The OpenSSL command line knows nothing about JWK, but a P-256 public key can still be converted both ways with openssl pkey and a few shell tools: the SPKI DER ends with the point 04 ‖ x ‖ y, and a JWK's x and y prepended with the fixed SPKI header become a DER key again. The run converts the RFC 7515 key to a JWK and back to an identical PEM.

to-jwk.sh — the last 64 bytes of the SPKI DER are x and y

1# PEM -> JWK for a P-256 key: the SPKI DER ends with the point 04 ‖ x ‖ y
2b64url() { openssl base64 -A | tr '+/' '-_' | tr -d '='; }
3spki=$(openssl pkey -pubin -in pub.pem -outform DER | xxd -p | tr -d '\n')
4x=$(printf '%s' "${spki: -128:64}" | xxd -r -p | b64url)
5y=$(printf '%s' "${spki: -64}" | xxd -r -p | b64url)
6printf '{"kty":"EC","crv":"P-256","x":"%s","y":"%s"}\n' "$x" "$y" | tee out.jwk.json

to-pem.sh — fixed SPKI header + 04 + x + y, then openssl pkey

1# JWK -> PEM for a P-256 key: the fixed 26-byte SPKI header, then 04 ‖ x ‖ y
2b64url_decode() { local v; v=$(tr '_-' '/+' <<< "$1"); while (( ${#v} % 4 )); do v+="="; done; openssl base64 -d -A <<< "$v"; }
3json_field() { grep -o "\"$1\" *: *\"[^\"]*\"" pub.jwk.json | sed 's/.*: *"\(.*\)"/\1/'; }
4{
5  printf '3059301306072a8648ce3d020106082a8648ce3d03010703420004' | xxd -r -p
6  b64url_decode "$(json_field x)"
7  b64url_decode "$(json_field y)"
8} > pub.der
9openssl pkey -pubin -inform DER -in pub.der -out out.pem   # also checks that the point is on the curve
10cat out.pem

How it works

openssl pkey -pubin -outform DER gives the 91-byte SPKI of a P-256 key: a 26-byte header, the byte 04, and the 32-byte coordinates x and y.
xxd -r -p turns the hex back into bytes, and the b64url helper encodes them in the unpadded base64url form JWK uses.
For the reverse, the header 3059…420004 is the same for every P-256 public key; the decoded x and y complete the DER.
openssl pkey -pubin -inform DER parses that DER — which checks that the point is on the curve — and writes the standard PEM.

Gotchas

The offsets and the header are specific to P-256 public keys. P-384 keys have a different header and 48-byte coordinates, RSA and Ed25519 keys a different structure altogether.
A point that is not on the curve fails with the misleading Could not find private key of Public Key from pub.der (and STORE routines … unsupported): the problem is the point, not a missing private key.
Base64url has no padding and uses -_; openssl base64 -d expects standard base64 with padding, which b64url_decode restores first.
json_field is a grep over the JSON, good enough for a single well-formed JWK; for JWKS files or arbitrary JSON, use jq or one of the language recipes.

How to convert a PEM public key to a JWK and back with OpenSSL

How it works

Gotchas

Related recipes