+	pkcs1  bool
+	derOut bool
+)
+
+// Register the "derive" subcommand.
+func Register(root *cobra.Command) {
+	cmd := &cobra.Command{
+		Use:   "derive input.pem [output.pem]",
+		Short: "Derive public key from private, and/or change encoding",
+		Run:   Derive,
+		Args:  cobra.RangeArgs(1, 2),
+	}
+
+	cmd.Flags().BoolVarP(&public, "public", "", false, "Only write public key part")
+	cmd.Flags().BoolVarP(&pkcs1, "pkcs1", "", false, "Write key as PKCS#1 rather than PKCS#8 / PKIX")
+	cmd.Flags().BoolVarP(&derOut, "der", "", false, "Write key as DER rather than PEM")
+
+	root.AddCommand(cmd)
+}
+
+// Derive a new form of output from the input file. Can derive public key from
+// private, and/or change encoding.
+func Derive(cmd *cobra.Command, args []string) {
+	if err := deriveAux(cmd, args); err != nil {
+		fmt.Fprintln(os.Stderr, err)
+		os.Exit(1)
+	}
+}
+
+func deriveAux(cmd *cobra.Command, args []string) error {
+	// prepare output stream
+	var (
+		out    io.Writer = os.Stdout
+		commit           = func() error { return nil }
+	)
+
+	if len(args) > 1 {
+		ff, f, err := writefile.New(args[1])
+		if err != nil {
+			return err
+		}
+		out = f
+		commit = func() error { return writefile.Commit(ff, f) }
+		defer writefile.Abort(f)
+	}
+
+	// prepare input stream
+	var (
+		in     io.Reader
+		infile string
+	)
+	if args[0] == "-" {
+		in = stdinprompt.New()
+		infile = "(stdin)"
+	} else {
+		infile = args[0]
+		f, err := os.Open(infile)
+		if err != nil {
+			return err
+		}
+		defer f.Close()
+		in = f
+	}
+
+	// read all input data to memory
+	raw, err := io.ReadAll(in)
+	if err != nil {
+		return err
+	}
+
+	// parse PEM blocks from the input
+	var (
+		didSomething bool
+		entryCount   int
+	)
+parseLoop:
+	for len(raw) > 0 {
+		block, rest := pem.Decode(raw)
+		if block == nil {
+			break parseLoop
+		}
+		raw = rest
+		entryCount++
+
+		derivation := deriveNoop
+		switch block.Type {
+		case pemfile.TypePKCS1PrivateKey:
+			didSomething = true
+			derivation = derivePKCS1PrivateKey
+
+		case pemfile.TypePKCS8PrivateKey:
+			didSomething = true
+			derivation = derivePKCS8PrivateKey
+
+		case pemfile.TypePKCS1PublicKey:
+			didSomething = true
+			derivation = derivePKCS1PublicKey
+
+		case pemfile.TypePKIXPublicKey:
+			didSomething = true
+			derivation = derivePKIXPublicKey
+
+		case pemfile.TypeX509Certificate:
+			didSomething = true
+			derivation = deriveX509Certificate
+		}
+
+		if err := derivation(out, block.Bytes); err != nil {
+			return fmt.Errorf("PEM block #%d (%s): %w", entryCount, block.Type, err)
+		}
+	}
+
+	if !didSomething {
+		return &fs.PathError{
+			Path: infile,
+			Op:   "parse PEM",
+			Err:  errors.New("no PEM-format RSA keys found"),
+		}
+	}
+
+	return commit()
+}
+
+func deriveNoop(io.Writer, []byte) error {
+	return nil
+}
+
+func derivePKCS1PrivateKey(out io.Writer, der []byte) error {
+	key, err := x509.ParsePKCS1PrivateKey(der)
+	if err != nil {
+		return err
+	}
+
+	if public {
+		return writePublic(out, &key.PublicKey)
+	}
+	return writePrivate(out, key)
+}
+
+func derivePKCS8PrivateKey(out io.Writer, der []byte) error {
+	key, err := x509.ParsePKCS8PrivateKey(der)
+	if err != nil {
+		return err
+	}
+
+	rsakey, ok := key.(*rsa.PrivateKey)
+	if !ok {
+		return errors.New("not an RSA key")
+	}
+
+	if public {
+		return writePublic(out, &rsakey.PublicKey)
+	}
+	return writePrivate(out, rsakey)
+}
+
+func derivePKCS1PublicKey(out io.Writer, der []byte) error {
+	key, err := x509.ParsePKCS1PublicKey(der)
+	if err != nil {
+		return err
+	}
+	return writePublic(out, key)
+}
+
+func derivePKIXPublicKey(out io.Writer, der []byte) error {
+	key, err := x509.ParsePKIXPublicKey(der)
+	if err != nil {
+		return err
+	}
+
+	rsakey, ok := key.(*rsa.PublicKey)
+	if !ok {
+		return errors.New("not an RSA key")
+	}
+
+	return writePublic(out, rsakey)
+}
+
+func deriveX509Certificate(out io.Writer, der []byte) error {
+	cert, err := x509.ParseCertificate(der)
+	if err != nil {
+		return err
+	}
+
+	key, ok := cert.PublicKey.(*rsa.PublicKey)
+	if !ok {
+		return errors.New("not an RSA key")
+	}
+
+	return writePublic(out, key)
+}
+
+func writePrivate(out io.Writer, key *rsa.PrivateKey) error {
+	var (
+		der     []byte
+		pemType string
+		err     error
+	)
+	if pkcs1 {
+		der = x509.MarshalPKCS1PrivateKey(key)
+		pemType = pemfile.TypePKCS1PrivateKey
+	} else {
+		der, err = x509.MarshalPKCS8PrivateKey(key)
+		pemType = pemfile.TypePKCS8PrivateKey
+	}
+	if err != nil {
+		return err
+	}
+
+	if derOut {
+		_, err = out.Write(der)
+		return err
+	}
+
+	return pem.Encode(out, &pem.Block{
+		Type:  pemType,
+		Bytes: der,
+	})
+}
+
+func writePublic(out io.Writer, key *rsa.PublicKey) error {
+	var (
+		der     []byte
+		pemType string
+		err     error
+	)
+	if pkcs1 {
+		der = x509.MarshalPKCS1PublicKey(key)
+		pemType = pemfile.TypePKCS1PublicKey
+	} else {
+		der, err = x509.MarshalPKIXPublicKey(key)
+		pemType = pemfile.TypePKIXPublicKey
+	}
+	if err != nil {
+		return err
+	}
+
+	if derOut {
+		_, err = out.Write(der)
+		return err
+	}
+
+	return pem.Encode(out, &pem.Block{
+		Type:  pemType,
+		Bytes: der,
+	})
+}
diff --git a/main.go b/main.go
index 4a7f40a..2ed9c98 100644
--- a/main.go
+++ b/main.go
@@ -6,6 +6,7 @@ import (
 	"github.com/spf13/cobra"
 	"src.lwithers.me.uk/go/rsa/cmd/ca"
 	"src.lwithers.me.uk/go/rsa/cmd/csr"
+	"src.lwithers.me.uk/go/rsa/cmd/derive"
 	"src.lwithers.me.uk/go/rsa/cmd/inspect"
 	"src.lwithers.me.uk/go/rsa/cmd/keygen"
 )
@@ -20,6 +21,7 @@ func main() {
 	keygen.Register(root)
 	csr.Register(root)
 	ca.Register(root)
+	derive.Register(root)
 
 	if err := root.Execute(); err != nil {
 		// error will already have been displayed