A soot accumulation computing and displaying device for displaying information regarding the amount of soot accumulated in a filter provided in a flow path of an exhaust gas from an internal-combustion engine, comprising: a first calculating part that is configured to calculate a first inferred value of a present soot accumulation amount, based on a main fuel injection amount having contributed to driving of the internal-combustion engine, the main fuel injection amount being estimated to the present time from the ending time of the latest completed regeneration processing of the filter; and a second calculating part that is configured to calculate a second inferred value of a present soot accumulation amount, based on a driving time of the internal-combustion engine and a first predetermined relation between the driving time of the internal-combustion engine and the soot accumulation amount; and a determining part configured to determine the maximum of the inferred values; characterized in that the first calculating part is configured to calculate the first inferred value based on the main fuel injection amount having contributed to driving of the internal-combustion engine, and a post fuel injection amount having contributed to regeneration processing of the filter, the post fuel injection amount being estimated to the present time from the ending time of the latest complete regeneration processing of the filter; the second calculating part is configured to calculate the second inferred value based on the driving time of the internal-combustion engine estimated to the present time from the starting time of the latest regeneration processing of the filter; and in that the device optionally comprises a third calculating part in addition to or as an alternative to the second calculating part, the third calculating part being configured to calculate a third inferred value of a present soot accumulation amount, based on a driving time of the internal-combustion engine, which is estimated to the present time from the ending time of the latest completed regeneration processing of the filter, and a second predetermined relation between the driving time of the internal-combustion engine and the soot accumulation amount; wherein the determining part is configured to determine the maximum inferred value among the first and second inferred values, the first and third inferred values, or the first, second, and third inferred values; and wherein the device further comprises a displaying part that is configured to display the maximum inferred value determined by the determining part. a first calculating part that is configured to calculate a first inferred value of a present soot accumulation amount, based on a main fuel injection amount having contributed to driving of the internal-combustion engine, the main fuel injection amount being estimated to the present time from the ending time of the latest completed regeneration processing of the filter; and a second calculating part that is configured to calculate a second inferred value of a present soot accumulation amount, based on a driving time of the internal-combustion engine and a first predetermined relation between the driving time of the internal-combustion engine and the soot accumulation amount; and a determining part configured to determine the maximum of the inferred values; characterized in that the first calculating part is configured to calculate the first inferred value based on the main fuel injection amount having contributed to driving of the internal-combustion engine, and a post fuel injection amount having contributed to regeneration processing of the filter, the post fuel injection amount being estimated to the present time from the ending time of the latest complete regeneration processing of the filter; the second calculating part is configured to calculate the second inferred value based on the driving time of the internal-combustion engine estimated to the present time from the starting time of the latest regeneration processing of the filter; and in that the device optionally comprises a third calculating part in addition to or as an alternative to the second calculating part, the third calculating part being configured to calculate a third inferred value of a present soot accumulation amount, based on a driving time of the internal-combustion engine, which is estimated to the present time from the ending time of the latest completed regeneration processing of the filter, and a second predetermined relation between the driving time of the internal-combustion engine and the soot accumulation amount; wherein the determining part is configured to determine the maximum inferred value among the first and second inferred values, the first and third inferred values, or the first, second, and third inferred values; and wherein the device further comprises a displaying part that is configured to display the maximum inferred value determined by the determining part.