We present the first estimate of the evolution of tropospheric ozone (O3(T)) radiative forcing since 1860 and into the future. The UKMO 3-D chemistry-transport model (STOCHEM) was used to simulate the tropospheric composition in 1860, 1950, 1970, 1990 and 2100, by changing trace gas emissions. The future scenario used a doubled CO2 climate. STOCHEM includes extensive non-methane hydrocarbon (NMHC) chemistry, and produces a reasonable simulation of present-day O3(T). Radiative forcings caused by the modelled changes in O3(T) since 1860 were calculated using the UKMO radiation code, and included clouds and stratospheric temperature adjustment. Calculated changes in the global annual mean forcing since 1860 were 0.13, 0.22, 0.29 and 0.48 Wm-2 for the four years. Up to 1990 this forcing scales linearly with the change in total NOx emissions since 1860; this linearity breaks down in 2100. The 1990 forcing is at the lower end of the range from previous modelling studies (0.28-0.51 Wm-2), but is still significant, enhancing the well-mixed greenhouse gas forcing by over 10%.