How is a biorhythm calculated?

Three sine waves and a day count — that really is all of it. So we counted a whole cycle to see what the arithmetic actually says.

The short answer

Count the whole days between the date you were born and the date you are looking at. Feed that one number into three sine waves: one that comes back round every 23 days, one every 28, one every 33. Multiply each result by 100, round it to a whole number, and you have the three values on the screen, each somewhere between −100 and +100. That is the entire calculation and there is nothing else in it. Nothing is drawn, no table is consulted, your birth time is not used, and the same birth date read on the same day will always give the same three numbers to everybody. The three curves are traditionally labelled physical, emotional and intellectual, and Bokki turns each number into one short sentence by asking which of four bands it fell into.

This is the one screen here that is not a tradition

Every other calculation on Bokki traces back to a documented lineage we can check ourselves against, and where the schools disagree we say which one we followed. Biorhythm has no such lineage, and we would rather say that at the top than let it sit quietly among the others. It is a late-nineteenth and twentieth-century idea, attached to Wilhelm Fliess and Hermann Swoboda and later to Alfred Teltscher, and it became popular in the 1970s. Controlled studies have looked for predictive validity and repeatedly failed to find any; it is generally regarded as pseudoscience. Our own source file states all of that in a comment above the first line of code, so that nobody maintaining it can mistake what it is. We keep the screen because a three-number daily mirror can be a pleasant nudge to notice how you actually feel, and we label it as a modern model wherever it appears. But it does leave us in an unusual position for this site: the only thing here we can be accurate about is the arithmetic itself. So we went and counted it.

The four bands are not four quarters

Bokki sorts each value into one of four bands and prints a sentence for it: high, good, turning point, low. The cut-offs are +60, +15 and −15 on a scale that runs from −100 to +100, which means high needs a value of sixty or more, while low is everything from −15 all the way down. Written out as slices of the scale that is 40 points wide for high, 45 for good, 30 for the turning point and 85 for low — the negative half is almost entirely one band. So we ran the actual code across a whole cycle, 21,252 days, and counted where the days landed. The physical curve came back low on 9,240 of them, which is 43.5%, and high on 6,468, which is 30.4%. The emotional curve was low on 46.4% of days and high on 32.1%. The intellectual curve was low on 45.5% and high on 30.3%. Almost half of your days come back labelled low on any given curve. Taking all three at once, 9.2% of days have every curve in the low band and only 3.0% have every curve high. We want to be careful about the cause: the slices of the scale above are not the same thing as the share of days, because a sine wave lingers near its extremes and hurries through the middle. But the direction is the same, and the point stands. If your chart tells you most days that you are running low, that is a fact about where three lines were drawn, not a fact about you.

Why almost half of your days come back 'low'Two stacked panels. The upper panel has three horizontal bars, one for each curve — physical, emotional, intellectual — each bar divided into the four bands the code sorts a value into: high, good, turning point and low. Every bar is dominated by the low band, which takes 43.5% of days for the physical curve, 46.4% for the emotional and 45.5% for the intellectual, while high takes 30.4%, 32.1% and 30.3%. A dashed line marks 25%, where each band would sit if the four were equal quarters. The counts come from running the code across a whole cycle of 21,252 days. The lower panel shows where the band edges sit on the value scale. The scale runs from +100 at the top to −100 at the bottom, and the cuts are at +60, +15 and −15, so the high band is only 40 points tall while the low band is 85 points tall — the negative half of the scale is almost entirely one band.share of days in each band — counted over one full 21,252-day cyclephysical (23d)30.4%43.5%emotional (28d)32.1%46.4%intellectual (33d)30.3%45.5%equal quarters would be 25%highgoodturning pointlowwhere the band edges sit on the −100…+100 scale+60+15-15+100−100high · 40good · 45turning point · 30low · 85Slices of the scale and shares of days are not the same thing — a sine lingers at its extremes.

It does repeat, and there is one day it all goes flat

Because 23, 28 and 33 share no factor between them, the three curves cannot come back into the same alignment until 23 × 28 × 33 days have passed. That is 21,252 days, about 58.2 years. We did not want to take that on faith, so we took 400 consecutive days and compared each one against the same day exactly one cycle later: all 400 matched to the number. There is also exactly one day inside a lifetime when all three curves read zero at the same moment, and it is your 10,626th day, which arrives at roughly twenty-nine years and one month. We ran it and got 0, 0, 0; the day before reads −27, +22 and −19. One more thing came out of the counting that we did not expect. The emotional curve is coarser than the other two. Twenty-eight is even and the other two lengths are odd, and a sine wave read on whole days is mirror-symmetric, so an even cycle makes the back half repeat the numbers of the front half. Over its twenty-eight days the emotional curve prints only fifteen different numbers, while the physical curve prints twenty-three in twenty-three days and the intellectual thirty-three in thirty-three. It also sits on exactly zero twice per cycle where the other two do it once.

What we don't calculate

We do not predict anything from this, and there is no code here that could. Nothing is called a critical day or a dangerous day; no value is read as a warning about your body, your driving, your training or your money; and we do not put two people's curves side by side and call the result compatibility. The chart is three numbers and one short sentence each, and the sentence is an invitation to check in with yourself rather than a forecast. We do not use your birth time, so the calculation cannot be made more precise by giving us one — only the date counts, and two people born twenty minutes apart across midnight will be one day apart for the rest of their lives. We do not weight the three curves against each other or combine them into a single score. And we do not present any of it as a tradition. If you want the part of this site with a lineage behind it, the four pillars are next door.

← See your four pillars

Read next

See your own three curves for today
What is 사주 (saju)? — the part of this site with a lineage behind it
How do I read my Saju reading? — the seam between what never changes and today
How a life path number is calculated — the other arithmetic-only screen
What is 삼재 (Samjae)? — a three-year cycle that is a tradition

Questions about the biorhythm chart

How is a biorhythm calculated?

Count the whole days between your birth date and the day you are looking at, then read three sine waves at that day number: one that repeats every 23 days, one every 28, one every 33. Each value is sin(2π × days ÷ cycle length), multiplied by 100 and rounded to a whole number, so every reading lands between −100 and +100. That is the entire calculation. Nothing is drawn, nothing is looked up, and the same birth date on the same day always gives the same three numbers.

Is biorhythm part of Saju or any traditional system?

No, and our own source file says so at the top before any code runs. It is a late-19th and 20th-century construct, popularised in the 1970s, with no connection to Saju, Zi Wei, or any classical divination lineage. Controlled studies have repeatedly found no predictive validity. We keep it as a gentle daily mirror and label it as a modern model wherever it appears, so it is never mistaken for the traditional engines sitting next to it.

Are the four bands — high, good, turning point, low — four equal quarters?

They are not, and this is the thing we most wanted to write down. The cut-offs are +60, +15 and −15 on a scale that runs from −100 to +100, so high needs a value of +60 or more while low is anything at −15 or below. We ran the code across a whole 21,252-day cycle and counted: the physical curve reads low on 43.5% of days and high on 30.4%; emotional low on 46.4% and high on 32.1%; intellectual low on 45.5% and high on 30.3%. Almost half your days come back labelled low. That is a property of where the lines were drawn, not a statement about you.

Does the whole pattern ever repeat?

Yes, and we checked it rather than assuming it. Because 23, 28 and 33 share no common factor, the three curves only line up again after 23 × 28 × 33 = 21,252 days, which is about 58.2 years. We compared 400 consecutive days against the same 400 days one full cycle later and all 400 matched exactly. There is also a single day when all three read exactly zero together: your 10,626th day, roughly 29 years and one month old. We ran it — 0, 0, 0 — and the day before reads −27, +22, −19.

Why does the emotional curve look coarser than the other two?

Because 28 is an even number and the other two are odd. A sine wave read on whole days is mirror-symmetric, so an even cycle length makes the second half repeat the numbers of the first. Over its 28-day cycle the emotional curve prints only 15 different numbers, while the physical curve prints 23 different numbers in 23 days and the intellectual one 33 in 33. It also lands on exactly zero twice per cycle, where the other two land on zero once.

Does my birth time change the numbers?

No. The day count is taken between two calendar dates at midnight UTC, so only the date matters and the clock time of birth is not used at all. One consequence worth knowing: two people born twenty minutes apart across midnight get day numbers one apart for the rest of their lives, and their charts never line up.

What does Bokki not claim from this?

That it predicts anything. We do not tell you a day is dangerous, we do not call anything a critical day, we do not give medical, athletic or financial advice from it, and we do not compare two people's curves and call it compatibility. There is no such code. The chart shows three numbers and one short sentence per curve, and the sentence is a prompt to notice how you feel, not a forecast of what will happen.