How can I calculate an area on a CT image. I can calculate volumes (mm^3) but not areas (mm^2)

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In recent Slicer Preview Releases, you can draw curves and get their surface area (2D surface, as you would expect - only one side, no thickness).

Select “Closed Curve” from the “Create and place” toolbar button:

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Left-click on the image to place curve control points and right-click to finish placement:

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Measurements on curves are still work in progress, but you can open the Python console (Ctrl-3) and copy-paste the code below to see the surface area:

curves=slicer.util.getNodesByClass("vtkMRMLMarkupsClosedCurveNode")
for curve in curves:
    surfaceAreaMm2 = slicer.modules.markups.logic().GetClosedCurveSurfaceArea(curve)
    print("Curve {0}: surface area = {1:.2f} mm2".format(curve.GetName(), surfaceAreaMm2))