Archimedean spiral patterns are formed by the directed self-assembly of diblock copolymer thin films within a circular template. The presence of a notch in the template promotes the formation of a spiral compared to concentric rings, and the notch shape determines the chirality of the spiral. Double spirals occur when the notch width is increased or when there are two notches. The spiral followed an Archimedean form with exponent ≈0.9. Self-consistent field theory reproduces the experimentally observed morphologies and demonstrates the templating of spirals in cylindrical-morphology block copolymer films.