This paper describes a programmable capacitor intended for use as the reference impedance in an inductance measurement system. The capacitor is programmable from 1 pF to 39 $\mu \text{F}$ with a resolution of 1 pF and consists of a parallel combination of commercially available capacitors with values that follow the Fibonacci series progression. This paper presents a novel calibration procedure for the programmable capacitor that uses an $LCR$ meter performing only difference measurements and requires only three reference capacitance standards within the device’s programmable range. Design details and major sources of error for the use of the capacitor in an inductance measurement system are also discussed.