We present absolute frequency measurements of $2{\mathrm{S}}_{1/2}\text{−}\mathrm{n}{\mathrm{S}}_{1/2}$ two-photon transitions with $n=8$, 9, and 10 in a cryogenic beam of atomic hydrogen. Each transition has been measured with a fractional uncertainty of $\approx 2.6\times {10}^{-12}$. Combining the results from this Letter and the $1{\mathrm{S}}_{1/2}\text{−}2{\mathrm{S}}_{1/2}$ transition frequency, we extract a root-mean-square proton radius of $r_p=0.8433(31)\mathrm{fm}$ and a Rydberg frequency of $c{R}_{\infty }=3289841960252.9(9.7)\mathrm{kHz}$. These are in good agreement with the CODATA 2022 recommended values.

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• Atomic spectra
• Precision measurements