We have used infrared transmission and nuclear-reaction analysis to determine the ir absorption strength of the Si-H wagging and stretching modes in hydrogenated amorphous silicon (a-Si:H). The films were deposited by plasma-assisted chemical vapor deposition and reactive magnetron sputtering. We show that the widely used ir-data-analysis method of Brodsky, Cardona, and Cuomo can lead to significant errors in determining the absorption coefficients, particularly for films less than \ensuremath{\sim}1 \ensuremath{\mu}m thick. To eliminate these errors we explicitly take into account the effects of optical interference to analyze our data. We show that the hydrogen content can be determined from the stretching modes at \ensuremath{\omega}=2000 and 2100 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ as well as the wagging mode at \ensuremath{\omega}=640 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. By assigning different oscillator strengths to the 2000- and 2100-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ modes, we show that the absorption strength of the stretching modes does not depend on the details of sample preparation, contrary to hypotheses previously invoked to explain experimental data. We obtain ${\mathit{A}}_{640}$=(2.1\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, ${\mathit{A}}_{2000}$=(9.0\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, and ${\mathit{A}}_{2100}$=(2.2\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{20}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ for the proportionality constants between the hydrogen concentration and the integrated absorbance of the wagging and stretching modes. The value of ${\mathit{A}}_{640}$ is \ensuremath{\sim}30% larger than the generally used value. We show that previously published data for both the wagging and stretching modes are consistent with the proportionality factors determined in the present study.