diff --git a/package/__test__/SliderNativeComponent.web.test.tsx b/package/__test__/SliderNativeComponent.web.test.tsx
new file mode 100644
index 00000000..566857da
--- /dev/null
+++ b/package/__test__/SliderNativeComponent.web.test.tsx
@@ -0,0 +1,95 @@
+import React from "react";
+import {fireEvent, render} from "@testing-library/react-native";
+import RCTSliderWebComponent from "../src/SliderNativeComponent.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 = async (props: object, pageX: number) => {
+    const onSlidingComplete = jest.fn();
+    const {getByTestId} = await render(
+      <WebSlider
+        testID="slider"
+        onSliderSlidingComplete={onSlidingComplete}
+        {...props}
+      />,
+    );
+    await 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 = async (props: object, actionName: string) => {
+    const onSlidingStart = jest.fn();
+    const {getByTestId} = await render(
+      <WebSlider
+        testID="slider"
+        onSliderSlidingStart={onSlidingStart}
+        {...props}
+      />,
+    );
+    await fireEvent(getByTestId("slider"), "accessibilityAction", {
+      nativeEvent: {actionName},
+    });
+    await fireEvent(getByTestId("slider"), "responderGrant");
+    return onSlidingStart.mock.calls[0][0].nativeEvent.value;
+  };
+
+  it("Counts steps from the minimum value", async () => {
+    const props = {
+      minimumValue: 1,
+      maximumValue: 10,
+      lowerLimit: 1,
+      upperLimit: 10,
+      step: 2,
+    };
+    // 1 + 9 * 0.25 = 3.25, the nearest step is 3
+    expect(await releaseAt(props, 0.25)).toBe(3);
+    // 1 + 9 * 0.5 = 5.5, the nearest step is 5
+    expect(await releaseAt(props, 0.5)).toBe(5);
+  });
+
+  it("Counts steps from the minimum value when inverted", async () => {
+    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(await releaseAt(props, 0.75)).toBe(3);
+  });
+
+  it("Counts accessibility action steps from the minimum value", async () => {
+    const props = {
+      value: 5,
+      minimumValue: 1,
+      maximumValue: 13,
+      lowerLimit: 1,
+      upperLimit: 13,
+      step: 3,
+    };
+    // 5 + 3 = 8, the nearest step is 7
+    expect(await valueAfterAction(props, "increment")).toBe(7);
+    // 5 - 3 = 2, the nearest step is 1
+    expect(await valueAfterAction(props, "decrement")).toBe(1);
+  });
+});
diff --git a/package/src/SliderNativeComponent.web.tsx b/package/src/SliderNativeComponent.web.tsx
index e406cc97..afb71358 100644
--- a/package/src/SliderNativeComponent.web.tsx
+++ b/package/src/SliderNativeComponent.web.tsx
@@ -281,7 +281,7 @@ 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;
@@ -307,10 +307,20 @@ 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;
       }
     };