Advances in laser spectroscopy have enabled many scientific breakthroughs in physics, chemistry, biology, and astronomy. Optical frequency combs pushed measurement limits with ultrahigh-frequency accuracy and fast-measurement speed, while tunable-diode-laser spectroscopy is used in scenarios that require high power and continuous spectral coverage. Despite these advantages of tunable-diode-laser spectroscopy, it is challenging to precisely determine the instantaneous laser frequency because of fluctuations in the scan speed. Here, we demonstrate a simple spectroscopy scheme with a frequency-modulated diode laser that references the laser on-the-fly to a fiber cavity. The fiber cavity’s free spectral range is on-the-fly calibrated with sub-10-Hz frequency precision. We achieve a relative precision of the laser frequency of 2 × ^{10 - 8} for an 11-THz frequency range at a measurement speed of 1 THz / s. This is an improvement of more than 2 orders of magnitude compared to existing diode-laser-spectroscopy methods. Our scheme provides precise frequency calibration markers, while simultaneously tracking the instantaneous scan speed of the laser. We demonstrate the versatility of our method through various applications, including dispersion measurement of a fiber, ultrahigh-Q microresonators, and spectroscopy of a hydrogen fluoride gas cell. The simplicity, robustness, and low cost of this spectroscopy scheme are valuable for out-of-the-lab applications like lidar and environmental monitoring.