# Find symbol duration from symbol rate

How can one find symbol duration if bit rate is 100 kbs (as BPSK is used, symbol rate = bit rate)?

The symbol duration $$T_p$$ is related to the symbol rate $$R_s$$ by the simple relationship $$T_p = \frac{1}{R_p}$$
In the case of BPSK, $$R_p$$ is equal to the bit rate $$R_b$$, and $$T_p = \frac{1}{R_b}$$
For constellations with $$M$$ elements, each symbol encodes $$k = \log_2(M)$$ bits, the symbol rate is $$R_p = R_b / k$$, and the symbol duration is $$T_p = \frac{1}{R_p} = \frac{k}{R_b}$$