diff --git a/packages/opentelemetry-core/src/platform/browser/id.ts b/packages/opentelemetry-core/src/platform/browser/id.ts
index ab1c8188ac..02af4b220e 100644
--- a/packages/opentelemetry-core/src/platform/browser/id.ts
+++ b/packages/opentelemetry-core/src/platform/browser/id.ts
@@ -21,24 +21,38 @@ declare type WindowWithMsCrypto = Window & {
 const cryptoLib = window.crypto || (window as WindowWithMsCrypto).msCrypto;
 
 const SPAN_ID_BYTES = 8;
-const spanBytesArray = new Uint8Array(SPAN_ID_BYTES);
+const TRACE_ID_BYTES = 16;
+const randomBytesArray = new Uint8Array(TRACE_ID_BYTES);
 
 /** Returns a random 16-byte trace ID formatted as a 32-char hex string. */
 export function randomTraceId(): string {
-  return randomSpanId() + randomSpanId();
+  cryptoLib.getRandomValues(randomBytesArray);
+  return toHex(randomBytesArray.slice(0, TRACE_ID_BYTES));
 }
 
 /** Returns a random 8-byte span ID formatted as a 16-char hex string. */
 export function randomSpanId(): string {
-  let spanId = '';
-  cryptoLib.getRandomValues(spanBytesArray);
-  for (let i = 0; i < SPAN_ID_BYTES; i++) {
-    const hexStr = spanBytesArray[i].toString(16);
+  cryptoLib.getRandomValues(randomBytesArray);
+  return toHex(randomBytesArray.slice(0, SPAN_ID_BYTES));
+}
 
-    // Zero pad bytes whose hex values are single digit.
-    if (hexStr.length === 1) spanId += '0';
+/**
+ * Get the hex string representation of a byte array
+ *
+ * @param byteArray
+ */
+function toHex(byteArray: Uint8Array) {
+  const chars: number[] = new Array(byteArray.length * 2);
+  const alpha = 'a'.charCodeAt(0) - 10;
+  const digit = '0'.charCodeAt(0);
 
-    spanId += hexStr;
+  let p = 0;
+  for (let i = 0; i < byteArray.length; i++) {
+    let nibble = (byteArray[i] >>> 4) & 0xf;
+    chars[p++] = nibble > 9 ? nibble + alpha : nibble + digit;
+    nibble = byteArray[i] & 0xf;
+    chars[p++] = nibble > 9 ? nibble + alpha : nibble + digit;
   }
-  return spanId;
+
+  return String.fromCharCode.apply(null, chars);
 }
diff --git a/packages/opentelemetry-core/src/platform/node/id.ts b/packages/opentelemetry-core/src/platform/node/id.ts
index 75350e6eff..fa4cd6a916 100644
--- a/packages/opentelemetry-core/src/platform/node/id.ts
+++ b/packages/opentelemetry-core/src/platform/node/id.ts
@@ -17,13 +17,14 @@
 import * as crypto from 'crypto';
 
 const SPAN_ID_BYTES = 8;
+const TRACE_ID_BYTES = 16;
 
 /**
  * Returns a random 16-byte trace ID formatted/encoded as a 32 lowercase hex
  * characters corresponding to 128 bits.
  */
 export function randomTraceId(): string {
-  return randomSpanId() + randomSpanId();
+  return crypto.randomBytes(TRACE_ID_BYTES).toString('hex');
 }
 
 /**
diff --git a/packages/opentelemetry-core/test/platform/id.test.ts b/packages/opentelemetry-core/test/platform/id.test.ts
index 4a7226d392..8c4b7d0dc4 100644
--- a/packages/opentelemetry-core/test/platform/id.test.ts
+++ b/packages/opentelemetry-core/test/platform/id.test.ts
@@ -18,15 +18,31 @@ import * as assert from 'assert';
 import { randomSpanId, randomTraceId } from '../../src/platform';
 
 describe('randomTraceId', () => {
-  it('returns different 32-char hex strings', () => {
+  it('returns 32 character hex strings', () => {
     const traceId = randomTraceId();
     assert.ok(traceId.match(/[a-f0-9]{32}/));
+    assert.ok(!traceId.match(/^0+$/));
+  });
+
+  it('returns different ids on each call', () => {
+    const traceId1 = randomTraceId();
+    const traceId2 = randomTraceId();
+
+    assert.notDeepStrictEqual(traceId1, traceId2);
   });
 });
 
 describe('randomSpanId', () => {
-  it('returns different 16-char hex string', () => {
+  it('returns 16 character hex strings', () => {
     const spanId = randomSpanId();
     assert.ok(spanId.match(/[a-f0-9]{16}/));
+    assert.ok(!spanId.match(/^0+$/));
+  });
+
+  it('returns different ids on each call', () => {
+    const spanId1 = randomSpanId();
+    const spanId2 = randomSpanId();
+
+    assert.notDeepStrictEqual(spanId1, spanId2);
   });
 });