The survivability is usually critical for wireless sensor networks,which are often deployed in the unattended harsh environment.Lots of technical schemes to improve the survivability depend on the redundant resources of the sensor networks.The amount of resources is usually determined by the node density during the deployment phase.For the random deployment and random node failures,the quantitative relation between the survivability and the node density is studied.Based on the conditional survivability,the node density to meet the required survivability level is presented.Finally,the survivability for unpredictable failures and the optimal node density to maximize the price–performance ratio are also discussed. The survivability is usually critical for wireless sensor networks, which are often deployed in the unattended harsh environment. Lots of technical schemes to improve the survivability depend on the redundant resources of the sensor networks the amount of resources is usually determined by the node density during the deployment phase. For the random deployment and random node failures, the quantitative relation between the survivability and the node density is studied.Based on the conditional survivability, the node density to meet the required survivability level is presented .Finally, the survivability for unpredictable failures and the optimal node density to maximize the price-performance ratio are also discussed.