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Mobile ad hoc networks (MANETs) are gaining increasing significance with computing devices becoming ubiquitous and equipped with wireless communication modules. Many applications for such networks require the devices to know their position within the network or their distance to other devices. Precise determination of these parameters often fails due to lack of information, missing hardware, or inaccessibility of needed resources, making an approximation necessary. We introduce an algorithm to calculate hop counts and, thereby, derive distances between devices. The algorithm is based on synchronization of all devices in the MANET. We show that an intentional phase shift of a periodically sent signal allows to estimate the distance between all devices in a network and a specific reference device. This approach significantly reduces the communication overhead leading to a more resource-efficient operation of the communication module and, thus, potentially extending the lifetime of the mobile devices. Experiments demonstrate that a network with an average of ten devices within communication range can be synchronized using a firefly-inspired decentralized synchronization algorithm. Also, we show that the resulting distance estimates have a higher accuracy compared to the results of an algorithm which is based on asynchronous exchange of messages.