Successive-approximation ADCs use a switched capacitor array architecture. This tool calculates the settling time of an Analog-to-Digital Converter due to the input circuit  shown in the picture below.
- Number of bits in the ADC (N)
- LSB Accuracy (1/M)
- Resistance (R)
- Capacitance (C)
t = Loge(2N*M*R*C)
What is ADC Settling Time?
It is the time required for the analog input voltage to converge to a level where the error is a specified fraction of the least significant bit.
The LSB accuracy is the equivalent number of additional resolution bits to resolve one LSB into M levels to achieve the accuracy of 1/M of an LSB.
The input voltage should settle to this value in a shorter time than the sampling period TS of the ADC. In other words, t < TS. This is the consideration that Atmel for instance has used when they specify that the input impedance to the Arduino ADC should be no greater than 10 kΩ.
If an Opamp is used to drive the ADC, the output impedance should be low enough that it doesn’t increase the RC time constant and therefore the settling time.
Using the settling time formula, it can be seen that the higher the resolution of the ADC, the longer the settling time.
For a 12-bit ADC, where 1/8 LSB accuracy is needed and R = 100 kΩ, C = 10 pF, the settling time is 10.4 μs.