Strong magnetic fields are required in many fields, such as medicine (magnetic resonance imaging), pharmacy (nuclear magnetic resonance), particle accelerators (such as the Large Hadron Collider) and fusion devices (for example, the International Thermonuclear Experimental Reactor, ITER), as well as for other diverse scientific and industrial uses. For almost two decades, 45 tesla has been the highest achievable direct-current (d.c.) magnetic field; however, such a field requires the use of a 31-megawatt, 33.6-tesla resistive magnet inside 11.4-tesla low-temperature superconductor coils1, and such high-power resistive magnets are available in only a few facilities worldwide2. By contrast, superconducting magnets are widespread owing to their low power requirements. Here we report a high-temperature superconductor coil that generates a magnetic field of 14.4 tesla inside a 31.1-tesla resistive background magnet to obtain a d.c. magnetic field of 45.5 tesla—the highest field achieved so far, to our knowledge. The magnet uses a conductor tape coated with REBCO (REBa 2 Cu 3 O x , where RE = Y, Gd) on a 30-micrometre-thick substrate3, making the coil highly compact and capable of operating at the very high winding current density of 1,260 amperes per square millimetre. Operation at such a current density is possible only because the magnet is wound without insulation4, which allows rapid and safe quenching from the superconducting to the normal state5,6,7,8,9,10. The 45.5-tesla test magnet validates predictions11 for high-field copper oxide superconductor magnets by achieving a field twice as high as those generated by low-temperature superconducting magnets.