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An accelerometer measures proper acceleration, the acceleration associated with nongravitational support and applied forces on its sensing mass. A common design suspends a proof mass on springs inside a housing. Housing motion displaces the mass relative to the support; a capacitive accelerometer reads the resulting change in capacitance. At frequencies well below mechanical resonance, Hooke's law and Newton's second law give displacement magnitude $|x|\simeq m|a|/k$, with spring constant $k$.^[ref]

A simple calibration rotates a stationary sensor so one axis points up, sideways and down. Near Earth's surface, the axis reading changes approximately from $+g$ through zero to $-g$, where $g\simeq 9.81\mathrm{m}{\mathrm{s}}^{-2}$. A supported stationary device therefore has a nonzero reading even though its position is constant; in ideal free fall, the mass and housing fall together and the reading approaches zero. This experimentally separates the measured support acceleration from coordinate acceleration.^[ref]

For a horizontal ideal sensor with $m=10^{-6}\mathrm{kg}$ and $k=1\mathrm{N}{\mathrm{m}}^{-1}$, an acceleration of $2\mathrm{m}{\mathrm{s}}^{-2}$ gives a displacement magnitude of $2\mu \mathrm{m}$. The readout converts a tiny mechanical displacement into an electrical signal; its scale, bias and frequency response must be calibrated.