diff --git a/package/__test__/RNCSliderNativeComponent.web.test.tsx b/package/__test__/RNCSliderNativeComponent.web.test.tsx
new file mode 100644
index 00000000..272de863
--- /dev/null
+++ b/package/__test__/RNCSliderNativeComponent.web.test.tsx
@@ -0,0 +1,95 @@
+import React from 'react';
+import {fireEvent, render} from '@testing-library/react-native';
+import RCTSliderWebComponent from '../src/RNCSliderNativeComponent.web';
+
+// Only the props relevant to the tests are passed
+const WebSlider = RCTSliderWebComponent as React.ComponentType<any>;
+
+describe('RCTSliderWebComponent', () => {
+  beforeAll(() => {
+    // The web component subscribes to DOM events, which the
+    // react-native test environment doesn't provide
+    const listeners = {
+      addEventListener: jest.fn(),
+      removeEventListener: jest.fn(),
+    };
+    Object.assign(global, listeners, {document: listeners});
+  });
+
+  // Without a layout the track is 1px wide and starts at x = 0,
+  // so `pageX` is the fraction of the track left of the touch
+  const releaseAt = (props: object, pageX: number) => {
+    const onSlidingComplete = jest.fn();
+    const {getByTestId} = render(
+      <WebSlider
+        testID="slider"
+        onRNCSliderSlidingComplete={onSlidingComplete}
+        {...props}
+      />,
+    );
+    fireEvent(getByTestId('slider'), 'responderRelease', {
+      nativeEvent: {pageX},
+    });
+    return onSlidingComplete.mock.calls[0][0].nativeEvent.value;
+  };
+
+  // Accessibility actions don't report a value change, so the value is
+  // read from the sliding start event that the next touch emits
+  const valueAfterAction = (props: object, actionName: string) => {
+    const onSlidingStart = jest.fn();
+    const {getByTestId} = render(
+      <WebSlider
+        testID="slider"
+        onRNCSliderSlidingStart={onSlidingStart}
+        {...props}
+      />,
+    );
+    fireEvent(getByTestId('slider'), 'accessibilityAction', {
+      nativeEvent: {actionName},
+    });
+    fireEvent(getByTestId('slider'), 'responderGrant');
+    return onSlidingStart.mock.calls[0][0].nativeEvent.value;
+  };
+
+  it('Counts steps from the minimum value', () => {
+    const props = {
+      minimumValue: 1,
+      maximumValue: 10,
+      lowerLimit: 1,
+      upperLimit: 10,
+      step: 2,
+    };
+    // 1 + 9 * 0.25 = 3.25, the nearest step is 3
+    expect(releaseAt(props, 0.25)).toBe(3);
+    // 1 + 9 * 0.5 = 5.5, the nearest step is 5
+    expect(releaseAt(props, 0.5)).toBe(5);
+  });
+
+  it('Counts steps from the minimum value when inverted', () => {
+    const props = {
+      minimumValue: 1,
+      maximumValue: 10,
+      lowerLimit: 1,
+      upperLimit: 10,
+      step: 2,
+      inverted: true,
+    };
+    // 10 - 9 * 0.75 = 3.25, the nearest step is 3
+    expect(releaseAt(props, 0.75)).toBe(3);
+  });
+
+  it('Counts accessibility action steps from the minimum value', () => {
+    const props = {
+      value: 5,
+      minimumValue: 1,
+      maximumValue: 13,
+      lowerLimit: 1,
+      upperLimit: 13,
+      step: 3,
+    };
+    // 5 + 3 = 8, the nearest step is 7
+    expect(valueAfterAction(props, 'increment')).toBe(7);
+    // 5 - 3 = 2, the nearest step is 1
+    expect(valueAfterAction(props, 'decrement')).toBe(1);
+  });
+});
diff --git a/package/src/RNCSliderNativeComponent.web.tsx b/package/src/RNCSliderNativeComponent.web.tsx
index e11e1853..19c73cb2 100644
--- a/package/src/RNCSliderNativeComponent.web.tsx
+++ b/package/src/RNCSliderNativeComponent.web.tsx
@@ -291,7 +291,7 @@ const RCTSliderWebComponent = React.forwardRef(
           : minimumValue + ((maximumValue - minimumValue) * x) / width;
 
         const valueAfterStep = step
-          ? Math.round(newValue / step) * step
+          ? minimumValue + Math.round((newValue - minimumValue) / step) * step
           : newValue;
         const valueAfterLowerLimit =
           valueAfterStep < lowerLimit ? lowerLimit : valueAfterStep;
@@ -317,10 +317,20 @@ const RCTSliderWebComponent = React.forwardRef(
       const tenth = (maximumValue - minimumValue) / 10;
       switch (event.nativeEvent.actionName) {
         case 'increment':
-          updateValue(value + (step || tenth));
+          updateValue(
+            step
+              ? Math.round((value + step - minimumValue) / step) * step +
+                  minimumValue
+              : value + tenth,
+          );
           break;
         case 'decrement':
-          updateValue(value - (step || tenth));
+          updateValue(
+            step
+              ? Math.round((value - step - minimumValue) / step) * step +
+                  minimumValue
+              : value - tenth,
+          );
           break;
       }
     };