We have developed a sensitive, multipurpose torsional magnetometer with optical detection of the torque. The use of a feedback system with a current coil mounted with the sample allows direct, quantitative determination of the magnetization with a sensitivity of 10−12 J/T in a Bitter-magnet and 2×10−13 J/T at 15 T in a superconducting magnet. The system can be used over a wide range of temperatures and up to high magnetic fields. To demonstrate the sensitivity and versatility of our magnetometer, we present magnetization measurements of a multisubband two-dimensional electron gas (3×1011 spins) and of a 0.13 mg crystal of the organic conductor κ-(BEDT-TTF)2Cu(NCS)2.