We present a broadband (~0.5-79 keV) spectral and temporal analysis of multiple NuSTAR observations combined with archival Suzaku and Chandra data of NGC4945, the brightest extragalactic source at 100 keV. We observe hard X-ray (> 10 keV) flux and spectral variability, with flux variations of a factor 2 on timescales of 20 ksec. A variable primary continuum dominates the high energy spectrum (>10 keV) in all the states, while the reflected/scattered flux which dominates at E< 10 keV stays approximately constant. From modelling the complex reflection/transmission spectrum we derive a Compton depth along the line of sight of tau_Thomson ~ 2.9, and a global covering factor for the circumnuclear gas of ~ 0.15. This agrees with the constraints derived from the high energy variability, which implies that most of the high energy flux is transmitted, rather that Compton-scattered. This demonstrates the effectiveness of spectral analysis in constraining the geometric properties of the circumnuclear gas, and validates similar methods used for analyzing the spectra of other bright, Compton-thick AGN. The lower limits on the e-folding energy are between 200-300 keV, consistent with previous BeppoSAX, Suzaku and Swift BAT observations. The accretion rate, estimated from the X-ray luminosity and assuming a bolometric correction typical of type 2 AGN, is in the range ~0.1-0.3 lambda_Edd depending on the flux state. The substantial observed X-ray luminosity variability of NGC4945 implies that large errors can arise from using single-epoch X-ray data to derive L/L_Edd values for obscured AGNs.
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