Strength(t) = max · (1 − e−kt). The rate depends on what is still left in the leaf, so it starts fast and tails off, the shape of Newton’s law of cooling.
Arrhenius, with an activation energy of 45 kJ/mol: about ×1.5 per 10°C, so 80°C water extracts at 44% of the speed of boiling.
Newton’s law of cooling, with a time constant from the vessel, calibrated so a 200 ml mug sits at 20 minutes. Extraction slows as it cools.
A 200 ml mug is about 300 g of ceramic; about 70% of its mass joins in. It takes real energy out of the water in the first seconds.
Diffusion out of a leaf slows as the concentration difference between leaf and water shrinks: the same principle as Newton’s law of cooling, moving a solute instead of heat. It is why “one more minute” matters far more early in the brew than after five.
A smaller mug with the same single bag has a higher tea-to-water ratio, raising the achievable maximum, not because the bag extracts faster but because less water dilutes the same extracted material. Many food-service bags are sized for a quick dunk, deliberately using less tea per cup than a home brewer would for a longer steep.
Green tea is brewed cooler and briefer because its delicate catechins extract fast and turn bitter if over-steeped. The same exponential-approach model applies, calibrated very differently.
Three hundred grams of cold ceramic takes real energy to warm, and takes it out of your water in the first few seconds. Boiling water into a cold 200 ml mug arrives at about 85°C. Rinsing the mug with hot water first is worth 11°C, more than any other single free thing you can do to a cup of tea.
The cooling time constant is heat capacity over surface area, and drinking removes capacity but leaves most of the area. A quarter-full 200 ml mug cools with a time constant under eight minutes against twenty for a full one: about two and a half times faster.
The time to fall from 60°C to 50°C is the time constant times ln(40/30), and the starting temperature cancels out. Boiling or barely hot, the drinkable window is the same length, about six minutes for a mug. A hotter start moves the window later; it does not widen it. Only a bigger vessel or a warmer room does.
The IARC reviewed very hot drinks in 2016 and drew its line at 65°C, on oesophageal risk rather than taste. A boiling mug of black tea in a 20°C room does not cross that line for about ten minutes. Milk gets you there roughly three minutes sooner, a better argument for it than the ones people usually give.
Teabag tea is typically CTC-processed — crushed, torn and curled into small fragments with far more exposed surface area than whole or lightly-broken loose leaves. More surface area means faster diffusion, which is exactly why this tool uses a slower rate constant for loose leaf.
Not the rate — but it raises the ceiling. More tea relative to the water means more extractable material available, so the same brew time reaches a darker maximum, even though the underlying diffusion rate per leaf fragment is unchanged.
Colour is what you actually judge a cup by — this tool solves the extraction equation backward, working out exactly how long your specific tea amount and mug size need to reach the shade you tapped, rather than you guessing at a generic "3 minutes" that assumes a specific ratio.
It depends entirely on when it goes in, which is why that is now a control.
Milk at the end — once the leaves are out — cannot touch extraction. It only dilutes what you end up drinking, and by more than people expect: a 30 ml splash in a 200 ml mug takes 13% off the strength, and a proper builder's 50 ml takes 20%.
Milk in the mug first is a different drink. Thirty millilitres straight from the fridge drops a 200 ml brew from 96 °C to about 85 °C before the leaves have done anything, and the extraction runs at that lower temperature for the whole steep. Three minutes then gets you 44% of the maximum instead of 59% — about a sixth of your tea, gone. This page used to say milk could not affect brewing. That was only ever true of milk added at the end.
Yes, and by almost nothing. It is a real effect and the physics is sound: a cooler cup loses heat more slowly, because the rate depends on the gap to the room. But over the few minutes between "in first" and "just before drinking" it comes to under one degree at the fifteen-minute mark. Weigh that against the sixth of the extraction it costs you.
What milk does do for temperature is immediate and large: any splash drops the cup six or seven degrees at once, which is why a milky tea is drinkable about three minutes sooner than a black one.
Because a cold mug is a bigger thief than a cooling kettle. A 200 ml mug is around 300 g of ceramic, and ceramic takes real energy to warm up. Boiling water poured into a cold one lands at about 85 °C, not 100. Rinse it with hot water first and you pour at 96 °C instead — a gain of 11 °C, which is worth more than anything else on this page costs you.
That extraction is first-order: the rate depends on how much is still left in the leaf, so it starts fast and tails off. That is why half the strength arrives in the first 97 seconds at a rolling boil and the remaining half takes five and a half minutes — and why "leave it a bit longer" does less than you would think.
That the rate is Arrhenius in temperature, with an activation energy of 45 kJ/mol — the middle of the band the tea-infusion kinetics literature reports for caffeine and the polyphenols. That works out at roughly ×1.5 per 10 °C, so 80 °C water extracts at 44% of the speed of boiling. Pick a different activation energy and every time on this page moves; the shape does not.
That the cup obeys Newton's law of cooling, with a time constant worked out from the vessel rather than guessed, calibrated so a 200 ml mug sits at 20 minutes. That constant quietly bundles in evaporation and radiation as well as convection, which is why it is larger than a textbook figure — and evaporation is the bigger term while the cup is near boiling, so in reality the first couple of minutes run a shade faster than an exponential.
That the mug, the water and the milk reach a common temperature instantly, and that about 70% of the vessel's mass joins in. A real mug's outside lags, and a real pour takes a few seconds.
Still absent: agitation, water hardness, leaf grade beyond bag-versus-loose, and a second
steeping. And strength is not bitterness — tannins come out more slowly than caffeine
does, which is why a long brew is not simply a strong one. The 65 °C line is the
one the IARC drew for very hot drinks; the 60–50 °C band is comfort, not a
measurement. Verified in tea_model.py.
Releases in which this page changed, newest last. Derived from the archived copy of every release, not from notes written afterwards — so it reflects what actually shipped. Site-wide passes are left out; they are in the full changelog.