diff --git a/changelog/7118.feature.rst b/changelog/7118.feature.rst
new file mode 100644
index 00000000000..40d41a45aef
--- /dev/null
+++ b/changelog/7118.feature.rst
@@ -0,0 +1 @@
+Added a :meth:`sunpy.coordinates.Helioprojective.is_visible` method to return whether the coordinate is visible (i.e., not obscured from the observer assuming that the Sun is an opaque sphere).
diff --git a/sunpy/coordinates/frames.py b/sunpy/coordinates/frames.py
index 4606188946f..04143b0ffbf 100644
--- a/sunpy/coordinates/frames.py
+++ b/sunpy/coordinates/frames.py
@@ -609,6 +609,85 @@ def make_3d(self):
                                                           lat=lat,
                                                           distance=d))
 
+    @u.quantity_input
+    def is_visible(self, *, tolerance: u.m = 1*u.m):
+        """
+        Returns whether the coordinate is on the visible side of the Sun.
+
+        A coordinate is visible if it can been seen from the observer (the ``observer``
+        frame attribute) assuming that the Sun is an opaque sphere with a fixed radius
+        (the ``rsun`` frame attribute).  The visible side of the Sun is always smaller
+        than a full hemisphere.
+
+        Parameters
+        ----------
+        tolerance : `~astropy.units.Quantity`
+            The depth below the surface of the Sun that should be treated as
+            transparent.
+
+        Notes
+        -----
+        If the coordinate is 2D, it is automatically deemed visible.  A 2D coordinate
+        describes a look direction from the observer, who would simply see whatever is
+        in "front", and thus cannot correspond to a point hidden from the observer.
+
+        The ``tolerance`` parameter accommodates situations where the limitations of
+        numerical precision would falsely conclude that a coordinate is not visible.
+        For example, a coordinate that is expressly created to be on the solar surface
+        may be calculated to be slightly below the surface, and hence not visible if
+        there is no tolerance.  However, a consequence of the ``tolerance`` parameter
+        is that a coordinate that is formally on the far side of the Sun but is
+        extremely close to the solar limb can be evaluated as visible.  With the
+        default ``tolerance`` value of 1 meter, a coordinate on the surface of the Sun
+        can be up to 11 arcseconds of heliographic longitude past the solar limb and
+        still be evaluated as visible.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> import astropy.units as u
+        >>> from astropy.coordinates import SkyCoord
+        >>> from sunpy.coordinates import HeliographicStonyhurst, Helioprojective
+
+        >>> hpc_frame = Helioprojective(observer='earth', obstime='2023-08-03')
+
+        >>> in_front = SkyCoord(0*u.arcsec, 0*u.arcsec, 0.5*u.AU, frame=hpc_frame)
+        >>> print(in_front.is_visible())
+        True
+
+        >>> behind = SkyCoord(0*u.arcsec, 0*u.arcsec, 1.5*u.AU, frame=hpc_frame)
+        >>> print(behind.is_visible())
+        False
+
+        >>> hgs_array = SkyCoord(np.arange(-180, 180, 60)*u.deg, [0]*6*u.deg,
+        ...                      frame='heliographic_stonyhurst', obstime='2023-08-03')
+        >>> print(hgs_array)
+        <SkyCoord (HeliographicStonyhurst: obstime=2023-08-03T00:00:00.000, rsun=695700.0 km): (lon, lat) in deg
+            [(-180., 0.), (-120., 0.), ( -60., 0.), (   0., 0.), (  60., 0.),
+             ( 120., 0.)]>
+        >>> print(hgs_array.transform_to(hpc_frame).is_visible())
+        [False False  True  True  True False]
+        """
+        # If the coordinate is 2D, it must be visible
+        if self._is_2d:
+            return np.ones_like(self.data, dtype=bool)
+
+        # Use a slightly smaller solar radius to accommodate numerical precision
+        solar_radius = self.rsun - tolerance
+
+        data = self.cartesian
+        data_to_sun = self.observer.radius * CartesianRepresentation(1, 0, 0) - data
+
+        # When representing the helioprojective point as true Cartesian, the X value is the
+        # distance from the observer to the point in the sunward direction
+        is_behind_observer = data.x < 0
+        # When comparing heliocentric angles, we compare the sine values and hence avoid calling arcsin()
+        is_beyond_limb = np.sqrt(data.y **2 + data.z **2) / data.norm() > solar_radius / self.observer.radius
+        is_above_surface = data_to_sun.norm() >= solar_radius
+        is_on_near_side = data.dot(data_to_sun) >= 0
+
+        return is_behind_observer | is_beyond_limb | (is_on_near_side & is_above_surface)
+
     _spherical_screen = None
 
     @classmethod
diff --git a/sunpy/coordinates/tests/test_frames.py b/sunpy/coordinates/tests/test_frames.py
index b8db7236356..fe90fe708f5 100644
--- a/sunpy/coordinates/tests/test_frames.py
+++ b/sunpy/coordinates/tests/test_frames.py
@@ -242,6 +242,29 @@ def test_hpc_obstime_from_observer():
     assert hpc.obstime is None
 
 
+def test_hpc_is_visible_2d():
+    hpc = Helioprojective(2000*u.arcsec, 2000*u.arcsec,
+                          observer='earth', obstime='2023-08-03')
+    assert hpc.is_visible()
+
+
+def test_hpc_is_visible():
+    hpc = Helioprojective([0]*2*u.arcsec, [0]*2*u.arcsec, [0.5, 1.5]*u.AU,
+                          observer='earth', obstime='2023-08-03')
+    assert (hpc.is_visible() == [True, False]).all()
+
+
+def test_hpc_is_visible_tolerance():
+    hpc = Helioprojective(200*u.arcsec, 0*u.arcsec,
+                          observer='earth', obstime='2023-08-03').make_3d()
+
+    # Due to the limitations of numerical precision, the coordinate will be computed to be slightly
+    # below the solar surface, and thus invisible when the tolerance is set to zero
+    assert not hpc.is_visible(tolerance=0*u.m)
+
+    assert hpc.is_visible(tolerance=1*u.m)
+
+
 # ==============================================================================
 # ## Heliographic Tests
 # ==============================================================================