1. An area information estimating device comprising: a camera that photographs an image within a sensing area; a person detector that detects a person from the image from the camera; a position calculator that calculates an existence position of the person in the sensing area based on a coordinate on the image in which the person is detected by the person detector, wherein the person detector excludes the person in whom a relationship between the coordinate and a size on the image does not satisfy a predetermined condition from a detection target; and an estimator that estimates an existence allowable area where a person can exist in the sensing area based on a distribution of the existence position of the person detected in a predetermined period in the sensing area, wherein the estimator superposes each detected existence position on plan view in a form of a probability density distribution, and determines an area where a cumulative probability becomes greater than or equal to a predetermined level as the existence allowable area, and wherein the area information estimating device is included in an air conditioner that performs air conditioning control based on information estimated by the area information estimating device.