diff --git a/core/waveform.py b/core/waveform.py
index bb697b9..b973a71 100644
--- a/core/waveform.py
+++ b/core/waveform.py
@@ -5,6 +5,20 @@ import numpy as np
 from core.paths import _bin
 
 
+def x_to_t(x: float, width: float, view_start: float, view_dur: float) -> float:
+    """Map a pixel x in [0,width] to a time in [view_start, view_start+view_dur]."""
+    if width <= 0 or view_dur <= 0:
+        return view_start
+    return view_start + (x / width) * view_dur
+
+
+def t_to_x(t: float, width: float, view_start: float, view_dur: float) -> int:
+    """Map a time to a pixel x in [0,width] (rounded)."""
+    if width <= 0 or view_dur <= 0:
+        return 0
+    return int(round((t - view_start) / view_dur * width))
+
+
 def peaks(samples, buckets: int = 128) -> list[float]:
     """Reduce a 1-D sample array to *buckets* normalized peak magnitudes (0..1)."""
     if samples is None or len(samples) == 0:
diff --git a/tests/test_utils.py b/tests/test_utils.py
index fc9946f..a9c1ac6 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -607,3 +607,20 @@ def test_load_region_samples_bad_path_returns_empty():
     out = load_region_samples("/no/such/file.mp4", 0.0, 1.0)
     assert isinstance(out, np.ndarray)
     assert out.size == 0
+
+
+def test_time_pixel_roundtrip():
+    from core.waveform import t_to_x, x_to_t
+    assert x_to_t(0, 400, 10.0, 4.0) == 10.0
+    assert x_to_t(400, 400, 10.0, 4.0) == 14.0
+    assert x_to_t(200, 400, 10.0, 4.0) == 12.0
+    assert t_to_x(12.0, 400, 10.0, 4.0) == 200
+    for x in (0, 37, 200, 399):
+        assert abs(t_to_x(x_to_t(x, 400, 10.0, 4.0), 400, 10.0, 4.0) - x) <= 1
+
+
+def test_time_pixel_guards():
+    from core.waveform import t_to_x, x_to_t
+    assert x_to_t(50, 0, 10.0, 4.0) == 10.0        # zero width -> view_start
+    assert x_to_t(50, 400, 10.0, 0.0) == 10.0      # zero span -> view_start
+    assert t_to_x(12.0, 400, 10.0, 0.0) == 0       # zero span -> 0