We present a laser-based atomic magnetometer that allows inferring the modulus of a magnetic field from the free Larmor precession of spin-oriented Cs vapour atoms. The detection of free spin precession (FSP) is not subject to systematic readout errors that occur in phase feedback-controlled magnetometers in which the spin precession is actively driven by an oscillating field or a modulation of light parameters, such as frequency, amplitude, or polarization. We demonstrate that an FSP-magnetometer can achieve a ∼200 fT/√Hz sensitivity (<100 fT/√Hz in the shotnoise limit) and an absolute accuracy at the same level.