A failure determination device for an angle detector for a rotating machine, the failure determination device comprising: an angle detector, which includes n pole pairs, and is configured to output a sine wave signal and a cosine wave signal in accordance with a rotational position of a rotating machine including a multi-phase winding and m pole pairs, wherein m is a natural number of 2 or more and n is a natural number that is smaller than m; and a failure determiner configured to determine failure of the angle detector based on signals from the angle detector, wherein the angle detector is configured to output the sine wave signal including a first sine wave signal and a second sine wave signal having a phase that is different by 180° from a phase of the first sine wave signal, and the cosine wave signal including a first cosine wave signal and a second cosine wave signal having a phase that is different by 180° from a phase of the first cosine wave signal, and wherein the failure determiner is configured to determine that the angle detector is out of order when the failure is determined with use of: first failure determination using a sum of the first sine wave signal and the second sine wave signal and a sum of the first cosine wave signal and the second cosine wave signal, and second failure determination using a sum of squares or a square root of a sum of squares of the sine wave signals and the cosine wave signals, characterized in that the failure determiner is further configured to determine the failure with use of the second failure determination when failure has failed to be determined in the first failure determination. an angle detector, which includes n pole pairs, and is configured to output a sine wave signal and a cosine wave signal in accordance with a rotational position of a rotating machine including a multi-phase winding and m pole pairs, wherein m is a natural number of 2 or more and n is a natural number that is smaller than m; and a failure determiner configured to determine failure of the angle detector based on signals from the angle detector, wherein the angle detector is configured to output the sine wave signal including a first sine wave signal and a second sine wave signal having a phase that is different by 180° from a phase of the first sine wave signal, and the cosine wave signal including a first cosine wave signal and a second cosine wave signal having a phase that is different by 180° from a phase of the first cosine wave signal, and wherein the failure determiner is configured to determine that the angle detector is out of order when the failure is determined with use of: first failure determination using a sum of the first sine wave signal and the second sine wave signal and a sum of the first cosine wave signal and the second cosine wave signal, and second failure determination using a sum of squares or a square root of a sum of squares of the sine wave signals and the cosine wave signals, first failure determination using a sum of the first sine wave signal and the second sine wave signal and a sum of the first cosine wave signal and the second cosine wave signal, and second failure determination using a sum of squares or a square root of a sum of squares of the sine wave signals and the cosine wave signals, characterized in that the failure determiner is further configured to determine the failure with use of the second failure determination when failure has failed to be determined in the first failure determination.