ABSTRACT Stars that are both pulsating and eclipsing offer an important opportunity to better understand many of the physical phenomena that occur in stars, because it is possible to measure the pulsation frequencies of stars for which the masses and radii are known precisely and accurately. KIC 9851944 is a double-lined detached eclipsing binary containing two F-stars which show both pressure and gravity mode pulsations. We present an analysis of new high-resolution spectroscopy of the system and high-quality light curves from the Kepler and TESS space missions. We determine the masses and effective temperatures of the stars to 0.6 per cent precision, and their radii to 1.0 and 1.5 per cent precision. The secondary component is cooler, but larger and more massive than the primary so is more evolved; both lie inside the δ Scuti and γ Doradus instability strips. We measure a total of 133 significant pulsation frequencies in the light curve, including 14 multiplets that each contain between 3 and 19 frequencies. We find evidence for tidal perturbations to some of the p and g modes, attribute a subset of the frequencies to either the primary or secondary star, and measure a buoyancy radius and near-core rotational frequency for the primary component. KIC 9851944 is mildly metal-rich and MIST isochrones from the MESA evolutionary code agree well with the observed properties of the system for an age of 1.25 Gyr.