diff --git a/pyirf/tests/test_utils.py b/pyirf/tests/test_utils.py
index 50d348446..64cbf84b1 100644
--- a/pyirf/tests/test_utils.py
+++ b/pyirf/tests/test_utils.py
@@ -1,7 +1,8 @@
 import numpy as np
 import astropy.units as u
-from astropy.table import QTable
+from astropy.table import QTable, Table
 import pytest
+from pyirf.exceptions import MissingColumns, WrongColumnUnit
 
 
 def test_is_scalar():
@@ -31,9 +32,7 @@ def test_cone_solid_angle():
 
 
 def test_check_table():
-    from pyirf.exceptions import MissingColumns, WrongColumnUnit
     from pyirf.utils import check_table
-    from astropy.table import Table
 
     t = QTable({'bar': [0, 1, 2] * u.TeV})
 
@@ -54,3 +53,55 @@ def test_check_table():
     t = Table({'bar': [0, 1, 2]})
     with pytest.raises(WrongColumnUnit):
         check_table(t, required_units={'bar': u.cm})
+
+def test_calculate_theta():
+    from pyirf.utils import calculate_theta
+
+    true_az = true_alt = u.Quantity([1.0], u.deg)
+    t = QTable({'reco_alt': true_alt, 'reco_az': true_az})
+
+    assert u.isclose(
+        calculate_theta(
+            events=t,
+            assumed_source_az=true_az,
+            assumed_source_alt=true_alt,
+        ),
+        0.0 * u.deg,
+    )
+
+    t = Table({'reco_alt': [1.0], 'reco_az': [1.0]})
+    with pytest.raises(WrongColumnUnit):
+        calculate_theta(t, true_az, true_alt)
+
+def test_calculate_source_fov_offset():
+    from pyirf.utils import calculate_source_fov_offset
+
+    a = u.Quantity([1.0], u.deg)
+    t = QTable({
+        'pointing_az': a,
+        'pointing_alt': a,
+        'true_az': a,
+        'true_alt': a,
+    })
+
+    assert u.isclose(calculate_source_fov_offset(t), 0.0 * u.deg)
+
+def test_check_histograms():
+    from pyirf.binning import create_histogram_table
+    from pyirf.utils import check_histograms
+
+    events1 = QTable({
+        'reco_energy': [1, 1, 10, 100, 100, 100] * u.TeV,
+    })
+    events2 = QTable({
+        'reco_energy': [100, 100, 100] * u.TeV,
+    })
+    bins = [0.5, 5, 50, 500] * u.TeV
+
+    hist1 = create_histogram_table(events1, bins)
+    hist2 = create_histogram_table(events2, bins)
+    check_histograms(hist1, hist2)
+
+    hist3 = create_histogram_table(events1, [0, 10] * u.TeV)
+    with pytest.raises(ValueError):
+        check_histograms(hist1, hist3)