Why two sleep calculators disagree

The four

1. The cycle length. Ninety is the convention, and where it came from has its own page, but nothing obliges a calculator to use it or to say what it uses instead. A ten-minute difference becomes fifty minutes by the fifth cycle.
2. The drop-off allowance. Some calculators add one and some do not, and one that never mentions it is allowing nothing without saying so.
3. Which cycle counts are offered. Some print every count from three to six, and some leave the shorter ones out. A site that never prints the three-cycle line is making an editorial choice and presenting it as a calculation.
4. Whether the allowance is inside or outside the count. Whether the printed time is when to get into bed or when to be asleep changes every row by the size of the allowance.

Most sites publish the first and are quiet about the other three. The difference between two calculators is almost always in the quiet ones.

What this site does

Ninety and fifteen, both shown on the page and both adjustable. Six, five, four and three cycles, always all four, including the short one. The printed time is when to get into bed, with the allowance added on top of the cycles rather than taken out of them.

You can therefore reproduce every number here by hand, which is the only test of a calculator that means anything.

Reproducing it

Multiply the cycle length by the number of cycles. Subtract that from the alarm. Subtract the drop-off allowance as well. That is the bedtime, and it is the whole algorithm.