What is the approximate pressure at the mantle-outer core interface?

Answer 1

The calculation for pressure is 10Kbar (1GPa) = 30 Km. The crust is anywhere from about 30-65 Km thick, and the mantle is about 2885 Km thick. That's a total of 2915-2950 Km depth so the pressure is probably in the 970-980 Kbar (97-98 GPa) range.
1 Kbar = 1000 bars, pressure at sea level = 1 bar.
I work in a high pressure lab and we only get around 3GPa, that's nothing compared to the pressures at the mantle-core boundary.

Answer 2

According to PREM (Preliminary Reference Earth Model), published in 1981, the pressure at the core-mantle boundary is 136 GPa. This corresponds to 1,360 kbar, or 1.3 million times atmospheric pressure. There may be a more recent reference, but this gets close enough.
The previous poster assumed a density of 3400 kg/m^3, which is characteristic of the upper mantle. However, the density of the lower mantle is higher, approaching 5500 kg/m^3.