This study proposes an algorithm for calculating the outputs of a stepless, tunable, four-chip LED according to a black body radiation curve; the proposed algorithm is based on the generalized reduced gradient method. The lumen outputs of the four-chip LEDs were calculated in real time at color temperatures ranging between 2500 K and 6500 K without using a lookup table, enabling achieving high-quality lighting designs. Finally, the algorithms for the stepless dimming method, with average color shift Duv 0.0027, is proposed. This algorithm has much smaller memory size requirements for the microcontroller unit than the current method.