  We present and validate simple and efficient methods to estimate the
chaoticity of orbits in low dimensional dynamical systems from computations of
Lagrangian descriptors (LDs) on short time scales. Two quantities are proposed
for determining the chaotic or regular nature of orbits in a system's phase
space, which are based on the values of the LDs of these orbits and of nearby
ones: The difference (DNLD) and ratio (RNLD) of neighboring orbits' LDs. We
find that, typically, these indicators are able to correctly characterize the
chaotic or regular nature of orbits to better than 90 % agreement with results
obtained by implementing the Smaller Alignment Index (SALI) method, which is a
well established chaos detection technique. Further investigating the
performance of the two introduced quantities we discuss the effects of the
total integration time and of the spacing between the used neighboring orbits
on the accuracy of the methods, finding that even typical short time, coarse
grid LD computations are sufficient to provide a reliable quantification of a
system's chaotic component, using less CPU time than the SALI. In addition to
quantifying chaos, the introduced indicators have the ability to reveal details
about the systems' local and global chaotic phase space structure. Our findings
clearly suggest that LDs can also be used to quantify and investigate chaos in
continuous and discrete low dimensional dynamical systems.
