Thermal Touch: Why Metal Feels Colder Than Wood

Choose something to touch and a temperature for it. The page works out the temperature the surface of your own skin reaches, how much heat leaves you while you hold it, and how far into both of you the disturbance travels.

Worked example — Thermal Touch: Why Metal Feels Colder Than Wood

Effusivity of skin, e₁	1,179.6
Effusivity of the object, e₂	24,047.0
Temperature at the contact	20.61 °C
How far your skin’s surface moves	12.39 K
Heat leaving your skin now	8,247 W/m²
Heat gone by this moment	1.649 J/cm²
Thermal diffusivity of the object	9.713 × 10⁻⁵ m²/s
How deep the disturbance has got	39.42 mm

These are the values the calculator shows when the page opens. Change any input above to recompute them.

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Lesson

The theory — Thermal Touch: Why Metal Feels Colder Than Wood

Thermal effusivity e = √(kρc) says how readily a material takes heat in across its surface. It combines the two properties that a touch depends on: conductivity k, which is how fast heat travels onward, and volumetric heat capacity ρc, which is how much heat the material must be given to warm by one kelvin. Press two deep bodies together at temperatures T₁ and T₂ and their surfaces jump at once to a shared temperature and hold it while heat flows: Tᵢ = (e₁T₁ + e₂T₂)/(e₁ + e₂), an average of the two starting temperatures weighted by effusivity. Nothing in it depends on time, which is why a cold handrail feels exactly as cold in the first instant as it does two seconds later.

What each symbol means

k: thermal conductivity, W m⁻¹ K⁻¹. How fast heat moves through the material once it is in
ρc: volumetric heat capacity, J m⁻³ K⁻¹. How much heat a cubic metre must absorb to rise one kelvin. Water holds 4.17 MJ, still air holds 1,170 J
e: effusivity √(kρc), J m⁻² K⁻¹ s^−½. The weight each body carries in deciding the contact temperature
α: diffusivity k/(ρc), m² s⁻¹. How fast the disturbance spreads inward, which is a different question from how hard the material pulls
Tᵢ: the temperature both surfaces hold during the contact. Your skin reports this, never the temperature of the object

Assumes: Perfect contact between two bodies deep enough that neither far side is ever reached, and no heat moving by anything but conduction across the interface. The depth condition is tested on the page and the verdict says when it fails; the perfect contact is not. A real fingertip meets a solid on its ridges with air trapped between them, so every contact temperature here is the coldest the object could possibly feel rather than what a thermocouple would measure. Skin is one uniform material with the properties of dermis, which describes its outer millimetre, and a second of contact reaches 1.25 mm into it.
Breaks when: Still air is in the list because an oven is worth computing, and it is also where this model is at its thinnest, because air moves. Convection and radiation are both absent here and both are what actually cook the food, so the 33.78 °C in the air row should not be read as a licence to leave a hand in a hot oven. Water has the same trouble with the sign reversed: a cold bath carries heat away from you faster than still conduction manages, so it feels colder for longer than the water row says.

Both benches are at 20 °C, and one of them takes 12 degrees off your hand 🖖

Press Aluminium block, then Oak table. Nothing has changed except what the object is made of: both sit at 20 °C, both are touched by skin at 33 °C. Against the aluminium the surface of your skin falls to 20.61 °C, two thirds of a degree above the metal itself. Against the oak it stops at 29.30 °C. The aluminium moved your skin 12.39 K and the oak moved it 3.70 K, so cold is not a quantity the aluminium has more of. You are reading your own temperature, and the metal takes it much further down.

Plate glass carries heat twice as fast as water and feels the same 🖖

The conductivity column in the table runs from 0.0263 in still air to 401 in copper, and on its own it will not tell you how anything feels. Glass moves heat 2.3 times faster than water, 1.40 against 0.613 W/m·K, and the two land 0.04 °C apart on the skin: 25.48 against 25.52. Water makes up the difference in the other property, holding 4.17 MJ per cubic metre per kelvin against glass’s 1.88. A touch is decided by e = √(kρc), which asks how fast heat arrives at the surface and how much the material behind it can swallow, and the rows of the table are in that order rather than in conductivity order.

Your own skin is the bottleneck, which is why every metal feels alike 🖖

Copper conducts heat 1.7 times better than aluminium and has 1.5 times its effusivity. On the curve their dots are a fifth of a degree apart: 20.40 °C and 20.61 °C. Past an effusivity of a few thousand the curve has flattened, because the contact is already sitting on the object’s own temperature and what limits the heat leaving you is your skin at 1,179.6 rather than the metal. Everything a hand can actually distinguish lives at the bottom of the axis: oak and expanded polystyrene are 17 times apart in effusivity and 3.40 °C apart at the contact, which is a difference you can feel, where the copper and the aluminium is not.

Problem solved in full

Why you can put your hand in a 200 °C oven 7 steps
An oven has been at 200 °C for an hour. Your fingers pass through the air on the way to the tray without harm, then brush the steel rack and are burned at once. Both are at 200 °C. Find the temperature the surface of your skin reaches in each case, and the heat that crosses one square centimetre in the first second. Skin at 33 °C, with k = 0.37 W/m·K, ρ = 1,109 kg/m³ and c = 3,391 J/kg·K.

Open this problem in the tool
1. Both answers come out of one quantity, and conductivity is not it. When two bodies touch, their surfaces settle immediately on a temperature that then stays put: Tᵢ = (e₁T₁ + e₂T₂)/(e₁ + e₂), weighted by effusivity e = √(kρc). For skin that is √(0.37 × 1,109 × 3,391) = 1,179.6.
  
  $e = k ρ c, e_{skin} = 0.37 \cdot 1109 \cdot 3391 = 1179.6 J m^{- 2} K^{- 1} s^{- 1/2}$
2. Still air at oven temperature: k = 0.0263 W/m·K, ρ = 1.1614 kg/m³, c = 1,007 J/kg·K. Its effusivity is √(30.76) = 5.5, smaller than skin’s by a factor of more than 200. A cubic metre of that air holds 1,170 J per kelvin; a cubic metre of your hand holds 3.76 million.
  
  $e_{air} = 0.0263 \cdot 1.1614 \cdot 1007 = 30.76 = 5.5$
3. So the weighted average is almost entirely yours: Tᵢ = (1,179.6 × 33 + 5.5 × 200) / (1,179.6 + 5.5) = 33.78 °C. Air 167 degrees hotter than your hand moves the surface of it by three quarters of a kelvin.
  
  $T_{i} = \frac{e _{1} T _{1} + e _{2} T _{2}}{e _{1} + e _{2}} = \frac{1179 . 6 \cdot 33 + 5 . 5 \cdot 200}{1179 . 6 + 5 . 5} = 33.78^{\circ} C$
4. Now the rack. Stainless steel has k = 14.9, ρ = 7,900 and c = 477, giving e = 7,493.2, and the weighting runs the other way by a factor of 6.4. The same formula returns Tᵢ = 177.29 °C, which is the temperature the outer cells of your fingertip are taken to while the contact lasts.
  
  $e_{steel} = 14.9 \cdot 7900 \cdot 477 = 7493.2 ⟹ T_{i} = \frac{1179 . 6 \cdot 33 + 7493 . 2 \cdot 200}{1179 . 6 + 7493 . 2} = 177.29^{\circ} C$
5. How much heat, and how fast. The flux is q = e₁e₂(T₁ − T₂)/((e₁ + e₂)√(πt)), and because it falls as one over the square root of time, the heat delivered by time t is exactly 2qt. In the first second the rack sends 19.205 J into each square centimetre of skin and the air sends 0.104 J.
  
  $q = \frac{e _{1} e _{2} ( T _{1} - T _{2} )}{( e _{1} + e _{2} ) π t}, Q = \int_{0}^{t} q d t^{'} = 2 q t : 19.205 J c m^{- 2} vs 0.104 J c m^{- 2}$
6. The two effusivities differ by a factor of 1,351 and the heat delivered by a factor of about 185. The gap between those two numbers is you: in the steel case your own effusivity is the smaller of the pair, so it is your skin rather than the metal that sets how fast heat can be taken in. Switch the material to copper, five times the effusivity of steel, and the heat delivered rises by an eighth, from 19.205 to 21.544 J per square centimetre.
  
  $\frac{e _{steel}}{e _{air}} = 1351, \frac{Q _{steel}}{Q _{air}} = 185, \frac{e _{1} e _{2}}{e _{1} + e _{2}} e_{2} ≫ e_{1} e_{1}$
7. Whether that is a burn is a question this page cannot answer. It needs how long the contact lasts, a damage integral rather than a temperature, and the contact resistance of a real fingertip, whose ridges and trapped air the perfect contact assumed here leaves out. What is not in doubt is the direction: 33.78 °C is body temperature and 177.29 °C is well past the point where protein denatures.
Answer

The air puts the surface of your skin at 33.78 °C and delivers 0.104 J to each square centimetre in the first second. The rack puts it at 177.29 °C and delivers 19.205 J. One oven, one temperature, 185 times the heat.

$T_{i}^{air} = 33.78^{\circ} C vs T_{i}^{steel} = 177.29^{\circ} C$

References (4)

Where the two-semi-infinite-solids result comes from, and still the reference for every closed form on this page: H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd edition, Clarendon Press, Oxford, 1959.
The property tables the fourteen materials are drawn from, in the shape they are given here (k, rho, c at or near 300 K): T. L. Bergman, A. S. Lavine, F. P. Incropera and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, 7th edition, Wiley, 2011.
Where per-tissue thermal properties are compiled, including the dermis triple this page models skin with: IT'IS Foundation, Tissue Properties Database V5.0, 2025. DOI 10.13099/VIP21000-05-0
How wide the spread on any tissue property really is, which is why skin is modelled here with one representative triple and not with a measurement: L. Bianchi, F. Cavarzan, L. Ciampitti, M. Cremonesi, F. Grilli and P. Saccomandi, "Thermophysical and mechanical properties of biological tissues as a function of temperature: a systematic literature review." International Journal of Hyperthermia 39(1), 2022, pp. 297-340. DOI 10.1080/02656736.2022.2028908

By the 42Math team · Reviewed against published sources. Corrections welcome.