  Thermal energy can be directly converted to electrical energy as a result of
thermoelectric effects. Because this conversion realises clean energy
technology, such as waste heat recovery and energy harvesting, substantial
efforts have been made to search for thermoelectric materials. Under the belief
that the material figure of merit $zT$ represents the energy conversion
efficiencies of thermoelectric devices, various high peak-$zT$ materials have
been explored for half a century. However, thermoelectric properties vary
greatly with temperature $T$, so the single value $zT$ does not represent
device efficiency accurately. Here we show that the efficiency of
thermoelectric conversion is completely determined by \emph{three} parameters
$Z_{\mathrm{gen}}$, $\tau$, and $\beta$, which we call the \emph{thermoelectric
degrees of freedom}. The $Z_{\mathrm{gen}}$, which is an average of material
properties, is a generalisation of the traditional figure of merit. The $\tau$
and $\beta$, which reflect the gradients of the material properties, are
proportional to escaped heat caused by the Thomson effect and asymmetric Joule
heat, respectively. Our finding proposes new directions for achieving high
thermoelectric efficiency; increasing one of the thermoelectric degrees of
freedom results in higher efficiency. For example, thermoelectric efficiency
can be enhanced up to 176\% by tuning the thermoelectric degrees of freedom in
segmented legs, compared to the best efficiency of single-material legs.
