diff --git a/src/plot_api/plot_api.js b/src/plot_api/plot_api.js
index 0e26c4b8aa9..745e50ce7a3 100644
--- a/src/plot_api/plot_api.js
+++ b/src/plot_api/plot_api.js
@@ -1296,7 +1296,8 @@ function _restyle(gd, aobj, _traces) {
         'tilt', 'tiltaxis', 'depth', 'direction', 'rotation', 'pull',
         'line.showscale', 'line.cauto', 'line.autocolorscale', 'line.reversescale',
         'marker.line.showscale', 'marker.line.cauto', 'marker.line.autocolorscale', 'marker.line.reversescale',
-        'xcalendar', 'ycalendar'
+        'xcalendar', 'ycalendar',
+        'cumulative', 'cumulative.enabled', 'cumulative.direction', 'cumulative.currentbin'
     ];
 
     for(i = 0; i < traces.length; i++) {
diff --git a/src/plots/cartesian/axes.js b/src/plots/cartesian/axes.js
index 64dc21e4b71..14317b07cf8 100644
--- a/src/plots/cartesian/axes.js
+++ b/src/plots/cartesian/axes.js
@@ -609,7 +609,10 @@ function autoShiftNumericBins(binStart, data, ax, dataMin, dataMax) {
         // otherwise start half an integer down regardless of
         // the bin size, just enough to clear up endpoint
         // ambiguity about which integers are in which bins.
-        else binStart -= 0.5;
+        else {
+            binStart -= 0.5;
+            if(binStart + ax.dtick < dataMin) binStart += ax.dtick;
+        }
     }
     else if(midcount < dataCount * 0.1) {
         if(edgecount > dataCount * 0.3 ||
diff --git a/src/traces/histogram/attributes.js b/src/traces/histogram/attributes.js
index e6d1dad2593..889dda231fc 100644
--- a/src/traces/histogram/attributes.js
+++ b/src/traces/histogram/attributes.js
@@ -56,21 +56,69 @@ module.exports = {
             'If **, the span of each bar corresponds to the number of',
             'occurrences (i.e. the number of data points lying inside the bins).',
 
-            'If *percent*, the span of each bar corresponds to the percentage',
-            'of occurrences with respect to the total number of sample points',
-            '(here, the sum of all bin area equals 100%).',
+            'If *percent* / *probability*, the span of each bar corresponds to',
+            'the percentage / fraction of occurrences with respect to the total',
+            'number of sample points',
+            '(here, the sum of all bin HEIGHTS equals 100% / 1).',
 
             'If *density*, the span of each bar corresponds to the number of',
             'occurrences in a bin divided by the size of the bin interval',
-            '(here, the sum of all bin area equals the',
+            '(here, the sum of all bin AREAS equals the',
             'total number of sample points).',
 
-            'If *probability density*, the span of each bar corresponds to the',
+            'If *probability density*, the area of each bar corresponds to the',
             'probability that an event will fall into the corresponding bin',
-            '(here, the sum of all bin area equals 1).'
+            '(here, the sum of all bin AREAS equals 1).'
         ].join(' ')
     },
 
+    cumulative: {
+        enabled: {
+            valType: 'boolean',
+            dflt: false,
+            role: 'info',
+            description: [
+                'If true, display the cumulative distribution by summing the',
+                'binned values. Use the `direction` and `centralbin` attributes',
+                'to tune the accumulation method.',
+                'Note: in this mode, the *density* `histnorm` settings behave',
+                'the same as their equivalents without *density*:',
+                '** and *density* both rise to the number of data points, and',
+                '*probability* and *probability density* both rise to the',
+                'number of sample points.'
+            ].join(' ')
+        },
+
+        direction: {
+            valType: 'enumerated',
+            values: ['increasing', 'decreasing'],
+            dflt: 'increasing',
+            role: 'info',
+            description: [
+                'Only applies if cumulative is enabled.',
+                'If *increasing* (default) we sum all prior bins, so the result',
+                'increases from left to right. If *decreasing* we sum later bins',
+                'so the result decreases from left to right.'
+            ].join(' ')
+        },
+
+        currentbin: {
+            valType: 'enumerated',
+            values: ['include', 'exclude', 'half'],
+            dflt: 'include',
+            role: 'info',
+            description: [
+                'Only applies if cumulative is enabled.',
+                'Sets whether the current bin is included, excluded, or has half',
+                'of its value included in the current cumulative value.',
+                '*include* is the default for compatibility with various other',
+                'tools, however it introduces a half-bin bias to the results.',
+                '*exclude* makes the opposite half-bin bias, and *half* removes',
+                'it.'
+            ].join(' ')
+        }
+    },
+
     autobinx: {
         valType: 'boolean',
         dflt: null,
diff --git a/src/traces/histogram/bin_functions.js b/src/traces/histogram/bin_functions.js
index db631f00c73..d4219667903 100644
--- a/src/traces/histogram/bin_functions.js
+++ b/src/traces/histogram/bin_functions.js
@@ -47,8 +47,9 @@ module.exports = {
                 return v;
             }
             else if(size[n] > v) {
+                var delta = v - size[n];
                 size[n] = v;
-                return v - size[n];
+                return delta;
             }
         }
         return 0;
@@ -63,8 +64,9 @@ module.exports = {
                 return v;
             }
             else if(size[n] < v) {
+                var delta = v - size[n];
                 size[n] = v;
-                return v - size[n];
+                return delta;
             }
         }
         return 0;
diff --git a/src/traces/histogram/calc.js b/src/traces/histogram/calc.js
index 807afef8cf2..9b079438b98 100644
--- a/src/traces/histogram/calc.js
+++ b/src/traces/histogram/calc.js
@@ -33,22 +33,38 @@ module.exports = function calc(gd, trace) {
             trace.orientation === 'h' ? (trace.yaxis || 'y') : (trace.xaxis || 'x')),
         maindata = trace.orientation === 'h' ? 'y' : 'x',
         counterdata = {x: 'y', y: 'x'}[maindata],
-        calendar = trace[maindata + 'calendar'];
+        calendar = trace[maindata + 'calendar'],
+        cumulativeSpec = trace.cumulative;
 
     cleanBins(trace, pa, maindata);
 
     // prepare the raw data
     var pos0 = pa.makeCalcdata(trace, maindata);
+
     // calculate the bins
-    if((trace['autobin' + maindata] !== false) || !(maindata + 'bins' in trace)) {
-        trace[maindata + 'bins'] = Axes.autoBin(pos0, pa, trace['nbins' + maindata], false, calendar);
+    var binAttr = maindata + 'bins',
+        binspec;
+    if((trace['autobin' + maindata] !== false) || !(binAttr in trace)) {
+        binspec = Axes.autoBin(pos0, pa, trace['nbins' + maindata], false, calendar);
+
+        // adjust for CDF edge cases
+        if(cumulativeSpec.enabled && (cumulativeSpec.currentbin !== 'include')) {
+            if(cumulativeSpec.direction === 'decreasing') {
+                binspec.start = pa.c2r(pa.r2c(binspec.start) - binspec.size);
+            }
+            else {
+                binspec.end = pa.c2r(pa.r2c(binspec.end) + binspec.size);
+            }
+        }
 
-        // copy bin info back to the source data.
-        trace._input[maindata + 'bins'] = trace[maindata + 'bins'];
+        // copy bin info back to the source and full data.
+        trace._input[binAttr] = trace[binAttr] = binspec;
+    }
+    else {
+        binspec = trace[binAttr];
     }
 
-    var binspec = trace[maindata + 'bins'],
-        nonuniformBins = typeof binspec.size === 'string',
+    var nonuniformBins = typeof binspec.size === 'string',
         bins = nonuniformBins ? [] : binspec,
         // make the empty bin array
         i2,
@@ -59,8 +75,16 @@ module.exports = function calc(gd, trace) {
         total = 0,
         norm = trace.histnorm,
         func = trace.histfunc,
-        densitynorm = norm.indexOf('density') !== -1,
-        extremefunc = func === 'max' || func === 'min',
+        densitynorm = norm.indexOf('density') !== -1;
+
+    if(cumulativeSpec.enabled && densitynorm) {
+        // we treat "cumulative" like it means "integral" if you use a density norm,
+        // which in the end means it's the same as without "density"
+        norm = norm.replace(/ ?density$/, '');
+        densitynorm = false;
+    }
+
+    var extremefunc = func === 'max' || func === 'min',
         sizeinit = extremefunc ? null : 0,
         binfunc = binFunctions.count,
         normfunc = normFunctions[norm],
@@ -115,6 +139,10 @@ module.exports = function calc(gd, trace) {
     if(doavg) total = doAvg(size, counts);
     if(normfunc) normfunc(size, total, inc);
 
+    // after all normalization etc, now we can accumulate if desired
+    if(cumulativeSpec.enabled) cdf(size, cumulativeSpec.direction, cumulativeSpec.currentbin);
+
+
     var serieslen = Math.min(pos.length, size.length),
         cd = [],
         firstNonzero = 0,
@@ -142,3 +170,57 @@ module.exports = function calc(gd, trace) {
 
     return cd;
 };
+
+function cdf(size, direction, currentbin) {
+    var i,
+        vi,
+        prevSum;
+
+    function firstHalfPoint(i) {
+        prevSum = size[i];
+        size[i] /= 2;
+    }
+
+    function nextHalfPoint(i) {
+        vi = size[i];
+        size[i] = prevSum + vi / 2;
+        prevSum += vi;
+    }
+
+    if(currentbin === 'half') {
+
+        if(direction === 'increasing') {
+            firstHalfPoint(0);
+            for(i = 1; i < size.length; i++) {
+                nextHalfPoint(i);
+            }
+        }
+        else {
+            firstHalfPoint(size.length - 1);
+            for(i = size.length - 2; i >= 0; i--) {
+                nextHalfPoint(i);
+            }
+        }
+    }
+    else if(direction === 'increasing') {
+        for(i = 1; i < size.length; i++) {
+            size[i] += size[i - 1];
+        }
+
+        // 'exclude' is identical to 'include' just shifted one bin over
+        if(currentbin === 'exclude') {
+            size.unshift(0);
+            size.pop();
+        }
+    }
+    else {
+        for(i = size.length - 2; i >= 0; i--) {
+            size[i] += size[i + 1];
+        }
+
+        if(currentbin === 'exclude') {
+            size.push(0);
+            size.shift();
+        }
+    }
+}
diff --git a/src/traces/histogram/defaults.js b/src/traces/histogram/defaults.js
index 3f2635da7b7..534bddf3f8f 100644
--- a/src/traces/histogram/defaults.js
+++ b/src/traces/histogram/defaults.js
@@ -27,6 +27,12 @@ module.exports = function supplyDefaults(traceIn, traceOut, defaultColor, layout
     var x = coerce('x'),
         y = coerce('y');
 
+    var cumulative = coerce('cumulative.enabled');
+    if(cumulative) {
+        coerce('cumulative.direction');
+        coerce('cumulative.currentbin');
+    }
+
     coerce('text');
 
     var orientation = coerce('orientation', (y && !x) ? 'h' : 'v'),
diff --git a/test/image/baselines/hist_cum_stacked.png b/test/image/baselines/hist_cum_stacked.png
new file mode 100644
index 00000000000..a12f24cc4bf
Binary files /dev/null and b/test/image/baselines/hist_cum_stacked.png differ
diff --git a/test/image/mocks/hist_cum_stacked.json b/test/image/mocks/hist_cum_stacked.json
new file mode 100644
index 00000000000..6cfedaefe05
--- /dev/null
+++ b/test/image/mocks/hist_cum_stacked.json
@@ -0,0 +1,41 @@
+{
+    "data": [{
+        "x": [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10],
+        "type": "histogram",
+        "cumulative": {"enabled": true},
+        "xbins": {"start": 0.5, "end": 10.5, "size": 1},
+        "marker": {"color": "blue", "line": {"width": 2, "color": "#000"}},
+        "name": "A"
+    },
+    {
+        "x": [3, 3, 4, 5, 6, 7, 7],
+        "type": "histogram",
+        "cumulative": {"enabled": true, "currentbin": "exclude"},
+        "xbins": {"start": 0.5, "end": 10.5, "size": 1},
+        "marker": {"color": "red", "line": {"width": 2, "color": "#000"}},
+        "name": "B"
+    },
+    {
+        "x": [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10],
+        "type": "box",
+        "orientation": "h",
+        "yaxis": "y2",
+        "line": {"color": "blue"},
+        "showlegend": false
+    },
+    {
+        "x": [3, 3, 4, 5, 6, 7, 7],
+        "type": "box",
+        "orientation": "h",
+        "yaxis": "y2",
+        "line": {"color": "red"},
+        "showlegend": false
+    }],
+    "layout": {
+        "yaxis": {"domain": [0, 0.8]},
+        "yaxis2": {"domain": [0.8, 1], "showline": false, "showticklabels": false},
+        "height": 300,
+        "width": 400,
+        "barmode": "stack"
+    }
+}
diff --git a/test/jasmine/tests/axes_test.js b/test/jasmine/tests/axes_test.js
index fe98a9e13c1..3883cedb617 100644
--- a/test/jasmine/tests/axes_test.js
+++ b/test/jasmine/tests/axes_test.js
@@ -1809,7 +1809,7 @@ describe('Test axes', function() {
             );
 
             expect(out).toEqual({
-                start: -0.5,
+                start: 0.5,
                 end: 4.5,
                 size: 1
             });
@@ -1822,6 +1822,9 @@ describe('Test axes', function() {
                 2
             );
 
+            // when size > 1 with all integers, we want the starting point to be
+            // a half integer below the round number a tick would be at (in this case 0)
+            // to approximate the half-open interval [) that's commonly used.
             expect(out).toEqual({
                 start: -0.5,
                 end: 5.5,
diff --git a/test/jasmine/tests/histogram_test.js b/test/jasmine/tests/histogram_test.js
index 684d2320939..a9fed476675 100644
--- a/test/jasmine/tests/histogram_test.js
+++ b/test/jasmine/tests/histogram_test.js
@@ -246,5 +246,110 @@ describe('Test histogram', function() {
             ]);
         });
 
+        describe('cumulative distribution functions', function() {
+            var base = {
+                x: [0, 5, 10, 15, 5, 10, 15, 10, 15, 15],
+                y: [2, 2, 2, 14, 6, 6, 6, 10, 10, 2]
+            };
+
+            it('makes the right base histogram', function() {
+                var baseOut = _calc(base);
+                expect(baseOut).toEqual([
+                    {b: 0, p: 2, s: 1},
+                    {b: 0, p: 7, s: 2},
+                    {b: 0, p: 12, s: 3},
+                    {b: 0, p: 17, s: 4},
+                ]);
+            });
+
+            var CDFs = [
+                {p: [2, 7, 12, 17], s: [1, 3, 6, 10]},
+                {
+                    direction: 'decreasing',
+                    p: [2, 7, 12, 17], s: [10, 9, 7, 4]
+                },
+                {
+                    currentbin: 'exclude',
+                    p: [7, 12, 17, 22], s: [1, 3, 6, 10]
+                },
+                {
+                    direction: 'decreasing', currentbin: 'exclude',
+                    p: [-3, 2, 7, 12], s: [10, 9, 7, 4]
+                },
+                {
+                    currentbin: 'half',
+                    p: [2, 7, 12, 17, 22], s: [0.5, 2, 4.5, 8, 10]
+                },
+                {
+                    direction: 'decreasing', currentbin: 'half',
+                    p: [-3, 2, 7, 12, 17], s: [10, 9.5, 8, 5.5, 2]
+                },
+                {
+                    direction: 'decreasing', currentbin: 'half', histnorm: 'percent',
+                    p: [-3, 2, 7, 12, 17], s: [100, 95, 80, 55, 20]
+                },
+                {
+                    currentbin: 'exclude', histnorm: 'probability',
+                    p: [7, 12, 17, 22], s: [0.1, 0.3, 0.6, 1]
+                },
+                {
+                    // behaves the same as without *density*
+                    direction: 'decreasing', currentbin: 'half', histnorm: 'density',
+                    p: [-3, 2, 7, 12, 17], s: [10, 9.5, 8, 5.5, 2]
+                },
+                {
+                    // behaves the same as without *density*, only *probability*
+                    direction: 'decreasing', currentbin: 'half', histnorm: 'probability density',
+                    p: [-3, 2, 7, 12, 17], s: [1, 0.95, 0.8, 0.55, 0.2]
+                },
+                {
+                    currentbin: 'half', histfunc: 'sum',
+                    p: [2, 7, 12, 17, 22], s: [1, 6, 19, 44, 60]
+                },
+                {
+                    currentbin: 'half', histfunc: 'sum', histnorm: 'probability',
+                    p: [2, 7, 12, 17, 22], s: [0.5 / 30, 0.1, 9.5 / 30, 22 / 30, 1]
+                },
+                {
+                    direction: 'decreasing', currentbin: 'half', histfunc: 'max', histnorm: 'percent',
+                    p: [-3, 2, 7, 12, 17], s: [100, 3100 / 32, 2700 / 32, 1900 / 32, 700 / 32]
+                },
+                {
+                    direction: 'decreasing', currentbin: 'half', histfunc: 'min', histnorm: 'density',
+                    p: [-3, 2, 7, 12, 17], s: [8, 7, 5, 3, 1]
+                },
+                {
+                    currentbin: 'exclude', histfunc: 'avg', histnorm: 'probability density',
+                    p: [7, 12, 17, 22], s: [0.1, 0.3, 0.6, 1]
+                }
+            ];
+
+            CDFs.forEach(function(CDF) {
+                var p = CDF.p,
+                    s = CDF.s;
+
+                it('handles direction=' + CDF.direction + ', currentbin=' + CDF.currentbin +
+                        ', histnorm=' + CDF.histnorm + ', histfunc=' + CDF.histfunc, function() {
+                    var traceIn = Lib.extendFlat({}, base, {
+                        cumulative: {
+                            enabled: true,
+                            direction: CDF.direction,
+                            currentbin: CDF.currentbin
+                        },
+                        histnorm: CDF.histnorm,
+                        histfunc: CDF.histfunc
+                    });
+                    var out = _calc(traceIn);
+
+                    expect(out.length).toBe(p.length);
+                    out.forEach(function(outi, i) {
+                        expect(outi.p).toBe(p[i]);
+                        expect(outi.s).toBeCloseTo(s[i], 6);
+                        expect(outi.b).toBe(0);
+                    });
+                });
+            });
+        });
+
     });
 });