Free nutation is excited if the rotational equilibrium of a planetary body is disturbed. When viewed from space, it is expressed as a wobble of the planet around its rotation pole, and the duration of one cycle is referred to as the Chandler period. Because planets are not rigid, their free nutation period differs from their Euler period by the factor 1-k_X/k_f, where k_X/k_f is a ratio of two Love numbers. Here, we perform direct numerical simulations of free nutation and show that k_X is not the Love number at the frequency of the Chandler wobble itself, as is commonly assumed, but rather that it is close to k_e, the elastic Love number. This result is important when the Chandler periods of Earth and Mars are interpreted, because the measured frequency is related to the internal rheological structure in a different way than previously thought.