A phase-field model for brittle fracture is proposed and evaluated for strength and fracture analyses of composites. In addition to the elastic properties, this approach makes use of only the fracture toughness and the strength of the material. The capability of the method is shown in analyses of composites at two scales. In laminates, strengths of notched laminates are estimated, including hole size effects. In a lamina, cracks developed in both transverse tension and compression are analyzed and compared to other numerical methods in the literature. The effects of a spectral and a hydrostatic-deviatoric decomposition of the strain energy density, two variants often used in phase-field formulations, are studied. It is shown that the choice of the decomposition affects the fracture development. Results are compared to experiments and simulations in the literature showing the capabilities of the phase-field approach.