We propose a calibration equation for negative temperature coefficient thermistors. This equation is modified from the basic thermistor equation by a residual compensation method. The residual compensated equation includes a 2nd order error correction term. This equation is convenient for converting temperature to resistance and vice versa. Calibrations of various thermistors were performed in a high precision temperature bath to test the resistance-temperature relation. The thermistors were calibrated in glass tubes using a reference thermometer. Most calibrations are performed in a temperature span (15-35 degrees C). From the resistance-temperature curves, the fitting function of the basic thermistor equation and the residual compensated equation were evaluated and their fitting errors were compared. Standard fitting errors (1 sigma) in temperature of the basic equation and the residual compensated basic equation were 8.131 mK and 0.151 mK respectively. The residual compensated equation showed about 1/54 smaller fitting errors than the basic thermistor equation. 0 2015 Elsevier B.V. All rights reserved.