A vacuum compatible cryogenic accelerometer is proposed that could reach <0.5 pg Hz-1/2 sensitivity from 1 mHz to 10 Hz with a maximum sensitivity of 10 fg Hz-1/2 around 10 Hz. This figure can be translated to a displacement sensitivity <2 fm Hz-1/2 between 2-100 Hz, which is more than an order or magnitude better than any inertial sensor. The improvement is of interest to the fields of gravitational wave instrumentation, geophysics, accelerator physics and gravitation. In current particle accelerators and proposed future gravitational wave detectors < 10 K cryogenics are applied to the test masses in order to reduce thermal noise. This concept can benefit from the already present superconducting regime temperatures and reach a > 105 signal-To-noise ratio of all terrestrial seismic spectra. The sensor may be used for control of beam-focusing cryogenic electromagnets in particle accelerators, cryogenic inertial sensing for future gravitational wave detectors and other fields.