The idea
BPM means beats per minute. At a constant tempo, one beat lasts 60 / BPM seconds and a passage lasts bars × beats per bar × 60 / BPM. The formula needs you to define what a beat represents.
Try it
At 120 BPM, four beats per bar and eight bars, the duration is 16 seconds. One beat is 500 milliseconds. At 90 BPM the same 32 beats take about 21.333 seconds. Enter those values in the calculator and compare the JSON output.
What to watch for
Time signatures such as 6/8 can be counted as six eighth notes or two dotted-quarter beats. Use the beat unit that matches the BPM marking; otherwise the result can be off by a factor of three. Fermatas, count-ins, tempo ramps and swing are not included automatically.
Next step
Generate a metronome with the same tempo, bar count and beats per bar. The WAV duration and the numeric calculation should agree up to sample rounding. Add any intro or silence separately in an audio editor.