Extreme lasers capable of short, high-energy pulses are probing the frontiers of science and advancing practical technology. The utility of such lasers increases with their average power delivery, which enables faster data acquisition, higher flux of laser-driven particle and radiation sources and more efficient material processing. However, the same extreme energies and electric field strengths of these lasers are currently preventing their direct and high accuracy measurement for these experimental applications. To overcome this limitation, we use the momentum of the laser pulses as a measurement proxy for their energy. When light reflects from an ideal mirror, its momentum is transferred to the mirror, but its energy is reflected. We demonstrate here a force-sensing mirror configuration to measure laser pulse energies up to 100 J/pulse (10 ns duration, 10 Hz repetition rate) from a kilowatt-level average power multi-slab laser operated at the HiLASE facility of the Czech Academy of Sciences. We combine a radiation-pressure power meter with a charge integrator photodiode to form what we refer to as a Radiation Pressure Energy Meter. To our knowledge, this is the first demonstration of a high-accuracy, non-absorbing, SI traceable primary standard measurement of both single and average pulse energies of a 1-kW-average-power pulsed laser source. With this, we demonstrate a practical method for in-situ calibration of the traditional thermal instruments (pyroelectric detectors) currently used for indirect measurements of energy and power of such extreme lasers.