Why Hasn't Earth's Interior Cooled Off in 4.6 Billion Years?
― Half the Heat Is Still Being Made, Right Now, Inside the Rock
"Earth's interior is hot because the heat from its birth is still lingering." That's a common explanation, but it's only half right. About half of the heat escaping from the ground isn't leftover at all. At this very moment, trace elements mixed into the rock are quietly generating brand-new heat.
Step into a deep tunnel or mine, and even on a cool day outside, it gets stiflingly warm the further in you go. Underground, the temperature is said to rise by about 3°C for every 100 meters of depth.
A freshly brewed cup of tea turns lukewarm within half an hour. Hot things cool down — that's just how it normally goes.
So why does Earth, born 4.6 billion years ago, still have a core thousands of degrees hot? Can "it's big, so it cools slowly" really explain that on its own?
There are two reasons
The time it takes for heat to seep through something grows with the square of its thickness. If Earth cooled by rock conduction alone, the calculation says it would take over a trillion years to cool all the way through.
Rock contains tiny traces of uranium, thorium, and potassium, and every time one of their atoms breaks down, it releases heat. This is thought to account for roughly half of all the heat escaping from the surface.
The "it's just leftover heat" explanation drops the second reason entirely. And the history behind how we came to recognize that second reason includes a major misstep by one of science's biggest names.
The bigger something is, the absurdly slower it cools
Compare a cup of tea to a full bathtub. Even at the same starting temperature, the bathtub takes far longer to cool. The more there is, the longer it takes.
And the difference isn't simply proportional to size. The time for heat to travel from deep inside to the surface grows with the square of the distance. Ten times the distance means a hundred times the time.
Rock is a very poor conductor of heat. It's estimated that heat takes roughly 300 million years just to travel 100 kilometers through rock. Earth's radius is 6,400 kilometers. If heat only moved by conduction through rock, draining the heat from the core would take over a trillion years by that math.
In reality, though, Earth cools somewhat faster than that. Over tens of millions of years, the rock deep underground slowly flows and churns, turning over from top to bottom. Because hot rock itself rises to the surface, heat is carried out faster than conduction alone would manage.
Heat is still being generated inside the rock, right now
Heat is always leaking out of the ground, little by little. Per square meter, it's only about 0.09 watts — not even enough to light a small bulb. Yet added up across the whole planet, it comes to roughly 46 trillion watts: more than twice the energy humanity uses in total.
One source of this heat is the uranium, thorium, and potassium mixed into rock. These are called radioactive elements, and over long stretches of time they transform into other elements. Each transformation releases a tiny bit of heat.
The amount from any single atom is tiny, but add up all the rock on Earth and the picture changes. This heat was measured by a detector buried 1,000 meters underground in Gifu Prefecture, which caught "neutrinos" — particles flung out when elements break down. A 2011 report put uranium and thorium alone at about 20 trillion watts — roughly half of the heat escaping the surface.
Take a look at Figure 1. Turn the dial back through time, and you can see that there used to be far more heat being generated.
Radioactive elements decrease over time. So Earth's interior used to generate several times more heat than it does now. Today's Earth has burned through much of that "fuel" — but it's still supplying half the heat.
The great scientist who said "Earth is less than 100 million years old"
In the 1860s, Lord Kelvin — whose name is attached to the temperature scale — calculated Earth's age from how fast temperature rises with depth underground. Assuming Earth was just a hot ball cooling down, he arrived at an age of at most 100 million years, and later, just tens of millions of years.
That was far shorter than the time needed for the evolution of living things or the buildup of rock layers. Geologists and biologists of the day reportedly pushed back hard.
Then in 1896, radioactivity was discovered. If rock contains a "refill" of heat, the whole premise of the calculation collapses. In 1904, Rutherford pointed this out in a lecture — with Kelvin himself reportedly in the audience.
Recent research suggests the main reason Kelvin's answer came out too short wasn't radioactivity at all — it was his overlooking the fact that rock flows. If the interior is churned by flow, the deep interior stays hot, and the steep temperature rise near the surface persists much longer. His former assistant, Perry, had already pointed this out back in 1895.
The heat rising from Earth's interior is only about 1/2,700th of the heat the planet absorbs from sunlight. The warmth of sunlit ground, and the turning of the seasons, are almost entirely the sun's doing. Earth's internal heat works much deeper down, driving things like mountain-building and continental movement.
In summary
There are two reasons Earth's interior is still hot today. One: rock conducts heat poorly, and Earth is simply too big to cool quickly. Two: radioactive elements mixed into the rock are still generating heat right now. Roughly half the heat escaping the surface is thought to be this "freshly made" heat. Earth is cooling, bit by bit, but at a leisurely pace — reportedly around 100°C per billion years.
Earth isn't a dying ember.
A small fire is still burning inside it, even now.
For a look at Earth's innermost depths, see "Earth's Core Is as Hot as the Sun's Surface — So Why Hasn't It Melted?"; for a familiar example of this underground heat reaching the surface, see "Why Are Hot Springs Hot?"
- Pour water of the same temperature into a small cup and a large pot.
- Every 10 minutes, measure the temperature with a thermometer (without touching it with your finger). Record how long it takes the cup's water to drop 10°C.
- Compare how long the pot's water takes to drop by the same amount. Check this against how many times bigger the pot is than the cup.
Water moves on its own even without stirring, so the difference won't be as extreme as with rock cooling by conduction alone. Even so, you'll see that the bigger container stays warm for many times longer. Earth is hundreds of millions of times bigger than this pot.
Want to go deeper? ― Terms, formulas, and how this connects to the textbookWe've marked which level each part belongs to, from junior-high science to university-level courses
- JHSCovered in junior-high school science
- HSCovered in high-school physics or earth science
- HS+High-school enrichment material, or a textbook sidebar topic
- Univ.Not covered in high school — university-level geophysics or heat-transfer engineering
- ResearchNot even settled fact at university level — something researchers are actively investigating
JHSTerminology: this phenomenon has names
- Heat flow (heat flux): the amount of heat escaping from Earth's interior to the surface, per square meter per second.
- Geothermal gradient: the rate at which temperature rises with depth. On land, it's said to be about 25–30°C per kilometer.
- Radioactive decay: the process by which an unstable atom transforms into a different atom while emitting radiation. Heat is released each time.
- Geoneutrino: a neutrino released when a radioactive element inside Earth decays. Because it passes straight through rock and the whole planet, it carries information from deep underground.
JHSHSCheck with a formula: how long would cooling by rock alone take?
The time it takes for heat to seep through a material can be estimated with the formula below. The symbol κ (kappa) is the thermal diffusivity — how readily heat seeps through — measured in square meters per second.
| In symbols | t ≒ L² ÷ κ (together with Q ＝ q × A) |
| In words | Time for heat to arrive ≒ distance squared ÷ how readily heat seeps through. Total heat escaping Earth ＝ heat per square meter × surface area |
| Where it comes from | Heat flows from hotter to cooler, in proportion to the temperature difference (Fourier's law). Combined with conservation of heat, this gives the "heat conduction equation" — this is a rough order-of-magnitude estimate from it |
| t | Time for heat to travel distance L (years) |
| L | Distance heat travels (meters) |
| κ | Thermal diffusivity of rock (square meters per second) |
| q | Heat flux (watts per square meter) |
| A | Earth's surface area (square meters) |
| Rock thermal diffusivity κ | said to be about 0.000001 square meters per second |
| Length of one year | about 31.5 million seconds |
| Earth's radius | about 6,400 km |
| Global average heat flux q | about 0.09 watts per square meter (higher under the seafloor) |
| Earth's surface area A | about 510 trillion square meters |
| Heat from uranium and thorium (2011 measurement) | about 20 trillion watts |
| Convert κ to per-year units | 0.000001 × 31500000 ＝ 31.5 (square meters per year) |
| Square of 100 km (100,000 m) | 100000 × 100000 ＝ 10000000000 |
| Time to travel 100 km | 10000000000 ÷ 31.5 ≒ 317460317 (about 320 million years) |
| How many times is Earth's radius bigger than 100 km | 6400 ÷ 100 ＝ 64 |
| Time scales with the square | 64 × 64 ＝ 4096 |
| Time to reach the radius (hundred million years) | 3.2 × 4096 ≒ 13107 (about 1.3 trillion years) |
| How many times Earth's age (4.6 billion years) | 13107 ÷ 46 ≒ 285 |
| Total heat escaping Earth (trillion watts) | 0.09 × 510 ≒ 45.9 |
| Share from uranium and thorium | 20 ÷ 46 ≒ 0.43 |
If heat only moved through rock by conduction, cooling Earth would take more than 280 times its age. In reality, rock flows slowly and carries heat along, so cooling happens faster than that. Even so, radioactive elements are currently supplying over 40% of the heat that escapes.
HSHS+Splitting up where the heat comes from
HSRadioactive elements halve in quantity every half-life. Uranium-238 has a half-life of about 4.5 billion years, and thorium-232 about 14 billion years. Potassium-40, on the other hand, has a shorter half-life of about 1.3 billion years, and uranium-235 about 700 million years. This means that just after Earth formed, heat from potassium-40 and uranium-235 is thought to have made up a much larger share.
HS+Of the escaping heat, whatever isn't from radioactive elements is "leftover" from the heat of Earth's formation — the impacts that built the planet, and the heat released as heavy iron sank to the core. On top of that, as the liquid iron at the center gradually solidifies, it releases latent heat of solidification too. Leftover heat from birth, plus heat being made right now — together, these make up the heat escaping the surface.
Univ.The heat conduction equation, mantle convection, and the Urey ratio
The estimate above is the diffusion time from the heat conduction equation — distance squared divided by thermal diffusivity. In reality, the mantle has an extremely large Rayleigh number and convects while remaining solid. Because of this, heat transport differs greatly from the conduction-only case. The ratio of heat from radioactive decay to heat escaping the surface is called the "Urey ratio," a key quantity for thinking about Earth's thermal history. Geoneutrino observations put this ratio at roughly 0.5.
📖 For the derivation and further reading: Heat conduction equation (Japanese Wikipedia) ／ Mantle convection (Japanese Wikipedia)
ResearchWhat's still not fully understood
- Where exactly are radioactive elements located in Earth, and how much? Geoneutrino observations still carry large error bars, and estimates of how much is in the mantle vary from researcher to researcher.
- Is there potassium in the core too? How much radioactive material is dissolved into the core is unknown, and it's also tied up with debates over when Earth's magnetic field first formed.
- How fast is Earth actually cooling? How many tens of degrees the mantle has cooled per billion years is estimated from the properties of ancient rocks, but the figures still vary.
In short, this article too reflects "the best explanation we have right now." We've only just gained a new way to directly measure the source of Earth's internal heat, thanks to a new kind of "eye" — the neutrino.
Connections to the textbook (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| JHS | Science, "Changes in the Earth's crust" / "Energy" | Temperature rising with depth, how heat travels |
| HS | Earth science, "Earth's interior"; physics, "Atoms and nuclei" | Heat flux, half-lives and radioactive elements |
| HS+ | Earth science enrichment | Split between leftover heat and radiogenic heat, latent heat of the core |
| Univ. | Geophysics, heat-transfer engineering | Heat conduction equation, mantle convection, Urey ratio |
| Research | Neutrino geoscience | Distribution of radioactive elements, how Earth is cooling |
| ― | Connection to daily life | The ultimate source of the heat behind hot springs and geothermal power |
- KamLAND Collaboration (2011) Partial radiogenic heat model for Earth revealed by geoneutrino measurements. Nature Geoscience 4
- Davies, J. H. & Davies, D. R. (2010) Earth's surface heat flux. Solid Earth 1
- England, P., Molnar, P. & Richter, F. (2007) John Perry's neglected critique of Kelvin's age for the Earth: A missed opportunity in geodynamics. GSA Today 17
- Heat conduction (Japanese Wikipedia)
- National Astronomical Observatory of Japan (ed.), Rika Nenpyō (Chronological Scientific Tables), Maruzen Publishing (Earth data)
※This article is a general-audience science explainer. The figures given are approximate, meant to aid understanding of the underlying mechanisms. Estimates of Earth's internal heat output and the breakdown by element vary across studies.