The present invention is a thermal and acoustic insulating sphere that has an evacuated hollow interior. The spheres are constructed of insulating materials, and the inner and outer surfaces of each sphere have highly reflective coatings evenly applied to them. The coatings applied to the inner and outer surfaces reduce the transmission of heat by conduction, convection, and radiation. Additionally, the spheres provide superior acoustic insulation due to the inability of sound to travel through the interior vacuum. The spheres can be used to produce insulating materials, for example, by embedding or positioning them within or between other materials, to provide thermal and acoustic insulation.