Intensity-dependent transmission measurements of 310-nm femtosecond pulses show that diamond has a two-photon absorption coefficient of 0.75 +/- 0.15 cm/GW, in approximate agreement with universal scaling formulas for two-photon absorption in diamond-structure materials. We then demonstrate that two-photon absorption is strong enough to permit simple measurements of ultraviolet femtosecond pulse widths in single-crystal diamond plates that are thin enough (250-mu-m) to be both inexpensive and dispersion free. Autocorrelation measurements of 10-50-nJ, 0.18-1.4-ps pulses are presented. The method requires no phase matching and can be applied to pulses in the wavelength range of 220-550 nm.