The failure of culverts due to scour by flow at the outlet is a major concern for hydraulic engineers. However, existing deterministic equations for predicting scour depth at the outlet do not account for the randomness of parameters involved, making it difficult to assess the level of scouring risk. A probabilistic approach using a spreadsheet algorithm for the first-order reliability method (FORM) was used in this study to assess the reliability of scour depth prediction at culvert outlets; to study the influence of various random variables on the reliability-based design, sensitivity analysis was carried out. To achieve a desirable safety level in the culvert design reliability-based safety factors were proposed. The uncertainties in model correction factor and flow velocity were found to have the most influence on reliability and risk assessment. This study highlights the importance of considering uncertainties in determining the reliability or safety of culverts against scouring.