If the concentration of two acids are the same, their relative strengths can be compared by

Consider two acids ${\mathrm{HA}}_1$ and ${\mathrm{HA}}_2$ that have same concentration (C). 

For the first acid,

${\mathrm{HA}}_1\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{A}}_1^{-}$

According to Ostwald's Law of dilution,

$\begin{array}{l}{K}_{a_1}=C{\alpha }_1^2\\ {\alpha }_1=\sqrt{\frac{K_{a_1}}{C}}\end{array}$

For the second acid,

${\mathrm{HA}}_2\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{A}}_2^{-}$

According to Ostwald's Law of dilution,

$\begin{array}{l}{K}_{a_2}=C{\alpha }_2^2\\ {\alpha }_2=\sqrt{\frac{K_{a_2}}{C}}\end{array}$

Then, their ratio is 

$\frac{{\mathrm{\alpha }}_1}{{\mathrm{\alpha }}_2}=\sqrt{\frac{{\mathrm{K}}_{{\mathrm{a}}_1}}{{\mathrm{K}}_{{\mathrm{a}}_2}}}$

If concentration of two acids are same so their relative strength can be compared by their [H⁺] concentration.