diff --git a/src/shared/ui/Slider/slider-math.test.ts b/src/shared/ui/Slider/slider-math.test.ts
new file mode 100644
index 0000000..3e7da60
--- /dev/null
+++ b/src/shared/ui/Slider/slider-math.test.ts
@@ -0,0 +1,55 @@
+import {
+    pointerToValue,
+    snapToStep,
+} from './slider-math';
+
+describe('snapToStep', () => {
+    it('snaps a raw value to the nearest step on the grid', () => {
+        expect(snapToStep(53, { min: 0, max: 100, step: 10 })).toBe(50);
+        expect(snapToStep(56, { min: 0, max: 100, step: 10 })).toBe(60);
+    });
+
+    it('clamps below min and above max', () => {
+        expect(snapToStep(-20, { min: 0, max: 100, step: 1 })).toBe(0);
+        expect(snapToStep(200, { min: 0, max: 100, step: 1 })).toBe(100);
+    });
+
+    it('respects a non-zero min when snapping', () => {
+        expect(snapToStep(13, { min: 10, max: 90, step: 5 })).toBe(15);
+    });
+
+    it('preserves fractional step precision', () => {
+        expect(snapToStep(1.34, { min: 0, max: 2, step: 0.05 })).toBe(1.35);
+        expect(snapToStep(0.31, { min: 0, max: 1, step: 0.1 })).toBe(0.3);
+    });
+});
+
+describe('pointerToValue', () => {
+    const rect = { left: 100, right: 300, top: 50, bottom: 250, width: 200, height: 200 } as DOMRect;
+
+    it('maps horizontal pointer position left→min, right→max', () => {
+        const opts = { min: 0, max: 100, step: 1, orientation: 'horizontal' as const };
+        expect(pointerToValue({ clientX: 100, clientY: 0 }, rect, opts)).toBe(0);
+        expect(pointerToValue({ clientX: 200, clientY: 0 }, rect, opts)).toBe(50);
+        expect(pointerToValue({ clientX: 300, clientY: 0 }, rect, opts)).toBe(100);
+    });
+
+    it('inverts vertical: bottom→min, top→max', () => {
+        const opts = { min: 0, max: 100, step: 1, orientation: 'vertical' as const };
+        expect(pointerToValue({ clientX: 0, clientY: 250 }, rect, opts)).toBe(0);
+        expect(pointerToValue({ clientX: 0, clientY: 150 }, rect, opts)).toBe(50);
+        expect(pointerToValue({ clientX: 0, clientY: 50 }, rect, opts)).toBe(100);
+    });
+
+    it('clamps when pointer is outside the track', () => {
+        const opts = { min: 0, max: 100, step: 1, orientation: 'horizontal' as const };
+        expect(pointerToValue({ clientX: 0, clientY: 0 }, rect, opts)).toBe(0);
+        expect(pointerToValue({ clientX: 9999, clientY: 0 }, rect, opts)).toBe(100);
+    });
+
+    it('returns min for a zero-size track without NaN', () => {
+        const zero = { left: 0, right: 0, top: 0, bottom: 0, width: 0, height: 0 } as DOMRect;
+        const opts = { min: 5, max: 95, step: 1, orientation: 'horizontal' as const };
+        expect(pointerToValue({ clientX: 0, clientY: 0 }, zero, opts)).toBe(5);
+    });
+});
diff --git a/src/shared/ui/Slider/slider-math.ts b/src/shared/ui/Slider/slider-math.ts
new file mode 100644
index 0000000..43b8a08
--- /dev/null
+++ b/src/shared/ui/Slider/slider-math.ts
@@ -0,0 +1,59 @@
+import {
+    clampNumber,
+    roundToStepPrecision,
+} from '$shared/lib/utils';
+
+/**
+ * Geometry/range options shared by the math helpers.
+ */
+type SliderMathOpts = {
+    /**
+     * Minimum value (inclusive)
+     */
+    min: number;
+    /**
+     * Maximum value (inclusive)
+     */
+    max: number;
+    /**
+     * Step increment
+     */
+    step: number;
+};
+
+/**
+ * Snap a raw value onto the step grid, then clamp to [min, max].
+ *
+ * Snapping is anchored to `min` so non-zero ranges land on valid stops.
+ * `roundToStepPrecision` removes IEEE-754 drift from fractional steps.
+ */
+export function snapToStep(raw: number, { min, max, step }: SliderMathOpts): number {
+    if (step <= 0) {
+        return clampNumber(raw, min, max);
+    }
+    const snapped = min + Math.round((raw - min) / step) * step;
+    return clampNumber(roundToStepPrecision(snapped, step), min, max);
+}
+
+/**
+ * Convert a pointer coordinate into a slider value.
+ *
+ * Horizontal maps left→min, right→max. Vertical is inverted so that
+ * up→max, matching natural slider expectations. The DOMRect is passed in
+ * to keep this pure and unit-testable without layout.
+ */
+export function pointerToValue(
+    point: { clientX: number; clientY: number },
+    rect: DOMRect,
+    opts: SliderMathOpts & { orientation: 'horizontal' | 'vertical' },
+): number {
+    const { min, max, orientation } = opts;
+    const size = orientation === 'vertical' ? rect.height : rect.width;
+    if (size <= 0) {
+        return snapToStep(min, opts);
+    }
+    const ratio = orientation === 'vertical'
+        ? (rect.bottom - point.clientY) / size
+        : (point.clientX - rect.left) / size;
+    return snapToStep(min + clampNumber(ratio, 0, 1) * (max - min), opts);
+}