A disk drive is disclosed comprising a spindle motor having a plurality of windings including at least a first winding, a second winding, and a third winding. During a spin-up operation, a voltage is applied to the first winding and a first rise time is measured for current flowing through the first winding to reach a predetermined threshold. A voltage is applied to the second winding and a second rise time is measured for current flowing through the second winding to reach a predetermined threshold. A voltage is applied to the third winding and a third rise time is measured for current flowing through the third winding to reach a predetermined threshold. A difference is computed in response to the first rise time, the second rise time, and the third rise time, and an angular position of the spindle motor is estimated by computing an arctangent in response to the difference.