diff --git a/doc/api/crypto.md b/doc/api/crypto.md
index 7073cf2249d658..4c2354f52eb44d 100644
--- a/doc/api/crypto.md
+++ b/doc/api/crypto.md
@@ -656,6 +656,54 @@ assert.strictEqual(aliceSecret.toString('hex'), bobSecret.toString('hex'));
 // OK
 ```
 
+### ECDH.convertKey(key, curve[, inputEncoding[, outputEncoding[, format]]])
+<!-- YAML
+added: REPLACEME
+-->
+
+- `key` {string | Buffer | TypedArray | DataView}
+- `curve` {string}
+- `inputEncoding` {string}
+- `outputEncoding` {string}
+- `format` {string} Defaults to `uncompressed`.
+
+Converts the EC Diffie-Hellman public key specified by `key` and `curve` to the
+format specified by `format`. The `format` argument specifies point encoding
+and can be `'compressed'`, `'uncompressed'` or `'hybrid'`. The supplied key is
+interpreted using the specified `inputEncoding`, and the returned key is encoded
+using the specified `outputEncoding`. Encodings can be `'latin1'`, `'hex'`,
+or `'base64'`.
+
+Use [`crypto.getCurves()`][] to obtain a list of available curve names.
+On recent OpenSSL releases, `openssl ecparam -list_curves` will also display
+the name and description of each available elliptic curve.
+
+If `format` is not specified the point will be returned in `'uncompressed'`
+format.
+
+If the `inputEncoding` is not provided, `key` is expected to be a [`Buffer`][],
+`TypedArray`, or `DataView`.
+
+Example (uncompressing a key):
+
+```js
+const { ECDH } = require('crypto');
+
+const ecdh = ECDH('secp256k1');
+ecdh.generateKeys();
+
+const compressedKey = ecdh.getPublicKey('hex', 'compressed');
+
+const uncompressedKey = ECDH.convertKey(compressedKey,
+                                        'secp256k1',
+                                        'hex',
+                                        'hex',
+                                        'uncompressed');
+
+// the converted key and the uncompressed public key should be the same
+console.log(uncompressedKey === ecdh.getPublicKey('hex'));
+```
+
 ### ecdh.computeSecret(otherPublicKey[, inputEncoding][, outputEncoding])
 <!-- YAML
 added: v0.11.14
diff --git a/lib/internal/crypto/diffiehellman.js b/lib/internal/crypto/diffiehellman.js
index f6d525c215ca63..793f3fb351460e 100644
--- a/lib/internal/crypto/diffiehellman.js
+++ b/lib/internal/crypto/diffiehellman.js
@@ -14,7 +14,8 @@ const {
 const {
   DiffieHellman: _DiffieHellman,
   DiffieHellmanGroup: _DiffieHellmanGroup,
-  ECDH: _ECDH
+  ECDH: _ECDH,
+  ECDHConvertKey: _ECDHConvertKey
 } = process.binding('crypto');
 const {
   POINT_CONVERSION_COMPRESSED,
@@ -84,11 +85,9 @@ DiffieHellmanGroup.prototype.generateKeys =
     dhGenerateKeys;
 
 function dhGenerateKeys(encoding) {
-  var keys = this._handle.generateKeys();
+  const keys = this._handle.generateKeys();
   encoding = encoding || getDefaultEncoding();
-  if (encoding && encoding !== 'buffer')
-    keys = keys.toString(encoding);
-  return keys;
+  return encode(keys, encoding);
 }
 
 
@@ -100,12 +99,10 @@ function dhComputeSecret(key, inEnc, outEnc) {
   const encoding = getDefaultEncoding();
   inEnc = inEnc || encoding;
   outEnc = outEnc || encoding;
-  var ret = this._handle.computeSecret(toBuf(key, inEnc));
+  const ret = this._handle.computeSecret(toBuf(key, inEnc));
   if (typeof ret === 'string')
     throw new ERR_CRYPTO_ECDH_INVALID_PUBLIC_KEY();
-  if (outEnc && outEnc !== 'buffer')
-    ret = ret.toString(outEnc);
-  return ret;
+  return encode(ret, outEnc);
 }
 
 
@@ -114,11 +111,9 @@ DiffieHellmanGroup.prototype.getPrime =
     dhGetPrime;
 
 function dhGetPrime(encoding) {
-  var prime = this._handle.getPrime();
+  const prime = this._handle.getPrime();
   encoding = encoding || getDefaultEncoding();
-  if (encoding && encoding !== 'buffer')
-    prime = prime.toString(encoding);
-  return prime;
+  return encode(prime, encoding);
 }
 
 
@@ -127,11 +122,9 @@ DiffieHellmanGroup.prototype.getGenerator =
     dhGetGenerator;
 
 function dhGetGenerator(encoding) {
-  var generator = this._handle.getGenerator();
+  const generator = this._handle.getGenerator();
   encoding = encoding || getDefaultEncoding();
-  if (encoding && encoding !== 'buffer')
-    generator = generator.toString(encoding);
-  return generator;
+  return encode(generator, encoding);
 }
 
 
@@ -140,11 +133,9 @@ DiffieHellmanGroup.prototype.getPublicKey =
     dhGetPublicKey;
 
 function dhGetPublicKey(encoding) {
-  var key = this._handle.getPublicKey();
+  const key = this._handle.getPublicKey();
   encoding = encoding || getDefaultEncoding();
-  if (encoding && encoding !== 'buffer')
-    key = key.toString(encoding);
-  return key;
+  return encode(key, encoding);
 }
 
 
@@ -153,11 +144,9 @@ DiffieHellmanGroup.prototype.getPrivateKey =
     dhGetPrivateKey;
 
 function dhGetPrivateKey(encoding) {
-  var key = this._handle.getPrivateKey();
+  const key = this._handle.getPrivateKey();
   encoding = encoding || getDefaultEncoding();
-  if (encoding && encoding !== 'buffer')
-    key = key.toString(encoding);
-  return key;
+  return encode(key, encoding);
 }
 
 
@@ -197,7 +186,40 @@ ECDH.prototype.generateKeys = function generateKeys(encoding, format) {
 };
 
 ECDH.prototype.getPublicKey = function getPublicKey(encoding, format) {
-  var f;
+  const f = getFormat(format);
+  const key = this._handle.getPublicKey(f);
+  encoding = encoding || getDefaultEncoding();
+  return encode(key, encoding);
+};
+
+ECDH.convertKey = function convertKey(key, curve, inEnc, outEnc, format) {
+  if (typeof key !== 'string' && !isArrayBufferView(key)) {
+    throw new ERR_INVALID_ARG_TYPE(
+      'key',
+      ['string', 'Buffer', 'TypedArray', 'DataView']
+    );
+  }
+
+  if (typeof curve !== 'string') {
+    throw new ERR_INVALID_ARG_TYPE('curve', 'string');
+  }
+
+  const encoding = getDefaultEncoding();
+  inEnc = inEnc || encoding;
+  outEnc = outEnc || encoding;
+  const f = getFormat(format);
+  const convertedKey = _ECDHConvertKey(toBuf(key, inEnc), curve, f);
+  return encode(convertedKey, outEnc);
+};
+
+function encode(buffer, encoding) {
+  if (encoding && encoding !== 'buffer')
+    buffer = buffer.toString(encoding);
+  return buffer;
+}
+
+function getFormat(format) {
+  let f;
   if (format) {
     if (format === 'compressed')
       f = POINT_CONVERSION_COMPRESSED;
@@ -211,12 +233,8 @@ ECDH.prototype.getPublicKey = function getPublicKey(encoding, format) {
   } else {
     f = POINT_CONVERSION_UNCOMPRESSED;
   }
-  var key = this._handle.getPublicKey(f);
-  encoding = encoding || getDefaultEncoding();
-  if (encoding && encoding !== 'buffer')
-    key = key.toString(encoding);
-  return key;
-};
+  return f;
+}
 
 module.exports = {
   DiffieHellman,
diff --git a/src/node_crypto.cc b/src/node_crypto.cc
index b56b74b00515c1..3253b701f3bb82 100644
--- a/src/node_crypto.cc
+++ b/src/node_crypto.cc
@@ -4731,31 +4731,31 @@ void ECDH::GenerateKeys(const FunctionCallbackInfo<Value>& args) {
 }
 
 
-EC_POINT* ECDH::BufferToPoint(char* data, size_t len) {
+EC_POINT* ECDH::BufferToPoint(Environment* env,
+                              const EC_GROUP* group,
+                              char* data,
+                              size_t len) {
   EC_POINT* pub;
   int r;
 
-  pub = EC_POINT_new(group_);
+  pub = EC_POINT_new(group);
   if (pub == nullptr) {
-    env()->ThrowError("Failed to allocate EC_POINT for a public key");
+    env->ThrowError("Failed to allocate EC_POINT for a public key");
     return nullptr;
   }
 
   r = EC_POINT_oct2point(
-      group_,
+      group,
       pub,
       reinterpret_cast<unsigned char*>(data),
       len,
       nullptr);
   if (!r) {
-    goto fatal;
+    EC_POINT_free(pub);
+    return nullptr;
   }
 
   return pub;
-
- fatal:
-  EC_POINT_free(pub);
-  return nullptr;
 }
 
 
@@ -4772,7 +4772,9 @@ void ECDH::ComputeSecret(const FunctionCallbackInfo<Value>& args) {
   if (!ecdh->IsKeyPairValid())
     return env->ThrowError("Invalid key pair");
 
-  EC_POINT* pub = ecdh->BufferToPoint(Buffer::Data(args[0]),
+  EC_POINT* pub = ECDH::BufferToPoint(env,
+                                      ecdh->group_,
+                                      Buffer::Data(args[0]),
                                       Buffer::Length(args[0]));
   if (pub == nullptr) {
     args.GetReturnValue().Set(
@@ -4921,7 +4923,9 @@ void ECDH::SetPublicKey(const FunctionCallbackInfo<Value>& args) {
 
   MarkPopErrorOnReturn mark_pop_error_on_return;
 
-  EC_POINT* pub = ecdh->BufferToPoint(Buffer::Data(args[0].As<Object>()),
+  EC_POINT* pub = ECDH::BufferToPoint(env,
+                                      ecdh->group_,
+                                      Buffer::Data(args[0].As<Object>()),
                                       Buffer::Length(args[0].As<Object>()));
   if (pub == nullptr)
     return env->ThrowError("Failed to convert Buffer to EC_POINT");
@@ -5597,6 +5601,61 @@ void ExportChallenge(const FunctionCallbackInfo<Value>& args) {
   args.GetReturnValue().Set(outString);
 }
 
+
+// Convert the input public key to compressed, uncompressed, or hybrid formats.
+void ConvertKey(const FunctionCallbackInfo<Value>& args) {
+  Environment* env = Environment::GetCurrent(args);
+
+  CHECK_EQ(args.Length(), 3);
+
+  size_t len = Buffer::Length(args[0]);
+  if (len == 0)
+    return args.GetReturnValue().SetEmptyString();
+
+  node::Utf8Value curve(env->isolate(), args[1]);
+
+  int nid = OBJ_sn2nid(*curve);
+  if (nid == NID_undef)
+    return env->ThrowTypeError("Invalid ECDH curve name");
+
+  EC_GROUP* group = EC_GROUP_new_by_curve_name(nid);
+  if (group == nullptr)
+    return env->ThrowError("Failed to get EC_GROUP");
+
+  EC_POINT* pub = ECDH::BufferToPoint(env,
+                                      group,
+                                      Buffer::Data(args[0]),
+                                      len);
+
+  std::shared_ptr<void> cleanup(nullptr, [group, pub] (...) {
+    EC_GROUP_free(group);
+    EC_POINT_free(pub);
+  });
+
+  if (pub == nullptr)
+    return env->ThrowError("Failed to convert Buffer to EC_POINT");
+
+  point_conversion_form_t form =
+      static_cast<point_conversion_form_t>(args[2]->Uint32Value());
+
+  int size = EC_POINT_point2oct(group, pub, form, nullptr, 0, nullptr);
+  if (size == 0)
+    return env->ThrowError("Failed to get public key length");
+
+  unsigned char* out = node::Malloc<unsigned char>(size);
+
+  int r = EC_POINT_point2oct(group, pub, form, out, size, nullptr);
+  if (r != size) {
+    free(out);
+    return env->ThrowError("Failed to get public key");
+  }
+
+  Local<Object> buf =
+      Buffer::New(env, reinterpret_cast<char*>(out), size).ToLocalChecked();
+  args.GetReturnValue().Set(buf);
+}
+
+
 void TimingSafeEqual(const FunctionCallbackInfo<Value>& args) {
   CHECK(Buffer::HasInstance(args[0]));
   CHECK(Buffer::HasInstance(args[1]));
@@ -5739,6 +5798,8 @@ void InitCrypto(Local<Object> target,
   env->SetMethod(target, "certVerifySpkac", VerifySpkac);
   env->SetMethod(target, "certExportPublicKey", ExportPublicKey);
   env->SetMethod(target, "certExportChallenge", ExportChallenge);
+
+  env->SetMethod(target, "ECDHConvertKey", ConvertKey);
 #ifndef OPENSSL_NO_ENGINE
   env->SetMethod(target, "setEngine", SetEngine);
 #endif  // !OPENSSL_NO_ENGINE
diff --git a/src/node_crypto.h b/src/node_crypto.h
index 668781aca9da1e..1b2170ef851f95 100644
--- a/src/node_crypto.h
+++ b/src/node_crypto.h
@@ -627,6 +627,10 @@ class ECDH : public BaseObject {
   }
 
   static void Initialize(Environment* env, v8::Local<v8::Object> target);
+  static EC_POINT* BufferToPoint(Environment* env,
+                                 const EC_GROUP* group,
+                                 char* data,
+                                 size_t len);
 
  protected:
   ECDH(Environment* env, v8::Local<v8::Object> wrap, EC_KEY* key)
@@ -645,8 +649,6 @@ class ECDH : public BaseObject {
   static void GetPublicKey(const v8::FunctionCallbackInfo<v8::Value>& args);
   static void SetPublicKey(const v8::FunctionCallbackInfo<v8::Value>& args);
 
-  EC_POINT* BufferToPoint(char* data, size_t len);
-
   bool IsKeyPairValid();
   bool IsKeyValidForCurve(const BIGNUM* private_key);
 
diff --git a/test/parallel/test-crypto-ecdh-convert-key.js b/test/parallel/test-crypto-ecdh-convert-key.js
new file mode 100644
index 00000000000000..407178a1953250
--- /dev/null
+++ b/test/parallel/test-crypto-ecdh-convert-key.js
@@ -0,0 +1,101 @@
+'use strict';
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+
+const assert = require('assert');
+
+const { ECDH, getCurves } = require('crypto');
+
+// A valid private key for the secp256k1 curve.
+const cafebabeKey = 'cafebabe'.repeat(8);
+// Associated compressed and uncompressed public keys (points).
+const cafebabePubPtComp =
+    '03672a31bfc59d3f04548ec9b7daeeba2f61814e8ccc40448045007f5479f693a3';
+const cafebabePubPtUnComp =
+    '04672a31bfc59d3f04548ec9b7daeeba2f61814e8ccc40448045007f5479f693a3' +
+    '2e02c7f93d13dc2732b760ca377a5897b9dd41a1c1b29dc0442fdce6d0a04d1d';
+
+// Invalid test: key argument is undefined.
+common.expectsError(
+  () => ECDH.convertKey(),
+  {
+    code: 'ERR_INVALID_ARG_TYPE',
+    type: TypeError,
+  });
+
+// Invalid test: curve argument is undefined.
+common.expectsError(
+  () => ECDH.convertKey(cafebabePubPtComp),
+  {
+    code: 'ERR_INVALID_ARG_TYPE',
+    type: TypeError,
+  });
+
+// Invalid test: curve argument is invalid.
+common.expectsError(
+  () => ECDH.convertKey(cafebabePubPtComp, 'badcurve'),
+  {
+    type: TypeError,
+    message: 'Invalid ECDH curve name'
+  });
+
+if (getCurves().includes('secp256k1')) {
+  // Invalid test: format argument is undefined.
+  common.expectsError(
+    () => ECDH.convertKey(cafebabePubPtComp, 'secp256k1', 'hex', 'hex', 10),
+    {
+      code: 'ERR_CRYPTO_ECDH_INVALID_FORMAT',
+      type: TypeError,
+      message: 'Invalid ECDH format: 10'
+    });
+
+  // Point formats.
+  let uncompressed = ECDH.convertKey(cafebabePubPtComp,
+                                     'secp256k1',
+                                     'hex',
+                                     'buffer',
+                                     'uncompressed');
+  let compressed = ECDH.convertKey(cafebabePubPtComp,
+                                   'secp256k1',
+                                   'hex',
+                                   'buffer',
+                                   'compressed');
+  let hybrid = ECDH.convertKey(cafebabePubPtComp,
+                               'secp256k1',
+                               'hex',
+                               'buffer',
+                               'hybrid');
+  assert.strictEqual(uncompressed[0], 4);
+  let firstByte = compressed[0];
+  assert(firstByte === 2 || firstByte === 3);
+  firstByte = hybrid[0];
+  assert(firstByte === 6 || firstByte === 7);
+
+  // Format conversion from hex to hex
+  uncompressed = ECDH.convertKey(cafebabePubPtComp,
+                                 'secp256k1',
+                                 'hex',
+                                 'hex',
+                                 'uncompressed');
+  compressed = ECDH.convertKey(cafebabePubPtComp,
+                               'secp256k1',
+                               'hex',
+                               'hex',
+                               'compressed');
+  hybrid = ECDH.convertKey(cafebabePubPtComp,
+                           'secp256k1',
+                           'hex',
+                           'hex',
+                           'hybrid');
+  assert.strictEqual(uncompressed, cafebabePubPtUnComp);
+  assert.strictEqual(compressed, cafebabePubPtComp);
+
+  // Compare to getPublicKey.
+  const ecdh1 = ECDH('secp256k1');
+  ecdh1.generateKeys();
+  ecdh1.setPrivateKey(cafebabeKey, 'hex');
+  assert.strictEqual(ecdh1.getPublicKey('hex', 'uncompressed'), uncompressed);
+  assert.strictEqual(ecdh1.getPublicKey('hex', 'compressed'), compressed);
+  assert.strictEqual(ecdh1.getPublicKey('hex', 'hybrid'), hybrid);
+}