Sharon is located at 37°14'60N, 98°25'7W (37.249992, -98.418613). According to the United States Census Bureau, the city has a total area of 0.8 km² (0.3 mi²), all land.
As of the census of 2000, there were 210 people, 91 households, and 54 families residing in the city. The population density was 279.6/km² (713.4/mi²). There were 100 housing units at an average density of 133.1/km² (339.7/mi²). The racial makeup of the city was 95.24% White, 2.38% Native American, 0.48% Asian, 0.48% from other races, and 1.43% from two or more races. Hispanic or Latino of any race were 0.48% of the population.
There were 91 households out of which 25.3% had children under the age of 18 living with them, 56.0% were married couples living together, 4.4% had a female householder with no husband present, and 39.6% were non-families. 35.2% of all households were made up of individuals and 24.2% had someone living alone who was 65 years of age or older. The average household size was 2.31 and the average family size was 3.05.
In the city the population was spread out with 26.2% under the age of 18, 3.8% from 18 to 24, 20.0% from 25 to 44, 27.6% from 45 to 64, and 22.4% who were 65 years of age or older. The median age was 45 years. For every 100 females there were 85.8 males. For every 100 females age 18 and over, there were 80.2 males.
The median income for a household in the city was $37,188, and the median income for a family was $43,056. Males had a median income of $30,500 versus $20,625 for females. The per capita income for the city was $12,759. None of the families and 4.0% of the population were living below the poverty line, including no under eighteens and 5.6% of those over 64.