Method for determining the slip of a tyre mounted on a vehicle and running along the ground, said tyre being equipped with a sensor configured to acquire a measurement signal representative of the change in curvature of the tyre as it runs along the ground, the method comprising the following steps: - the acquisition, by the sensor, of a signal representative of the change in curvature of the tyre during running, - the determination of measurement data from the measurement signal representative of the change in curvature of the tyre during running, the measurement data comprising a first parameter representative of the duration of one revolution of the wheel bearing the tyre, - the obtaining of a measurement of the translational speed of the vehicle with respect to the ground, - the obtaining of a firmness factor representative of the condition of firmness of the ground, which is derived from measurements taken while the tyre is rolling over said ground, and characterized by: a) if the firmness factor is representative of firm ground on which the slip is negligible, the determination of a rolling circumference of the tyre as a function of the first parameter and of the translational speed of the vehicle with respect to the ground, or b) if the firmness factor is representative of ground that is not very firm and on which the tyre is liable to slip, the determination of the slip of the tyre as a function of the first parameter, of the translational speed of the vehicle with respect to the ground, and of a rolling circumference of the tyre as determined previously at a). - the acquisition, by the sensor, of a signal representative of the change in curvature of the tyre during running, - the determination of measurement data from the measurement signal representative of the change in curvature of the tyre during running, the measurement data comprising a first parameter representative of the duration of one revolution of the wheel bearing the tyre, - the obtaining of a measurement of the translational speed of the vehicle with respect to the ground, - the obtaining of a firmness factor representative of the condition of firmness of the ground, which is derived from measurements taken while the tyre is rolling over said ground, and characterized by: a) if the firmness factor is representative of firm ground on which the slip is negligible, the determination of a rolling circumference of the tyre as a function of the first parameter and of the translational speed of the vehicle with respect to the ground, or b) if the firmness factor is representative of ground that is not very firm and on which the tyre is liable to slip, the determination of the slip of the tyre as a function of the first parameter, of the translational speed of the vehicle with respect to the ground, and of a rolling circumference of the tyre as determined previously at a). a) if the firmness factor is representative of firm ground on which the slip is negligible, the determination of a rolling circumference of the tyre as a function of the first parameter and of the translational speed of the vehicle with respect to the ground, or b) if the firmness factor is representative of ground that is not very firm and on which the tyre is liable to slip, the determination of the slip of the tyre as a function of the first parameter, of the translational speed of the vehicle with respect to the ground, and of a rolling circumference of the tyre as determined previously at a).