diff --git a/docs/pages/api/slider.md b/docs/pages/api/slider.md
index 9abaed322be30c..ac7f04f7b3a76d 100644
--- a/docs/pages/api/slider.md
+++ b/docs/pages/api/slider.md
@@ -41,7 +41,7 @@ You can learn more about the difference by [reading this guide](/guides/minimizi
 | <span class="prop-name">onChange</span> | <span class="prop-type">func</span> |  | Callback function that is fired when the slider's value changed.<br><br>**Signature:**<br>`function(event: object, value: any) => void`<br>*event:* The event source of the callback.<br>*value:* The new value. |
 | <span class="prop-name">onChangeCommitted</span> | <span class="prop-type">func</span> |  | Callback function that is fired when the `mouseup` is triggered.<br><br>**Signature:**<br>`function(event: object, value: any) => void`<br>*event:* The event source of the callback.<br>*value:* The new value. |
 | <span class="prop-name">orientation</span> | <span class="prop-type">'horizontal'<br>&#124;&nbsp;'vertical'</span> | <span class="prop-default">'horizontal'</span> | The slider orientation. |
-| <span class="prop-name">step</span> | <span class="prop-type">number</span> | <span class="prop-default">1</span> | The granularity with which the slider can step through values. (A "discrete" slider.) When step is `null`, the thumb can only be slid onto marks provided with the `marks` prop. |
+| <span class="prop-name">step</span> | <span class="prop-type">number</span> | <span class="prop-default">1</span> | The granularity with which the slider can step through values. (A "discrete" slider.) The `min` prop serves as the origin for the valid values. We recommend (max - min) to be evenly divisible by the step.<br>When step is `null`, the thumb can only be slid onto marks provided with the `marks` prop. |
 | <span class="prop-name">ThumbComponent</span> | <span class="prop-type">elementType</span> | <span class="prop-default">'span'</span> | The component used to display the value label. |
 | <span class="prop-name">track</span> | <span class="prop-type">'normal'<br>&#124;&nbsp;false<br>&#124;&nbsp;'inverted'</span> | <span class="prop-default">'normal'</span> | The track presentation:<br>- `normal` the track will render a bar representing the slider value. - `inverted` the track will render a bar representing the remaining slider value. - `false` the track will render without a bar. |
 | <span class="prop-name">value</span> | <span class="prop-type">number<br>&#124;&nbsp;Array&lt;number&gt;</span> |  | The value of the slider. For ranged sliders, provide an array with two values. |
diff --git a/packages/material-ui/src/Slider/Slider.js b/packages/material-ui/src/Slider/Slider.js
index ad7f144e18055f..49afa013b91133 100644
--- a/packages/material-ui/src/Slider/Slider.js
+++ b/packages/material-ui/src/Slider/Slider.js
@@ -83,8 +83,8 @@ function getDecimalPrecision(num) {
   return decimalPart ? decimalPart.length : 0;
 }
 
-function roundValueToStep(value, step) {
-  const nearest = Math.round(value / step) * step;
+function roundValueToStep(value, step, min) {
+  const nearest = Math.round((value - min) / step) * step + min;
   return Number(nearest.toFixed(getDecimalPrecision(step)));
 }
 
@@ -492,7 +492,7 @@ const Slider = React.forwardRef(function Slider(props, ref) {
     event.preventDefault();
 
     if (step) {
-      newValue = roundValueToStep(newValue, step);
+      newValue = roundValueToStep(newValue, step, min);
     }
 
     newValue = clamp(newValue, min, max);
@@ -547,7 +547,7 @@ const Slider = React.forwardRef(function Slider(props, ref) {
       let newValue;
       newValue = percentToValue(percent, min, max);
       if (step) {
-        newValue = roundValueToStep(newValue, step);
+        newValue = roundValueToStep(newValue, step, min);
       } else {
         const marksValues = marks.map(mark => mark.value);
         const closestIndex = findClosest(marksValues, newValue);
@@ -946,6 +946,9 @@ Slider.propTypes = {
   orientation: PropTypes.oneOf(['horizontal', 'vertical']),
   /**
    * The granularity with which the slider can step through values. (A "discrete" slider.)
+   * The `min` prop serves as the origin for the valid values.
+   * We recommend (max - min) to be evenly divisible by the step.
+   *
    * When step is `null`, the thumb can only be slid onto marks provided with the `marks` prop.
    */
   step: PropTypes.number,
diff --git a/packages/material-ui/src/Slider/Slider.test.js b/packages/material-ui/src/Slider/Slider.test.js
index d33596eea2fb7f..b7161f924cce7c 100644
--- a/packages/material-ui/src/Slider/Slider.test.js
+++ b/packages/material-ui/src/Slider/Slider.test.js
@@ -306,22 +306,37 @@ describe('<Slider />', () => {
       key: 'ArrowRight',
     };
 
+    it('should use min as the step origin', () => {
+      const { getByRole } = render(<Slider defaultValue={150} step={100} max={750} min={150} />);
+      const thumb = getByRole('slider');
+      thumb.focus();
+
+      fireEvent.keyDown(document.activeElement, moveRightEvent);
+      expect(thumb).to.have.attribute('aria-valuenow', '250');
+
+      fireEvent.keyDown(document.activeElement, moveLeftEvent);
+      expect(thumb).to.have.attribute('aria-valuenow', '150');
+    });
+
     it('should reach right edge value', () => {
       const { getByRole } = render(<Slider defaultValue={90} min={6} max={108} step={10} />);
       const thumb = getByRole('slider');
       thumb.focus();
 
       fireEvent.keyDown(document.activeElement, moveRightEvent);
-      expect(thumb).to.have.attribute('aria-valuenow', '100');
+      expect(thumb).to.have.attribute('aria-valuenow', '96');
+
+      fireEvent.keyDown(document.activeElement, moveRightEvent);
+      expect(thumb).to.have.attribute('aria-valuenow', '106');
 
       fireEvent.keyDown(document.activeElement, moveRightEvent);
       expect(thumb).to.have.attribute('aria-valuenow', '108');
 
       fireEvent.keyDown(document.activeElement, moveLeftEvent);
-      expect(thumb).to.have.attribute('aria-valuenow', '100');
+      expect(thumb).to.have.attribute('aria-valuenow', '96');
 
       fireEvent.keyDown(document.activeElement, moveLeftEvent);
-      expect(thumb).to.have.attribute('aria-valuenow', '90');
+      expect(thumb).to.have.attribute('aria-valuenow', '86');
     });
 
     it('should reach left edge value', () => {
@@ -329,17 +344,14 @@ describe('<Slider />', () => {
       const thumb = getByRole('slider');
       thumb.focus();
 
-      fireEvent.keyDown(document.activeElement, moveLeftEvent);
-      expect(thumb).to.have.attribute('aria-valuenow', '10');
-
       fireEvent.keyDown(document.activeElement, moveLeftEvent);
       expect(thumb).to.have.attribute('aria-valuenow', '6');
 
       fireEvent.keyDown(document.activeElement, moveRightEvent);
-      expect(thumb).to.have.attribute('aria-valuenow', '20');
+      expect(thumb).to.have.attribute('aria-valuenow', '16');
 
       fireEvent.keyDown(document.activeElement, moveRightEvent);
-      expect(thumb).to.have.attribute('aria-valuenow', '30');
+      expect(thumb).to.have.attribute('aria-valuenow', '26');
     });
 
     it('should round value to step precision', () => {