Double-deck elevators are a very efficient mode of transport, especially in high rise buildings. This is due to the fact that they reduce the number of stops in a round trip (leading to a smaller value of the round trip time hence a higher handling capacity) and take up less space of the core of the building leading to high space usage efficiency. This paper provides a comprehensive treatment of the double-deck elevator traffic calculations. It derives an exact set of equations to find the value of the round trip time under incoming traffic conditions, for the cases of equal and unequal floor populations. Moreover, equations have also been derived for two performance coefficients. The first coefficient is called the passenger transfer efficiency coefficient and is representative of the time taken by passenger to alight from the double-deck elevator. The second coefficient is called the coincidental stopping coefficient and is representative of the stopping efficiency. All the results from the equations have been verified using the Monte Carlo simulation method. The method of stepwise verification has been used in order to verify the equations. Under stepwise verification, the equations are derived in stages and each stage is verified against the results from the Monte Carlo Simulation method. The paper ends by suggesting methods of dealing with two of the irregular conditions. Namely two cases are discussed: the case where the number of floors above the main entrance is odd; and the case where the floor heights are unequal and the rated speed is not attained in one double floor journey. Practical application: This paper presents a full set of equations that allow the elevator system designer to fully assess the expected performance of the double-deck elevator system under incoming traffic conditions. These equations (manually or within a software program) can be used to carry out a full design (thus selecting the number, speed, and capacity of the double-deck elevators). © The Chartered Institution of Building Services Engineers 2016.