The measurement of peak laser intensities exceeding 10 20 W/cm 2 is in general a very challenging task. We suggest a simple method to accurately measure such high intensities up to about 10 23 W/cm 2 , by colliding a beam of ultrarelativistic electrons with the laser pulse. The method exploits the high directionality of the radiation emitted by ultrarelativistic electrons via nonlinear Thomson scattering. Initial electron energies well within the reach of laser wake-field accelerators are required, allowing in principle for an all-optical setup. Accuracies of the order of 10% are theoretically envisaged. c 2018 Optical Society of America OCIS codes: 190.1900,020.2649 Since the successful application of the chirped pulse amplification technique to generate short laser pulses [1], records in terms of peak intensity are being continuously set. Intensities as high as 2 × 10 22 W/cm 2 have already been reached [2], and much higher ones are envisaged [3], allowing for investigations in different fields including strong-field quantum electrodynamics (QED) and plasma physics [4].The analysis of experiments employing ultrarelativistic optical laser pulses, i.e. optical pulses with intensities exceeding 10 20 W/cm 2 , requires the precise knowledge of quantities characterizing the pulse itself such as its peak intensity. However, ultrarelativistic peak intensity measurements are especially difficult because the damage threshold of the equipment is usually far exceeded by such strong laser pulses.To the best of our knowledge, the peak intensity of ultrarelativistic pulses is currently determined by measuring energy, duration and spot-size of the pulse, the latter however at a lower intensity. Therefore, this method is prone to errors since the spot-size can be affected by increasing the pulse intensity [2,5,6]. It is desirable to find precise methods in order to measure directly the peak intensity of the laser field. There are several suggestions for direct in situ measurements of peak intensities by employing multiply-charged ions. The general idea behind these methods is to place ions at the laser focus, with charge number selected according to the expected intensity. Then, by measuring either the photo-ion momentum distribution [7], or the ionization fraction [5,8], one can determine the laser peak intensity. An alternative method is based on the emission of electrons "born" via ionization within the laser pulse [9].In this Letter we suggest a novel method to determine the peak intensity of an ultrarelativistic laser pulse, by measuring the angular aperture of the radiation spectrum emitted via nonlinear Thomson scattering by an ultrarelativistic electron beam colliding head-on with the pulse. The method is practically insensitive to the precise temporal shape of the laser pulse and it allows for singleshot intensity measurements with theoretical accuracies in principle of the order of 10%. Units with c = = 1 and a metric with signature + − −− are employed throughout.Classically it is known that an accelerated ultrarel...