How every number here is calculated
Claritips only shows numbers you could recompute with a calculator. That is easy to claim and worth proving, so this page is the proof: for each of the six tools, the formula it runs, the constants it runs on, a worked example, and what the arithmetic cannot know.
THE SHORT ANSWER
There is no model and nothing is predicted. Every tool is a few lines of arithmetic over the values you pick, running in your browser - no account, and nothing sent anywhere. Each result on this page can be reproduced by hand from the formula above it.
Caffeine half-life calculatorSleep cycle calculatorSleep debt calculatorWhy am I tired?Chronotype quiz: owl or lark?Water intake calculator
Caffeine half-life calculator
How much caffeine is still in me at bedtime?
THE FORMULA
dose = mg per drink x number of drinks
remaining = dose x 0.5 ^ (hours until bed / half-life)
THE CONSTANTS
Half-lives offered 4 h (fast), 5 h (average), 6.5 h (slow)
Espresso 63 mg
Coffee, 8 oz 95 mg
Cold brew 200 mg
Latte 77 mg
Energy drink 160 mg
Black tea 47 mg
"Espressos still in you" remaining mg / 63
Worked example. Two 8 oz coffees (190 mg) at 2 pm, bed at 11 pm, 5-hour half-life: 190 x 0.5 ^ (9 / 5) = 55 mg, which the tool also reports as 0.9 espressos.
What it cannot know. Exponential decay with a single half-life is the standard model, and it is only as good as the half-life you pick. Yours is largely genetic and shifts with pregnancy, some medications and smoking, so the three options are population brackets rather than a measurement of you. Drink sizes vary hugely between cafes; the milligram figures are typical values, not your cup.
Sleep cycle calculator
What time should I go to bed to wake up at a given time?
THE FORMULA
bedtime = wake time - (cycles x 90 minutes) - time to fall asleep
THE CONSTANTS
Cycle length 90 minutes, fixed
Cycles offered 6 (9 h), 5 (7.5 h), 4 (6 h), 3 (4.5 h)
Time to fall asleep 0, 15 or 30 minutes (15 by default)
Wake times offered 5:30 am to 8:30 am, in half hours
Worked example. Wake at 7:00 am, 5 cycles, 15 minutes to fall asleep: 7:00 am minus 450 minutes minus 15 minutes = 11:15 pm.
What it cannot know. A 90-minute cycle is the population average; real cycles run roughly 70 to 120 minutes and change through the night, so treat every bedtime here as the middle of a window rather than a deadline. The calculator also cannot know how long you personally take to fall asleep, which is why that is a control and not an assumption.
Sleep debt calculator
How much sleep am I down over the last week, and how long to repay it?
THE FORMULA
debt = sum over the last 7 nights of (nightly need - hours slept)
repayment nights = debt / extra hours per night, rounded up
THE CONSTANTS
Nightly need options 7, 7.5, 8 or 8.5 hours
Hours per night accepted 3 to 12
Surplus debt of 0 or less
Light debt under 3 h, repaid at +30 min a night (minimum 2 nights)
Real debt 3 to 7 h, repaid at +45 min a night
Heavy debt 7 h or more, repaid at +54 min a night
Lie-in cap 1 hour, in every plan
Worked example. A need of 8 hours against nights of 6.5, 7, 6, 7.5, 6, 8.5 and 7 hours: 56 needed minus 48.5 slept = 7.5 hours of debt, which is the heavy band, and 7.5 / 0.9 rounds up to 9 nights.
What it cannot know. Sleep debt is arithmetic, not physiology: nothing is known about the quality of those hours, and the research on how much of a long-run deficit extra sleep actually recovers is unsettled. The nightly need is your own estimate, and it is the single number the whole total hangs on. Hours slept are what you report, not what a lab measured.
Why am I tired?
Which of the usual causes of tiredness fit my answers best?
THE FORMULA
each answer adds a weight to one or more of 8 candidate causes
score for a cause = sum of its weights across your 9 answers
percentage = score / that cause’s maximum possible score
the three highest-scoring causes are shown, strongest first
THE CONSTANTS
Questions 9
Candidate causes 8, each with its own maximum (3 to 8 points)
Strong signal 60 percent or more of that cause’s maximum
Worth testing 35 to 59 percent
Mild under 35 percent
Shown top 3 only, and only causes that scored above zero
Worked example. Answers adding 5 of a possible 8 points to plain sleep debt give 63 percent, a strong signal, and it is ranked first unless another cause scores a higher percentage of its own maximum.
What it cannot know. A percentage here is how much of one cause’s own evidence your answers matched, so the three bars do not add up to 100 and a bar is not a probability. The quiz ranks suspects from nine taps; it cannot rule out the medical causes of fatigue, and anything persistent belongs with a clinician rather than a quiz.
Chronotype quiz: owl or lark?
Am I a morning lark, a night owl, or in between?
THE FORMULA
score = sum of the 8 answers, each worth 1 to 5 (earlier answers score higher)
score runs from 8 to 40
THE CONSTANTS
34 to 40 Definite morning lark
27 to 33 Moderate morning type
19 to 26 Intermediate - genuinely in between
12 to 18 Moderate evening type
8 to 11 Definite night owl
Worked example. Eight answers of 4 give 32, which lands in the 27 to 33 band: moderate morning type.
What it cannot know. Eight self-reported questions put you in one of five bands. That is a sorting tool, not the full 19-item morningness questionnaire used in research, and it is not a diagnosis of a circadian rhythm disorder. The wake, bed and peak-focus windows each band reports are typical ranges for that band, not a prescription - your own two weeks of data will beat them.
Water intake calculator
How much water should I actually drink in a day?
THE FORMULA
total fluid (L) = body weight in kg x 0.033
+ activity (0 / 0.3 / 0.7 / 1.2 for sedentary / light / active / very active)
+ climate (0 / 0.2 / 0.6 for cool / temperate / hot)
+ caffeine (0 / 0.1 / 0.2 / 0.35 for none / 1-2 / 3-4 / 5+ cups)
water to drink = total x 0.8
glasses = litres to drink x 1000 / 250
THE CONSTANTS
Base 33 ml per kg of body weight
From food 20 percent of the total, so only 80 percent is drunk
Glass 250 ml
Weight range accepted 35 to 180 kg
Pounds displayed as kg x 2.20462; the maths always runs in kg
Worked example. 70 kg, light activity, temperate climate, 1 to 2 coffees: 2.31 + 0.3 + 0.2 + 0.1 = 2.91 L total, of which 80 percent is 2.3 L to drink (9 glasses, about 79 oz), with roughly 0.6 L coming from food.
What it cannot know. This is a starting estimate built from a per-kilo rule, not a measurement of your losses. It does not model illness, pregnancy, breastfeeding, altitude, medication, or a medical reason to restrict fluid, and the caffeine additions are small because the diuretic effect of habitual caffeine is itself small. Thirst and urine colour beat any formula, including this one.
And in the app
The tools on this site work from values you pick. The app works from your own check-ins, and the same rule applies: every figure it shows is an average or a comparison of averages over days you logged, with the number of days printed next to it. A before-and-after comparison needs at least 3 logged days on each side before it will show a result, and until then it says how many more days it needs rather than showing a difference it cannot support.
Nothing is inferred, predicted or scored by a model. That is a deliberate limit: a difference between two small averages is worth seeing only if you can also see how small they are.
If a number here looks wrong
Then one of us has made a mistake, and we would rather know. Write to research@claritips.com with the tool and the inputs you used. Confirmed corrections ship within a week with a dated note on the page, the same as for the Pattern Library.