Many engineers construct an inverting op amp attenuator by making Rg > Rf, extrapolating the inverting op amp gain stage equation into the region below a gain of -1. This is not a good idea, as most op amps are compensated to have a stable gain of -1. Below that value, the op amp actually becomes unstable due to multiple parastics in the IC causing the phase margin to approach -180 degrees and making the denominator of the loop gain equation go to zero. In other words, an op amp is least stable when it is operated at minimum gain, which is counter intuitive for most engineers. For more information, consult my book: Op Amps for Everyone.
The inverting attenuator below uses a "T" pad to accomplish attenuation and avoid the instability issue completely. The calculator only uses two values of resistor: R1 and R2. If you remove R1, the circuit reverts to an inverting gain stage, with Rg = R2A + R2B, and Rf = R2C + R2D. Since all R2's are the same value, the gain of the circuit is -1.
Adding R1 reduces the gain from 1 to a lower value. The calculation is not particularly complex:
Some more mathematically oriented people might be thinking about how that equation reduces to a gain of -1 if R1 is eliminated. If R1 is made infinite, the equation reduces to:
The last result in the calculator below is a stability check. The op amp sees its gain as (2 * R2) / ((R1 || R2) + R2). As R1 gets very low in value compared to R2, the op amp gain approaches -2. But as R1 gets very large, the op amp gain approaches -1. In other words, the op amp is always operated in its stable region, as long as a unity gain stable op amp has been selected.