diff --git a/package.json b/package.json
index 706033f49f3..232b6f3dd6c 100644
--- a/package.json
+++ b/package.json
@@ -90,7 +90,7 @@
     "tinycolor2": "^1.3.0",
     "topojson-client": "^2.1.0",
     "webgl-context": "^2.2.0",
-    "world-calendars": "^1.0.0"
+    "world-calendars": "^1.0.3"
   },
   "devDependencies": {
     "brfs": "^1.4.3",
diff --git a/src/components/calendars/index.js b/src/components/calendars/index.js
index 076411f4739..f475ed62932 100644
--- a/src/components/calendars/index.js
+++ b/src/components/calendars/index.js
@@ -106,6 +106,7 @@ var DFLTRANGE = {
 var UNKNOWN = '##';
 var d3ToWorldCalendars = {
     'd': {'0': 'dd', '-': 'd'}, // 2-digit or unpadded day of month
+    'e': {'0': 'd', '-': 'd'}, // alternate, always unpadded day of month
     'a': {'0': 'D', '-': 'D'}, // short weekday name
     'A': {'0': 'DD', '-': 'DD'}, // full weekday name
     'j': {'0': 'oo', '-': 'o'}, // 3-digit or unpadded day of the year
@@ -119,12 +120,12 @@ var d3ToWorldCalendars = {
     'w': UNKNOWN, // day of the week [0(sunday),6]
     // combined format, we replace the date part with the world-calendar version
     // and the %X stays there for d3 to handle with time parts
-    '%c': {'0': 'D M m %X yyyy', '-': 'D M m %X yyyy'},
-    '%x': {'0': 'mm/dd/yyyy', '-': 'mm/dd/yyyy'}
+    'c': {'0': 'D M d %X yyyy', '-': 'D M d %X yyyy'},
+    'x': {'0': 'mm/dd/yyyy', '-': 'mm/dd/yyyy'}
 };
 
 function worldCalFmt(fmt, x, calendar) {
-    var dateJD = Math.floor(x + 0.05 / ONEDAY) + EPOCHJD,
+    var dateJD = Math.floor((x + 0.05) / ONEDAY) + EPOCHJD,
         cDate = getCal(calendar).fromJD(dateJD),
         i = 0,
         modifier, directive, directiveLen, directiveObj, replacementPart;
@@ -132,7 +133,7 @@ function worldCalFmt(fmt, x, calendar) {
         modifier = fmt.charAt(i + 1);
         if(modifier === '0' || modifier === '-' || modifier === '_') {
             directiveLen = 3;
-            directive = fmt.charAt(i + 1);
+            directive = fmt.charAt(i + 2);
             if(modifier === '_') modifier = '-';
         }
         else {
diff --git a/src/lib/dates.js b/src/lib/dates.js
index 503acd6ef48..d73c5bec82c 100644
--- a/src/lib/dates.js
+++ b/src/lib/dates.js
@@ -366,16 +366,19 @@ exports.cleanDate = function(v, dflt, calendar) {
  * d3's vocabulary:
  * %{n}f where n is the max number of digits of fractional seconds
  */
-var fracMatch = /%(\d?)f/g;
+var fracMatch = /%\d?f/g;
 function modDateFormat(fmt, x, calendar) {
-    var fm = fmt.match(fracMatch),
-        d = new Date(x);
-    if(fm) {
-        var digits = Math.min(+fm[1] || 6, 6),
-            fracSecs = String((x / 1000 % 1) + 2.0000005)
-                .substr(2, digits).replace(/0+$/, '') || '0';
-        fmt = fmt.replace(fracMatch, fracSecs);
-    }
+
+    fmt = fmt.replace(fracMatch, function(match) {
+        var digits = Math.min(+(match.charAt(1)) || 6, 6),
+            fracSecs = ((x / 1000 % 1) + 2)
+                .toFixed(digits)
+                .substr(2).replace(/0+$/, '') || '0';
+        return fracSecs;
+    });
+
+    var d = new Date(Math.floor(x + 0.05));
+
     if(isWorldCalendar(calendar)) {
         try {
             fmt = Registry.getComponentMethod('calendars', 'worldCalFmt')(fmt, x, calendar);
@@ -393,15 +396,39 @@ function modDateFormat(fmt, x, calendar) {
  *   tr: tickround ('M', 'S', or # digits)
  * only supports UTC times (where every day is 24 hours and 0 is at midnight)
  */
+var MAXSECONDS = [59, 59.9, 59.99, 59.999, 59.9999];
 function formatTime(x, tr) {
-    var timePart = mod(x, ONEDAY);
+    var timePart = mod(x + 0.05, ONEDAY);
 
     var timeStr = lpad(Math.floor(timePart / ONEHOUR), 2) + ':' +
         lpad(mod(Math.floor(timePart / ONEMIN), 60), 2);
 
     if(tr !== 'M') {
         if(!isNumeric(tr)) tr = 0; // should only be 'S'
-        timeStr += ':' + String(100 + d3.round(mod(x / ONESEC, 60), tr)).substr(1);
+
+        /*
+         * this is a weird one - and shouldn't come up unless people
+         * monkey with tick0 in weird ways, but we need to do something!
+         * IN PARTICULAR we had better not display garbage (see below)
+         * for numbers we always round to the nearest increment of the
+         * precision we're showing, and this seems like the right way to
+         * handle seconds and milliseconds, as they have a decimal point
+         * and people will interpret that to mean rounding like numbers.
+         * but for larger increments we floor the value: it's always
+         * 2013 until the ball drops on the new year. We could argue about
+         * which field it is where we start rounding (should 12:08:59
+         * round to 12:09 if we're stopping at minutes?) but for now I'll
+         * say we round seconds but floor everything else. BUT that means
+         * we need to never round up to 60 seconds, ie 23:59:60
+         */
+        var sec = Math.min(mod(x / ONESEC, 60), MAXSECONDS[tr]);
+
+        var secStr = (100 + sec).toFixed(tr).substr(1);
+        if(tr > 0) {
+            secStr = secStr.replace(/0+$/, '').replace(/[\.]$/, '');
+        }
+
+        timeStr += ':' + secStr;
     }
     return timeStr;
 }
@@ -459,7 +486,7 @@ exports.formatDate = function(x, fmt, tr, calendar) {
         catch(e) { return 'Invalid'; }
     }
     else {
-        var d = new Date(x);
+        var d = new Date(Math.floor(x + 0.05));
 
         if(tr === 'y') dateStr = yearFormat(d);
         else if(tr === 'm') dateStr = monthFormat(d);
diff --git a/test/image/baselines/gl3d_world-cals.png b/test/image/baselines/gl3d_world-cals.png
index ffbc6fc552e..2c192891d1d 100644
Binary files a/test/image/baselines/gl3d_world-cals.png and b/test/image/baselines/gl3d_world-cals.png differ
diff --git a/test/jasmine/tests/lib_date_test.js b/test/jasmine/tests/lib_date_test.js
index 9df1ecfd99a..2c5cd93e615 100644
--- a/test/jasmine/tests/lib_date_test.js
+++ b/test/jasmine/tests/lib_date_test.js
@@ -468,4 +468,138 @@ describe('dates', function() {
             });
         });
     });
+
+    describe('formatDate', function() {
+        function assertFormatRounds(ms, calendar, results) {
+            ['y', 'm', 'd', 'M', 'S', 1, 2, 3, 4].forEach(function(tr, i) {
+                expect(Lib.formatDate(ms, '', tr, calendar))
+                    .toBe(results[i], calendar);
+            });
+        }
+
+        it('should pick a format based on tickround if no format is provided', function() {
+            var ms = Lib.dateTime2ms('2012-08-13 06:19:34.5678');
+            assertFormatRounds(ms, 'gregorian', [
+                '2012',
+                'Aug 2012',
+                'Aug 13\n2012',
+                '06:19\nAug 13, 2012',
+                '06:19:35\nAug 13, 2012',
+                '06:19:34.6\nAug 13, 2012',
+                '06:19:34.57\nAug 13, 2012',
+                '06:19:34.568\nAug 13, 2012',
+                '06:19:34.5678\nAug 13, 2012'
+            ]);
+
+            // and for world calendars - in coptic this is 1728-12-07 (month=Meso)
+            assertFormatRounds(ms, 'coptic', [
+                '1728',
+                'Meso 1728',
+                'Meso 7\n1728',
+                '06:19\nMeso 7, 1728',
+                '06:19:35\nMeso 7, 1728',
+                '06:19:34.6\nMeso 7, 1728',
+                '06:19:34.57\nMeso 7, 1728',
+                '06:19:34.568\nMeso 7, 1728',
+                '06:19:34.5678\nMeso 7, 1728'
+            ]);
+        });
+
+        it('should accept custom formats using d3 specs even for world cals', function() {
+            var ms = Lib.dateTime2ms('2012-08-13 06:19:34.5678');
+            [
+                // some common formats (plotly workspace options)
+                ['%Y-%m-%d', '2012-08-13', '1728-12-07'],
+                ['%H:%M:%S', '06:19:34', '06:19:34'],
+                ['%Y-%m-%e %H:%M:%S', '2012-08-13 06:19:34', '1728-12-7 06:19:34'],
+                ['%A, %b %e', 'Monday, Aug 13', 'Pesnau, Meso 7'],
+
+                // test padding behavior
+                // world doesn't support space-padded (yet?)
+                ['%Y-%_m-%_d', '2012- 8-13', '1728-12-7'],
+                ['%Y-%-m-%-d', '2012-8-13', '1728-12-7'],
+
+                // and some strange ones to cover all fields
+                ['%a%j!%-j', 'Mon226!226', 'Pes337!337'],
+                [
+                    '%W or un or space padded-> %-W,%_W',
+                    '33 or un or space padded-> 33,33',
+                    '48 or un or space padded-> 48,48'
+                ],
+                [
+                    '%B \'%y WOY:%U DOW:%w',
+                    'August \'12 WOY:32 DOW:1',
+                    'Mesori \'28 WOY:## DOW:##' // world-cals doesn't support U or w
+                ],
+                [
+                    '%c && %x && .%2f .%f', // %<n>f is our addition
+                    'Mon Aug 13 06:19:34 2012 && 08/13/2012 && .57 .5678',
+                    'Pes Meso 7 06:19:34 1728 && 12/07/1728 && .57 .5678'
+                ]
+
+            ].forEach(function(v) {
+                var fmt = v[0],
+                    expectedGregorian = v[1],
+                    expectedCoptic = v[2];
+
+                // tickround is irrelevant here...
+                expect(Lib.formatDate(ms, fmt, 'y'))
+                    .toBe(expectedGregorian, fmt);
+                expect(Lib.formatDate(ms, fmt, 4, 'gregorian'))
+                    .toBe(expectedGregorian, fmt);
+                expect(Lib.formatDate(ms, fmt, 'y', 'coptic'))
+                    .toBe(expectedCoptic, fmt);
+            });
+        });
+
+        it('should not round up to 60 seconds', function() {
+            // see note in dates.js -> formatTime about this rounding
+            assertFormatRounds(-0.1, 'gregorian', [
+                '1969',
+                'Dec 1969',
+                'Dec 31\n1969',
+                '23:59\nDec 31, 1969',
+                '23:59:59\nDec 31, 1969',
+                '23:59:59.9\nDec 31, 1969',
+                '23:59:59.99\nDec 31, 1969',
+                '23:59:59.999\nDec 31, 1969',
+                '23:59:59.9999\nDec 31, 1969'
+            ]);
+
+            // in coptic this is Koi 22, 1686
+            assertFormatRounds(-0.1, 'coptic', [
+                '1686',
+                'Koi 1686',
+                'Koi 22\n1686',
+                '23:59\nKoi 22, 1686',
+                '23:59:59\nKoi 22, 1686',
+                '23:59:59.9\nKoi 22, 1686',
+                '23:59:59.99\nKoi 22, 1686',
+                '23:59:59.999\nKoi 22, 1686',
+                '23:59:59.9999\nKoi 22, 1686'
+            ]);
+
+            // and using the custom format machinery
+            expect(Lib.formatDate(-0.1, '%Y-%m-%d %H:%M:%S.%f'))
+                .toBe('1969-12-31 23:59:59.9999');
+            expect(Lib.formatDate(-0.1, '%Y-%m-%d %H:%M:%S.%f', null, 'coptic'))
+                .toBe('1686-04-22 23:59:59.9999');
+
+        });
+
+        it('should remove extra fractional second zeros', function() {
+            expect(Lib.formatDate(0.1, '', 4)).toBe('00:00:00.0001\nJan 1, 1970');
+            expect(Lib.formatDate(0.1, '', 3)).toBe('00:00:00\nJan 1, 1970');
+            expect(Lib.formatDate(0.1, '', 0)).toBe('00:00:00\nJan 1, 1970');
+            expect(Lib.formatDate(0.1, '', 'S')).toBe('00:00:00\nJan 1, 1970');
+            expect(Lib.formatDate(0.1, '', 3, 'coptic'))
+                .toBe('00:00:00\nKoi 23, 1686');
+
+            // because the decimal point is explicitly part of the format
+            // string here, we can't remove it OR the very first zero after it.
+            expect(Lib.formatDate(0.1, '%S.%f')).toBe('00.0001');
+            expect(Lib.formatDate(0.1, '%S.%3f')).toBe('00.0');
+        });
+
+    });
 });