Sous vide time depends on thickness, never on weight
The single most useful fact about sous vide cooking is that a 200 g steak and a 600 g steak of the same thickness need the same time. Weight is irrelevant. What matters is how far heat has to travel from the surface to the coldest point, and how fast it travels through meat.
That distance appears squared. Double the thickness and you roughly quadruple the time. A 15 mm steak is up to temperature in about 25 minutes; a 30 mm steak of the same cut takes about 91 minutes; a 60 mm piece takes nearly five hours. This is why butterflying a thick chicken breast is not a small saving, and why a chef who wants forty portions ready at once portions thin and cooks them side by side rather than cooking one large piece.
Shape is the second lever, and it is nearly as strong. In a slab, heat enters from two faces and has to cross half the thickness. In a cylinder it enters from all around the circumference, and in a sphere from every direction at once, so the same characteristic dimension gives a much shorter time. At 25 mm in a 55 °C bath from the fridge, this model gives 68 minutes for a slab, 32 minutes for a cylinder of 25 mm diameter, and 20 minutes for a 25 mm sphere. If you are unsure, treat the food as a slab: it is the slowest case and therefore the safe one.
Note what is not on that list. The bath temperature barely affects the heating time, because it appears only inside a logarithm. Going from a 55 °C bath to a 65 °C bath shortens the time to temperature by well under a fifth. Bath temperature sets the doneness and the pasteurization rate; thickness sets the clock.
The heating model, and why it is a logarithm
Put a cold solid into a bath and the temperature everywhere inside it obeys the heat equation. After a short initial transient, the solution collapses to a single decaying mode: every point in the food approaches bath temperature exponentially, all at the same rate. The centre lags the surface by a fixed factor, and the whole thing is described by two numbers that depend on shape and on the Biot number.
The Biot number, Bi = h·L/k, compares the resistance of the water film at the surface with the resistance of the food itself. With a circulator running, h is around 95 W/m²·K and k for meat is about 0.48 W/m·K, so a 25 mm steak has Bi = 95 × 0.0125 / 0.48 = 2.47. Above about 10 the water stops mattering entirely; below about 0.5 the water film is the bottleneck and better circulation would genuinely speed the cook. Most sous vide sits in between, which is why the calculator solves for the eigenvalue rather than assuming a limit.
The eigenvalue λ₁ is the first root of the shape's characteristic equation — λ·tan λ = Bi for a slab, and its Bessel and cotangent analogues for a cylinder and a sphere. It sets the decay rate. The coefficient A₁ sets how far behind the centre starts.
The logarithm comes from inverting that exponential. You want the remaining temperature gap to shrink to θ = 0.5 °C divided by the original gap, so you take a log of the ratio. Because it is a log, the answer is remarkably insensitive to what you call “done”: tightening the definition from 0.5 °C to 0.1 °C adds only about 40% to the time, while doubling the thickness adds 300%.
Frozen food breaks the model, because melting ice absorbs about 334 kJ/kg without any temperature change at all. This calculator handles that the way Baldwin's guide does: it models the food as starting from a melting front at 0 °C, then adds 50% to the result as an allowance for the latent heat. It is a rule of thumb, not a derivation, and it is the least reliable number on this page.
Worked example: a 25 mm ribeye from the fridge into a 55 °C bath
You have a ribeye 25 mm thick, straight from a 5 °C fridge, going into a circulator set to 55 °C. Work through the five steps.
- Characteristic half-size. A steak is a slab, so L is half the thickness: 25 ÷ 2 = 12.5 mm = 0.0125 m.
- Biot number. Bi = 95 × 0.0125 ÷ 0.48 = 2.474.
- Eigenvalue and coefficient. Solve λ·tan λ = 2.474 on (0, π/2). The root is λ₁ = 1.1395, so λ₁² = 1.2984. The slab coefficient A₁ = 4 sin λ ÷ (2λ + sin 2λ) = 3.6337 ÷ 3.0385 = 1.1959.
- Target gap fraction. You want the centre within 0.5 °C of 55 °C, and the original gap was 55 − 5 = 50 °C. So θ = 0.5 ÷ 50 = 0.01.
- Fourier number and time. Fo = ln(1.1959 ÷ 0.01) ÷ 1.2984 = ln(119.59) ÷ 1.2984 = 4.784 ÷ 1.2984 = 3.685. Then t = Fo × L² ÷ α = 3.685 × (0.0125² ÷ 1.4×10⁻⁷) = 3.685 × 1116 s = 4112 s = 68.5 minutes.
Now the safety side. At 55 °C the D-value for Salmonella is 0.40 × 10^((60 − 55) ÷ 6.5) = 0.40 × 5.878 = 2.35 minutes, so a 6.5-log reduction needs 6.5 × 2.35 = 15.3 minutes after the centre arrives. Total for a pasteurized steak: 68.5 + 15.3 = 84 minutes. Since a whole intact steak carries its bacteria on the surface, most cooks pull at 68 minutes and sear; the extra quarter of an hour is what you add when the steak has been needled, rolled or ground.
How to read the three times this gives you
The heating time is a minimum, not a target. It tells you the earliest moment the centre is at temperature. Nothing bad happens if you leave the food longer, up to the texture limit, because the food cannot exceed bath temperature. That asymmetry is the whole appeal of sous vide: the penalty for going over is measured in hours, not minutes.
The pasteurization hold is separate and additive. This page reports it with no credit for the lethality that accumulates while the food is heating, which makes it deliberately conservative. The pasteurization calculator integrates that come-up lethality and therefore returns a total that is equal to or shorter than the one here, never longer.
The maximum hold is about texture, with one safety exception. A steak held at 55 °C for four hours is excellent; at eight it is noticeably mushy, because enzymes and slow collagen conversion keep working. Fish is the extreme case and starts to fall apart within an hour. Tough cuts are the opposite: chuck at 57 °C for 24 to 48 hours is the point of the technique. The exception is any bath below 54.4 °C (130 °F), where pathogens are not reliably reduced; the FDA Food Code treats food outside temperature control as limited to four hours in total, and the calculator caps the recommendation accordingly.
Check the Biot number if the time looks wrong. If it comes out below 0.5, the water film is doing more to slow the cook than the food is, which happens with a still bath, a crowded container, or bags that are floating rather than fully submerged. Fix the circulation before you change the time.
Heating times for a slab from 5 °C into a 55 °C bath
| Thickness | Biot number | Time to temperature | Plus 6.5-log hold at 55 °C |
|---|---|---|---|
| 10 mm (0.4 in) | 0.99 | 19 min | 34 min |
| 20 mm (0.8 in) | 1.98 | 49 min | 65 min |
| 25 mm (1.0 in) | 2.47 | 69 min | 84 min |
| 30 mm (1.2 in) | 2.97 | 91 min | 106 min |
| 40 mm (1.6 in) | 3.96 | 144 min | 159 min |
| 50 mm (2.0 in) | 4.95 | 208 min | 224 min |
| 60 mm (2.4 in) | 5.94 | 285 min | 300 min |
Read the third column as a quadratic: from 20 mm to 40 mm the thickness doubles and the time rises roughly three-fold rather than exactly four-fold, because the Biot number rises too and the surface film becomes proportionally less of the resistance.
Where sous vide timings go wrong
- Measuring the wrong dimension. Enter the shortest path from surface to centre, doubled. For an irregular piece that is the thickest part, not the average and not the length.
- Timing by weight. Recipes that say “45 minutes per kilo” are importing a roasting habit into a technique where it does not apply. Two steaks in one bath take exactly as long as one.
- Bags floating or stacked. Any surface not in moving water has a far lower heat-transfer coefficient, and the calculation silently assumes every surface is wetted. Weight the bags down and leave space between them.
- Trapped air in the bag. An air pocket against the food is an insulator with a diffusivity two orders of magnitude away from meat. Displace it or the centre will lag badly.
- Treating a rolled roast as a slab. A tied roast is a cylinder and heats faster than a slab of the same dimension — but a rolled roast has also had its outer surface folded inside, so it needs the pasteurization hold that an intact cut does not.
- Assuming frozen adds a fixed number of minutes. The latent heat allowance is proportional, not additive, and it is the roughest figure on this page.
What the model assumes
The one-term solution is valid once the Fourier number exceeds about 0.2, which every practical sous vide cook satisfies comfortably. It assumes constant thermal properties, a uniform starting temperature, a bath that does not sag when you drop cold food into it, and a single dominant dimension. Real food violates all of these a little: fat has a lower diffusivity than lean, bone lower still, and a bone-in chop heats unevenly around it. The published thermal diffusivity of 1.4×10⁻⁷ m²/s is a good average for lean muscle, and it is exposed as an input so you can change it. None of these caveats changes the shape of the answer; they change it by tens of percent, and thickness changes it by hundreds.
How this compares with roasting and smoking
Every method of cooking a large piece of meat is governed by the same conduction physics; what changes is the surrounding temperature and therefore how much the outside overshoots the inside. In a 250 °F oven the surrounding air is nearly 100 °C above the target, so the outer centimetre races past doneness while the centre catches up, and you have to subtract a carryover rise after the meat leaves the oven. In a sous vide bath the surroundings sit exactly at the target, so there is no overshoot anywhere, no carryover to subtract, and no grey band. The cost is that no crust forms, which is why a sear before serving is not optional.
Low-and-slow barbecue sits between the two. A brisket at 225 °F is close enough to sous vide in spirit that the same sub-linear scaling with size applies, but the target there is not a temperature at all — it is the point where collagen has converted to gelatin, which is a time-at-temperature process much like pasteurization.
The one place the sous vide model matters most is safety, because low bath temperatures only work if you hold long enough. That arithmetic is the subject of the pasteurization calculator, and the same thermal-death-time reasoning explains why a turkey must be thawed in the fridge or in cold water rather than on a counter: the outer layers spend hours in the growth range long before the centre has moved at all.