Pulsar characteristic age (${\tau }_c=P/(2\dot{P})$)

For a constant-coefficient braking law $\dot{\Omega }=-K{\Omega }^3$, integration gives $t={\tau }_c[1-(P_{\mathrm{birth}}/P{)}^2]$. The characteristic age approximates the actual elapsed time only when the birth period was short and torque evolution and kinematic timing contributions are negligible.