We present a facile and reproducible method for synthesizing monodisperse platinum (Pt) spheres with sizes ranging from 10 to 100 nm in diameter and exceptionally small standard deviations of 3% for large spheres. The reaction takes place in aqueous solution using a multistep seed-mediated approach. The Pt nanospheres consist of several small crystallites resulting in a surface roughness of 5-10 nm. Extinction spectra are measured from particles dispersed in water and calculated for single particles which are found to be in excellent agreement. We obtain a linear correlation between the plasmon extinction maximum (from UV to the visible regions) and the particle diameter which might be of value for experimentalists in the field.